Satellite Gravimetry - Earth Online - ESA · Satellite Gravimetry. Reiner Rummel. Institute of...

Satellite

Gravimetry

Reiner RummelInstitute of Advanced

Study

(IAS)

Technische Universitaumlt Muumlnchen

Lecture

Three

5th ESA Earth Observation Summer School

2-13 August 2010 ESA-ESRIN Frascati

Italy

Lecture

ThreeMeasurement

of the

free

fall of a test massInterpretation of the

motion

of a satellite

in its

orbit

as test mass

in free

fallFrom

the

orbit

to the

earthlsquos

gravitational

fieldThe

use

of several

test masses

in free

fallCase

One the

satellite

mission

GRACEMeasurement

of temporal changes

in gravitationCase

Two the

ESA Living

Planet mission

GOCEThe

principle

of gravitational

gradiometryOutlook

plan for

lecture

three

test mass

in free

fall

gravitationthe

story

of the

falling

apple

Reference R Westfall The

life of Isaac NewtonCambridge Univ

Press 1999[Compare

page

51 and 305]

the size of gravity from measuringpositionand time

test mass

in free

fall

0 0x t

1 1x t

2 2x t

Absolute-Gravimeter FG5atTU Hannover

test mass

in free

fall

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)

InterferometerTripod

SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber

Free-FallingCorner Cuber

Drag-FreeChamber

Laser

Internal

ReferenceCorner Cube

Servo

Coil

drop height 02m time 02s

600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer

time Rubidium atomic

clock

10-10

vacuum 10-4 Pa

residual drag compensation

micro

seismisity super spring

test mass

in free

fall


position laser interferometry

time atomic clock

air resistance to be eliminated

silence no vibrations

test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical

Earth10-3 flattening

amp centrifugal

acceleration

10-4 mountains valleys ocean

ridges subduction10-5 density

variations

in crust

and mantle

10-6 salt

domes sediment

basins ores10-7 tides atmospheric

pressure

10-8 temporal variations oceans hydrology10-9 ocean

topography polar motion

10-10 general

relativity

gravity

(in laboratory

at TU Muumlnchen)9807 246 72 ms2

stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements

I Newton ldquoDe mundi

systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant

conclusionOrbit motion

of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)

satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing

ellipse (spiral)Case 3 actual Earth modulation from gravitation

satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1

today LAGEOS I and II

test mass

in free

fall

Cox amp Chao Science 297 2002

steady decrease of earth flattening change of trend in recent years

satellites

-

test masses

in free

fall

Dickey Marcus de Viron Fukumori 2002

Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall

observatories ldquoseerdquo

onlyshort arc segments

satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites

(GPS GALILEO GLONASShellip)

satellites

-

test masses

in free

fall

Absolut-GravimeterFG5TU Hannover

bull location GPS

bull time synchronized atomic clocks

bull air resistance measured

bull silence no ground vibrations

satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude

laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar

satellites

-

test masses

in free

fall

Emiliani

C1992 p272

CHAMP satelliteGeoForschungsZentrum

Potsdam

mission life time 2000 ndash

2010

star

sensorsGPS receiver

accelerometerat centre

of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]

position difference between kinematic and reducedminusdynamic POD

positioning (orbit determination)of CHAMP by GPS

σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy

howevernon conservative

contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from

absolute to differential measurement

GRACENASA + DLR mission (in orbit since 2002)

Gravitation from very precise measurement (1μm) of changes of inter satellite distance

of two satellites following each other in the same orbit (200 km)

the

use

of several

free

falling

test masses

GRACE measures tiny changes of gravitational acceleration

Gerard Kruizinga JPL 2002

the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures

temporal gravitational

changesexample seasonal

changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational

measurementin a micro-g

environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite

mass ration 1 6middot1021

tidal attraction of earth acting on a satellite

x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz

g x g y g z V V Vg x g y g z V V Vg x g y g z V V V

gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes
(1) Curvature of level surfaces and plumb lines - (2) Einstein Riemann Curvature Tensor

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers

GOCE and gravitational

gradiometry

measurement

of bdquomicro-gldquo

with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients

angular accelerationscommon mode acc

A B


gradiometry

1

The

first

gravitationalgravitational

gradiometergradiometer

in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry

symmetric symmetric skew

symmetric

gravitationtensor

centrifugal

part(angular

velocities)

angularaccelerations

measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0

xx xy xz y z x y x z z y

yx yy yz y x z x y z z x

zx zy zz z x z y x y y x

V V VV V VV V V

Presenter
Presentation Notes
Separation of angular accelerations

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by

MStudinger LDEO Using

data

from

Siegert

et al (2005) and NSIDC

400 200 130 100 80 65

half wavelength [km]

50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8

spherical harmonic degree

Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula

GOCEGOCE maximum resolution (s= 100 km)

GRACEGRACE maximum precision (geoid

lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6

Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C

degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal

hydrology)GOCE gives

much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics

The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo

and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)

gravitation

and the

story

pf

the

apple

S Dali Sans titre 1948

summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement

of non-gravitational

forces

by

accelerometry

corresponds

to free

fall absolute gravimetry

in an laboratory

on earth

bull CHAMP (2000) was the

first

mission

of this

kindbull differential measurement

of the

relative motion

of two

satellites

increases

the

sensitivity (GRACE 2002)bull gravitational

gradiometry

is

differential accelerometry

between

several

test masses

inside

one

satellitebull GOCE is

the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

Lecture

ThreeMeasurement

of the

free

fall of a test massInterpretation of the

motion

of a satellite

in its

orbit

as test mass

in free

fallFrom

the

orbit

to the

earthlsquos

gravitational

fieldThe

use

of several

test masses

in free

fallCase

One the

satellite

mission

GRACEMeasurement

of temporal changes

in gravitationCase

Two the

ESA Living

Planet mission

GOCEThe

principle

of gravitational

gradiometryOutlook

plan for

lecture

three

test mass

in free

fall

gravitationthe

story

of the

falling

apple



Press 1999[Compare

page

51 and 305]


test mass

in free

fall

0 0x t

1 1x t

2 2x t


test mass

in free

fall

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)


SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber


Drag-FreeChamber

Laser

Internal


Servo

Coil


600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer


clock

10-10

vacuum 10-4 Pa


micro


test mass

in free

fall



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

test mass

in free

fall

gravitationthe

story

of the

falling

apple



Press 1999[Compare

page

51 and 305]


test mass

in free

fall

0 0x t

1 1x t

2 2x t


test mass

in free

fall

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)


SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber


Drag-FreeChamber

Laser

Internal


Servo

Coil


600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer


clock

10-10

vacuum 10-4 Pa


micro


test mass

in free

fall



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


test mass

in free

fall

0 0x t

1 1x t

2 2x t


test mass

in free

fall

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)


SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber


Drag-FreeChamber

Laser

Internal


Servo

Coil


600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer


clock

10-10

vacuum 10-4 Pa


micro


test mass

in free

fall



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


test mass

in free

fall

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)


SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber


Drag-FreeChamber

Laser

Internal


Servo

Coil


600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer


clock

10-10

vacuum 10-4 Pa


micro


test mass

in free

fall



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

Absolut-Gravimeter

FG5 (Micro-g

Solutions Inc)


SupportSprings

Superspring

Main Spring

APD

ION PUMPDrive Motor

Dropping

Chamber


Drag-FreeChamber

Laser

Internal


Servo

Coil


600 000 fringes

per drop

100 drops

per set 25 sets

Mach-Zender

laser

interferometer


clock

10-10

vacuum 10-4 Pa


micro


test mass

in free

fall



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



time atomic clock



test mass

in free

fall

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

test mass

in free

fall

terrestrial

absolute gravimetry

in the

mountains

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

10 0 spherical


amp centrifugal

acceleration



variations

in crust

and mantle

10-6 salt

domes sediment


pressure



10-10 general

relativity

gravity

(in laboratory


stat

iona

ryva

riabl

etest mass

in free

fall

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

test mass

in free

fall

map

with

global distribution

of in-situ

measurements


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


systemateldquo

1715

satellites

-

test masses

in free

fall

Newtonlsquos

brilliant


of planets

(Kepler) obeys

the

same

law

as a

free

falling

bdquoappleldquo

(Galileo)



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



satellites

-

test masses

in free

fall

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

1957 Sputnik 1

earth

flattening

J2

=108410-6

earth

oblateness

deduced

from

orbit

plane precession

satellites

-

test masses

in free

fall

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

1957 Sputnik 1


test mass

in free

fall



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



satellites

-

test masses

in free

fall


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


Temporal changes

of the

Earthlsquos

flattening What

are

the

causes

candidates

ocean

masses

melting

ice

caps

atmospheric

masses

hydrology

satellites

-

test masses

in free

fall



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



satellites

-

test masses

in free

fall

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

A new

era continuous

tracking

in 3D of low

earth

orbiters

(LEOs) by

navigation

satellites


satellites

-

test masses

in free

fall


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


bull location GPS




satellites

-

test masses

in free

fall

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

atmospheric

pressure

at satellite

altitude


satellites

-

test masses

in free

fall

Emiliani

C1992 p272


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


Potsdam


2010

star

sensorsGPS receiver


of mass

satellites

-

test masses

in free

fall

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]



σ

= 3 cm

(Rothacher

amp Svehla 2003)

from

the

orbit

to gravitation

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

gravitation from

0 5 10 15 20minus01

minus005

0

005

01

time at DoY 231 [h]

Δ x

[m]


2 2x t 0 0x t

1 1x t

from

the

orbit

to gravitation

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

energy

conservationkinetic

energy

= potential energy


contributions

residual air

resistance

andgravitation

changes

due

to

direct solid earth

amp ocean

tidesatmosphere

oceanshellip

21mv2

from

the

orbit

to gravitation

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

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Slide Number 33

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Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

gravitational

potential along

the

orbit

trajectory

σ

= 500 m2s2

from

the

orbit

to gravitation

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

gravitational

potential along

the

orbitmapped

onto

the

globe

from

the

orbit

to gravitation

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

0

0

60

60

120

120

180

180

240

240

300

300

360

360

-90 -90

-60 -60

-30 -30

0 0

30 30

60 60

90 90

-80 -60 -40 -20 0 20 40 60 80

potential along

the

orbitmapped

onto

the

globe

[ms2]

geoid

[m]

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

the

use

of several

free

falling

test masses

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

the

use

of several

free

falling

test masses

from





the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54




the

use

of several

free

falling

test masses



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



the

use

of several

free

falling

test masses

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

Tapley

et al Science 2004

the

use

of several

free

falling

test masses

GRACE measures



changes

of continental

hydrology

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

the

use

of several

free

falling

test masses

gravitational


environment

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

the

use

of several

free

falling

test masses

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

earth surface

260 km

satellite



x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

x x

y y

z z

g V x Vg g V y V V

g V z V

x x x xx xy xz

y y y yx yy yz

z z z zx zy zz


gravitational

gradiometry

ndash

principle

gravity

tensor

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

0 0

NS NSi

j ij OW OW

NS OW

k t fR V g t k f

gf f g z

gravitational

gradiometry

ndash

principle

gravity

tensor=

tidal

tensor=

curvature

tensor

Presenter
Presentation Notes

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

single

accelerometer

one

axisgradiometer

three

axesgradiometer

consisting

of 6 accelerometers


gradiometry

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

measurement


with

micro-precision


gradiometry

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

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Slide Number 31

Slide Number 32

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Slide Number 34

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Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

ion

thrusters

ion

thrustercontrol

unit

nitrogen

tankxenon

tank

gravity

gradiometer

star

sensor

GPS receiver

magneto-torquers

power supply

control

unit

source ESA

a perfect

laboratory

in space


gradiometry

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

instrument

and control

concept

translationalforces

angularforces

starsensors

drag control

angular control

GPSGLONASSSST -hl

GRAVITY GRADIOMETER

measures

gravity gradients


A B


gradiometry

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

1

The

first



in space

2

European geodetic

GPS-receiver

on board

3

Extremly

low

orbit

altitude

(260 km)

4

Free fall (air

drag is

compensated

along

track)

5

Very

bdquosoftldquo

angular

control

by

magnetic

torquing

6

Absolutely

quiet

and stiff

satellite

materials

and

environment


gradiometry


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


symmetric

gravitationtensor

centrifugal

part(angular

velocities)


measurement

in a rotating

frame


gradiometry

2 2

2 2

2 2

00

0




V V VV V VV V V

Presenter
Presentation Notes

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

A

A

A

A

A

A

X

X

X

X

X

X

Z

Z Z

Z

Z

Z

Y

Y Y

Y

Y

Y

O

O

O

O

O

O

1

2

1

1

1 1

2

2 2 44

4 4

4

33

3 3

3

5

5

5

5 5

66

66 6

2

O

X

ZY GRF

GRF

GRF

GRF

two

sensitive and one

less

sensitive

direction


gradiometry

2 2

2 2

2 2

00

0

xy x y z

yz y

xx xz y z x z y

yx yy y x z x z

zx zz z x x y

z x

zy yz y x

VV VV VV V

VV

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

x y

x

z

y

z

Vik

[E]

minus05 0 05


gradiometry

4 components

measured

with

high precision

and two

less

precise


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

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Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


gradiometry

trace

condition (Laplace

condition)the

sum

of the

measured

diagonal components

should

be

zero

Presenter
Presentation Notes
Comparison of trace

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

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Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

GOCE gravity

field

meters

a global geoid

map

based

on two

months

of data

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

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Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

GOCE gravity

field

Map

compiled

by


data

from

Siegert


400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

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Slide Number 13

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Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

400 200 130 100 80 65


50 100 150 200 250 30010

minus14

10minus13

10minus12

10minus11

10minus10

10minus9

10minus8


Deg

ree

RM

S

SGG

SST minus ll

SST minus hl

GMsKaula



lt μm)

GOCE versus

GRACE

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

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Slide Number 19

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Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

Degree

Mea

nS

igna

lper

Deg

ree

Deg

ree

Err

orM

edia

n

50 100 150 200

10-12

10-11

10-10

10-9

10-8

10-7

10-6


degree

variances

(median) of signal

and noise

GOCE versus

GRACE

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

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Slide Number 17

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Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

GOCE versus

GRACE

GRACE measures

the

long

wavelength

structure

of gravity

and geoid

with

extremely

high precision

GRACE can

therefore

even

detect

temporal changes

in the

earth

system

due

to mass

redistribition

(ice sea

level continetal


much

higher

spatial

resolution

This

resolution

is

needed

when

using

the

geoid eg as refence

level

surface

for

studies

of ocean

circulation

or

for

geodynamics



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

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Slide Number 17

Slide Number 18

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Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54



gravitation

and the

story

pf

the

apple


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

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Slide Number 21

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Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

Slide Number 47

Slide Number 48

Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54


summary

of lecture

three

bull uninterrupted

tracking

of a low

orbiting

satellite

(LEO) by

GPSin combination

with

measurement


forces

by

accelerometry

corresponds

to free


in an laboratory

on earth


first

mission

of this


of the

relative motion

of two

satellites

increases

the


gradiometry

is


between

several

test masses

inside

one


the

first

satellite

with

a gravitational

gradiometer

bull GRACE can

be

regarded

as one-arm

gradiometer

with

anarm length

of 200 km

Slide Number 1

Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5

Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

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Slide Number 45

Slide Number 46

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Slide Number 49

Slide Number 50

Slide Number 51

Slide Number 52

Slide Number 53

Slide Number 54

Satellite Gravimetry - Earth Online - ESA · Satellite Gravimetry. Reiner Rummel. Institute of...

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Transcript of Satellite Gravimetry - Earth Online - ESA · Satellite Gravimetry. Reiner Rummel. Institute of...