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Mars Express Radio Science Experiment MaRS

MaRS Radio Science Data:Level 3 & 4

Basics

S.Tellmann, M.Pätzold

ESACJune 2008

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OverviewLEVEL 3: • The Bending Angle & the Rayparameter• The Refractive Index/Refractivity & Radius

LEVEL 4:• The Neutral Atmosphere

• Density• Temperature• Pressure

• The Ionosphere• The Electron Density

The Twoway Problem

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Earth Occultations

Ionosphere

Mars

Neutral Atmosphere

frecw/o

f = f + frecw/o

sendMEX

dop

MEXf : signal transmitted from MEX

f : signal received w/o atmosphere

f : classical Doppler shift

MEXsendw/orec

dop

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Earth Occultations

Ionosphere

Mars

Neutral Atmosphere

frecw/o

f = f + frecw/o

sendMEX

dop

MEXf : signal transmitted from MEX

f : signal received w/o atmosphere

f : classical Doppler shift

f : signal received with atmosphere

f : frequency shift from atmosphere

MEXsendw/orec

dop

recwith

f = f + f + f + frecwith MEX

send dop iono

atm

recwithf

atm

bending angle

Ray Asymptote

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Bending Angle & Rayparameter

Retrieval based on geometrical optics [Fjeldbo et al., 1971]

: bending anglea : rayparameter

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Bending Angle & Rayparameter

[Fjeldbo et al., 1971]

Basic Idea:

f fwithrec fwo

rec

Input:

• Position of Spacecraft, Groundstation & Mars• Velocity of Spacecraft, Groundstation & Mars

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Doppler Effect

ftransmit

frec

1 ntransmit

1 nrec

vc

For vEarth << vS/C:

fSCtransmit fEarth

rec 1 nSC nEarth

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The Refractivity

• Calculation of Refractive index from bending angle and rayparameter• Reconstruction of a two-dimensional radial symmetric distribution f(r) from its projection g(y) inverse Abeltransform

The twodimensional function is given by:

[Pretzler et al., 1992]

[Jenkins, 1992]

Abel transform:

Inverse Abel transform:

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The Refractivity

• Inverse Abeltransform:

• Integration of bending angle and rayparameter over all layers already traversed

Refractive Index:

n1

n2n3

n4

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The Radius (ray peripasis)

r an

r : radiusa : rayparametern : refractive index

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Refractivity

Ionosphere: Negative Refractivity higher than ~ 80 km altitude approx. 3480 km radius

Transition Region: no significant bending approx. 60 km – 80 km altitude approx. 3450 km – 3480 km

Neutral Atmosphere: Positive Refractivity up to approx. 50 km altitude up to approx. 3450 km radiusNeutral Atmosphere

Ionosphere

Ionopause

Transition Region

Refractivity

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Retrieval of atmospheric parameter

2

031 f

hNCkhnCh e

f0 : Radio link frequency

Ne : electron density

C1, C3 : atm. constants

k : Boltzman constant

n: neutral number densityNeutral Atmosphere Ionosphere

Refractivity (h):

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The Ionosphere

2

031 f

hNCkhnCh e

f0 : Radio link frequency

Ne : electron density

C3 : atm. constant

Neutral Atmosphere Ionosphere

Refractivity (h) in Ionosphere (h>60km):

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The Electron Density

h C3

Ne

f20

f0 : Radio link frequency

Ne : electron density

C3 = 40.31 m3/s2

• refractivity is ~1/ f2 • S-band is more sensitive to electron density than X-band

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The Neutral Atmosphere

2

031 f

hNCkhnCh e

Neutral Atmosphere Ionosphere

Refractivity (h) in neutral atmosphere (h<50km):

Second term << first term

C1: atm. constants

k : Boltzman constant

n: neutral number density

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Neutral Number Density:

Pressure (assuming hydrostatic equilibrium):

Temperature: ideal gaslaw

Neutral Atmosphere

gmnr

p

nk

pT

h C1n h

k

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The Twoway Problem

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Ionosphere

Mars

Neutral Atmosphere

frecw/o

f = f + frecw/o

sendMEX

dop

MEXf : signal transmitted from MEX

f : signal received w/o atmosphere

f : classical Doppler shift

f : signal received with atmosphere

f : frequency shift from atmosphere

MEXsendw/orec

dop

recwith

f = f + f + f + frecwith MEX

send dop iono

atm

recwithf

atm

bending angle

So far assumed: Oneway

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But in Realty: Twoway Radio Link

Ionosphere

Mars

Neutral Atmosphere

f

f = f + frec sendEarth

MEX

MEX up

Earth

send

Up: X-band: 7.1 GHz

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Ionosphäre

Mars

Neutralatmosphäre

f

f = f + frec sendEarth

MEX

MEX up

f = {f + f }·k MEX

send

Earth

Earth

send

send

up

f · kMEX

rec

The Twoway Problem

Up: X-band: 7.1 GHz

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Ionosphere

Mars

Neutral Atmosphere

f

f = f + frec sendEarth

MEX

f = k· f + k·f + fEarthrec

Earthsend

up down

fEarthrec

MEX up

f = {f + f }·k MEX

send

Earth

Earth

send

send

up

The Twoway Problem

Up: X-band: 7.1 GHzDown:X-band: 8.4 GHzS-band: 2.3 GHz

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The Twoway Problem• Bending of Radio link on Uplink & Downlink• Difficult to seperate effects from Uplink & Downlink

• Different dependency on Radio frequency in Ionosphere and Neutral atmosphere

2

031 f

hNCkhnCh e

Neutral Atmosphere:Independent of frequency Ionosphere: ~ 1/ f2

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The Twoway Problem

• Different frequencies on Uplink and Downlink• Ionospheric Bending is ~ 1/f2 Different bending on Uplink &

Downlink• Bending in Neutral Atmosphere independent of frequency• Retrieval of bending angle and rayparameter is exclusively

dependent on measurement geometry!!!! No frequency dependeny taken into account!

Solution:• Retrieve Ionosphere and Neutral Atmosphere separately

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Twoway Problem: The Ionosphere

Best Solution: • Use Differential Doppler (~ pure Oneway S-band Downlink)• All effects ~ f are subtracted due to the use of to coherent frequencies

Other solution:

Make an iterative solution:• solve for „mean Ionosphere“• Calculate electron density refractivity for Uplink & Downlink• Make Raytracing: calculate bending in this „assumed“ atmosphere• Compare solution of ray tracing with true residual……

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Twoway Problem: Neutral Atmosphere

• Treat Uplink and Downlink explicitely with basic formulas from Oneway

• Solve Uplink & Downlink in the way already described

Literature: • Lipa, B. and Tyler, G.L., 1979. „Statistical and Computational Uncertainties

in Atmospheric Profiles from Radio Occultation: Mariner 10 at Venus“, Icarus 39, 192 – 208.

• Jenkins et al., 1994. „Radio Occultation Studies of the Venus Atmosphere with the Magellan Spacecraft“, Icarus 110, 79 – 49.

fSCsend fSC

rec k