Lecture 5 – Earth’s Gravity Field
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Transcript of Lecture 5 – Earth’s Gravity Field
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Lecture 5 – Earth’s Gravity Field
GISC-3325
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Schedule for next two weeks• You are responsible for material in
Chapters 1-4 in text as well as all lectures and labs to date.
• I will miss class 6 February as well as 18 and 20 February.
• The first exam, open-book and “take-home,” will take place on either 18 or 20 February.
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Some comments on Lab 2
• It is expected that students will review the reference materials on the NGS toolkit pages and the lecture materials on the web.
• Using the XYZ Coordinate Conversion tool for question 8 is NOT correct. It computes on the ellipse NOT sphere with uniform radius.
• When transforming be aware of significant digits! We must be able to do the inverse with our answer to transform back.
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Topics
• Definition of gravity
• Its importance to geodesy
• Measurement techniques
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What is Geodesy?
• “Geodesy is the discipline that deals with the measurement and representation of the earth, including its gravity field, in a three-dimensional time varying space.” – definition adopted by the National Research
Council of Canada in 1973. (Vanicek, P.K. and Edward Krakiwsky, E.(1986) Geodesy: The Concepts. Elsevier).
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Another definition
• “The task of geodesy is the determination of the potential function W(x,y,z)” i.e. of the gravity potential of the Earth. – By Heinrich Bruns (1878)
• Both definitions indicate the linkages between positioning and gravity field determination.
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Integrated Geodesy
• Also called “Operational Geodesy”
• Integrated geodesy is a method in which a wide variety of surveying measurements are modeled in terms of geometric positions and the earth’s geopotential.– Both geometric and gravimetric data are
simultaneously estimated using Least Squares.
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The System of Natural Coordinates
• Axes are defined by meaningful directions: the gravity vector and of the spin axis of the Earth.
• Gravity vector defines the up-down direction– Orthogonal to a level
surface.
• There is a difference between the gravity vector and normal to ellipsoid.
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Universal Law of Gravitation
• Newton formulated the law (1687) to reflect the attraction of two point masses separated by a distance.
• f = G* [ (m*m’)/l2]– ( f is force, m and m’ are point masses, l is
distance and G is Newton’s gravitational constant)
• Currently accepted value for G – 6.67259 x 10-11m3kg-1s-2
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Gravity and Geodesy
• Defines a plumb line (local vertical) defined by gravity.
• Gravity also serves as an important reference surface. It is the level surface that is perpendicular to the plumb line at all points.
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Some unit issues
• Your textbook uses– g = 6.67259 x 10-11m3kg-1s-2
• A 1998 free-fall determination experiment (published in Science, 282, 2230-2234, 1998) determined a value for g of – (6.6873+/- 0.0094) x 10-11m3kg-1sec-2
• We will discuss the instrument used in this measurement.
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Unit of measurement
• Standard unit of measurement is the gal – named after Galileo Galilei – 1cm/sec-2
• Units are expressed as either gals or fractional parts (e.g. milligals or microgals).
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Gravitational Constant
• Geocentric gravitational constant (GM) is considered a constant.
• The value for GM accepted by the International Association of Geodesy (IAG) is:– 3 986 005 x 108m3s-2
• This equation assumes the Earth’s mass is located at a finite point (center of mass) and includes the atmosphere.
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Absolute Gravity Meters
Mendenhall pendulum gravity meter Accuracy +/-0.6 to 5 mGals
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How does it work?
• Motion of a test mass free falling in a vacuum is interferometrically measured with respect an inertial reference.
• Controlled carriage assembly releases the test mass (a corner cube retroreflector mounted in an aluminum housing).
• The inertial reference is another corner cube retroreflector mounted on a force feedback long period (60sec) seismometer.
• Non-gravitational forces are minimized (air drag, electrostatics, and eddy current damping).
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Gravity change
• FG5 accuracy:
14
Instrument 1.1 Gals
Environmental: 1.5 Gals
Observational error: ~0.4 Gals
RMS of above at instrument height (131 cm): 1.9 Gals
RMS with relative transfer to mark or excenter: 3 to 8 Gals
• +3 Gals corresponds to -1 cm elevation change
+7½ foot rise in water-table
GPS to resolve ambiguity
• Can also measure magma insertion
sea level change (with tide record comparisons)
glacial ice mass change
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26
CHURCHILL, MANITOBA
-12
-8
-4
0
4
8
12
16
20
24
28
32
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
TIME (Yrs)
g - 9
8175
2800
µG
AL
Gravity Values
+ 95% Error Bound
- 95% Error Bound
Trend -1.91 ± 0.19 µGal/Yr
ICE-3G Theoretical (-1.11 Gal/yr)
2 cm uplift
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Two models provide similar but not identical results. Difference is 1 mgal.
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Which model to use?
• NAVD88 - Modeled Gravity uses a model developed for the NAVD88 adjustment rather than current gravity values.
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Review of Height Systems• Helmert Orthometric• NAVD 88
• local gravity field ( )• single datum point• follows MSL
g
HC
g
C
g H
g gh
G H
0 0 4 2 41
23
.
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Earth’s Gravity Field from Space• Satellite data was
used for global models– Only useful at
wavelengths of 700 km or longer
• Lower wavelength data from terrestrial or marine gravity of varying vintage, quality and geographic coverage
Terrestrial and marine gravity data in NGS data base.
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Note the discontinuity at the shoreline.
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Gravity
• Static gravity field – Based on long-term average within Earth
system
• Temporally changing component– Motion of water and air– Time scale ranges from hours to decades.
• Mean and time variable gravity field affect the motion of all Earth space vehicles.
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Gravity Recovery And Climate Experiment
www.csr.utexas.edu/grace/gravity/
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Geoid Model from Earth Orbiting Space Vehicles (pre-GRACE)
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GRACE 111 days of data
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GRACE 363 days of data
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Orbit inclination: 89.048 degrees
Eccentricity: 0.000775
Semi-major axis: 6,849,706.754m
Distance between satellites: 222,732.810 m
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GRACE
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How does GRACE work?
• Motion of two satellites differ because they are at different positions in space.
• When the lead SV approaches a higher gravity mass it accelerates as it moves beyond it decelerates.
• Distance changes between SVs is measured precisely.
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ITRF96/GRS-80 ellipsoid surface
global geopotential surface
NAVD 88 datum
G99
SS
S
G99
BM
Average of 52 cm
NAD 83 datum
GE
OID
99MSL
SS
T
NOTE: heights are not to scale
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