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CHAMPSatellite Gravity Field Determination
Satellite geodesyEva Howe
January 12 2006
January 12 2006 Satellite geodesy Eva Howe | Page 2
CHAMP
CHAMP
Weight 522 kgLength 8,3 m
Launched July 2000Near circular orbitInitial altitude 454kmInclination i=87.3º
January 12 2006 Satellite geodesy Eva Howe | Page 3
CHAMP
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CHAMP
Measurement bandwidth 10-4 - 10-1 HzLinear accelerations:
Measurement range ± 10-4 ms-2
Resolution:< 3 × 10-9 ms-2 (y- and z-axis)
< 3 × 10-8 ms-2 (x-axis)
STAR accelerometer
A proof mass is floating freelyinside a cage supported by anelectrostatic suspension.Electrodes inside the cage iscontrolling the motion of thetest-mass.The force needed is proportionalto the detected acceleration.
January 12 2006 Satellite geodesy Eva Howe | Page 5
CHAMP
Expected accuracy:A geoid with accuracy of cm with a resolution of L=650 km (degree and order 30)
Achieved accuracy:A geoid with accuracy of 5 cm.A gravity field model with accuracy of 0.5 mGal.Both with a resolution of 400 km (degree and order 50).
January 12 2006 Satellite geodesy Eva Howe | Page 6
Energy conservation
The Energy conservation Method
The general energy law: The sum of all energy in an isolated system is constant
outerpotkin FEE
Where Fouter represents the non-conservative outer forces.The gravitational potential V can be related to the kinetic energy Ekin of the satellite minus the energy loss.
January 12 2006 Satellite geodesy Eva Howe | Page 7
Energy conservation
Gravity field determination by Energy conservation
From the state vector (x, y, z, vx, vy, vz) and the accelerometer data (ax, ay, az) from CHAMP a model of the gravity field of the Earth can be estimated by energy conservation.
Data from the period July 2002 – June 2003 are used.
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Energy conservation
The outer forces must be considered:
•Tidal effects from the other planets -consider only the Sun and Moon
•Energy loss due to atmospheric drag, sun pressure, thermal forces
and cross winds -consider only the air drag in the solutions
•Rotation of the potential in the inertial frame
Earth normal potential is subtracted and the sum of all the integration
constants.
From this you get the anomalous potential.
January 12 2006 Satellite geodesy Eva Howe | Page 9
Energy conservation
dtavFdtavF
AU
rMg
rgV
UEFyvxvVVvT
y
sunsun
sunsun
xymoonsun
,
)1cos3(,2
)(2
1
23
02
where U Normal potential of the EarthE0 Integration constantω Angular velocity 7.292115*10-5 s-1
µ GMAU Astronomical unitr Distance from the satellite to the centre of the EarthΦ Zenith angle of the Sun
January 12 2006 Satellite geodesy Eva Howe | Page 10
Energy conservation
Chosen only to use the along-track component of the acceleration vector (ay)
The accelerometer suffer from bias and scale factor.
Determined a scale factor for each half day (recommendations are for every revolution) by correlating the friction with the difference between the calculated potential and an a priori model.
January 12 2006 Satellite geodesy Eva Howe | Page 11
Data processing
Accele-rationvector
statevector
Meanpole
coordi-nates
EGM96to
degree24
readaccReformat of
accelerations
stat2potCalculation of
anomalouspotential
GEOCOLRemoval of
reference field
correlEstimate scalefactor subtract
friction
Up-/downwardcontinuation
GEOCOLEstimation ofcoefficients
GEOGRIDGridding of
data
sphgricEstimation ofcoefficients
Type ofsolution
FSC
LSC
January 12 2006 Satellite geodesy Eva Howe | Page 12
Data processing
How do we represent the gravity field?
- by spherical harmonic coefficients!
2
0 0
2
0 0
sincossin,4
1
sincoscos,4
1
ddPmTb
ddPmTa
nmnm
nmnm
From these we can get for instance the anomalous potential
0 0
cossincos,n
n
mnmnmnm PmbmaT
January 12 2006 Satellite geodesy Eva Howe | Page 13
Results
Geoid heights of UCPH2004 [m]
January 12 2006 Satellite geodesy Eva Howe | Page 14
Results
Gravity anomalies of UCPH2004 [mGal]
January 12 2006 Satellite geodesy Eva Howe | Page 15
Gravity missions