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

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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.

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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

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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

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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

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Results

Geoid heights of UCPH2004 [m]

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Results

Gravity anomalies of UCPH2004 [mGal]

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Gravity missions