1. CHAMP Satellite Gravity Field Determination Satellite geodesy Eva Howe January 12 2006

2. January 12 2006 Satellite geodesy Eva Howe | Page 2 CHAMP Weight 522 kg Length 8,3 m Launched July 2000 Near circular orbit Initial altitude 454km Inclination i=87.3º

3. January 12 2006 Satellite geodesy Eva Howe | Page 3 CHAMP

4. January 12 2006 Satellite geodesy Eva Howe | Page 4 CHAMP Measurement bandwidth 10 -4 - 10 -1 Hz Linear 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 freely inside a cage supported by an electrostatic suspension. Electrodes inside the cage is controlling the motion of the test-mass. The force needed is proportional to the detected acceleration.

5. 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).

6. 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 Where F outer represents the non-conservative outer forces. The gravitational potential V can be related to the kinetic energy E kin of the satellite minus the energy loss.

7. January 12 2006 Satellite geodesy Eva Howe | Page 7 Energy conservation Gravity field determination by Energy conservation From the state vector (x, y, z, v x, v y, v z ) and the accelerometer data (a x, a y, a z ) 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.

8. January 12 2006 Satellite geodesy Eva Howe | Page 8 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.

9. January 12 2006 Satellite geodesy Eva Howe | Page 9 Energy conservation where UNormal potential of the Earth E 0 Integration constant ωAngular velocity 7.292115*10 -5 s -1 µGM AUAstronomical unit rDistance from the satellite to the centre of the Earth ΦZenith angle of the Sun

10. January 12 2006 Satellite geodesy Eva Howe | Page 10 Energy conservation Chosen only to use the along-track component of the acceleration vector (a y ) 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.

11. January 12 2006 Satellite geodesy Eva Howe | Page 11 Data processing

12. January 12 2006 Satellite geodesy Eva Howe | Page 12 Data processing How do we represent the gravity field? - by spherical harmonic coefficients! From these we can get for instance the anomalous potential

13. January 12 2006 Satellite geodesy Eva Howe | Page 13 Results Geoid heights of UCPH2004 [m]

14. January 12 2006 Satellite geodesy Eva Howe | Page 14 Results Gravity anomalies of UCPH2004 [mGal]

15. January 12 2006 Satellite geodesy Eva Howe | Page 15 Gravity missions