1. Lutetia Flyby Rosetta Radio Science Investigations RSI
Martin Pätzold (1), Tom Andert (2)
(1) RIU, Abt. Planetenforschung, Cologne
(2) UniBw München
SWT, ESTEC 12th June 2009

2. mass determination at flybys
Two-way radio carrier link at two frequencies (X & S-bands)
Gravity attraction from the asteroid perturbs the spacecraft trajectory => perturbed s/c velocity
velocity components are projected into the LOS to Earth => Doppler shift of radio carrier frequency
Perturbed velocity components => perturbed Doppler shift
Perturbing force extracted by substracting predicted Doppler shift (from extrapolated unperturbed trajectory) from observed Doppler shift => Doppler frequency residuals

3. geometry

4. mass determination at flybys
Velocity component along LOS depend on the angle between the direction of flyby velocity and the direction of LOS

5. mass determination at flybys
Velocity component along LOS depends on angle a between direction of flyby velocity and direction of LOS
Example a = 0°

6. mass determination at flybys
Velocity component along LOS depends on angle a between direction of flyby velocity and direction of LOS
Example a = 0°

7. mass determination at flybys
Velocity component along LOS depends on angle a between direction of flyby velocity and direction of LOS
Example a = 90°

8. MEX/Phobos flyby, 17th July 2008
f = ± 0.06 mHz
GM = ± x10-3 km3/sec2 (error 0.08%) (1)
Based on JPL Phobos ephemeris from Jacobson, 2008

9. mass determination at flybys
Velocity component along LOS depends on angle a between direction of flyby velocity and direction of LOS
Example a = 20°, 45°, 75°

10. simulated flyby: parameter

11. Simulation: dependence on mass

12. Simulation: dependence on mass
Simulation performed with:
Bulk density 2000 kg/m3
Frequency noise 12 mHz (1s)

13. Flyby reference case -- simulation with noise
-- nonlinear least squares fit

14. Flyby reference case mass: GM = (6.120 +/- 0.180)∙10-2 km3 s-2
-- simulation with noise
-- nonlinear least squares fit
mass: GM = ( / )∙10-2 km3 s-2
relative error: 2.9%
reference: GM = 6.086∙10-2 km3 s-2

15. case studies (1) Assumptions:
HGA Earth tracking stopps before closest approach
=> data end tbd minutes before closest approach
no tracking resumed after closest approach

16. HGA stopps tracking 20 min before c.a.

17. case studies (1) Assumptions:
HGA Earth tracking stopps before closest approach
=> data end tbd minutes before closest approach
no tracking resumed after closest approach

18. case studies (2) Assumptions:
HGA Earth tracking stopps before closest approach
tracking resumes after tbd hours after closest approach
=> data gap of tbd hours

19. tracking stopps 10 min before c.a. tracking resumes 2 hours after c.a.

20. case studies (2) Assumptions:
HGA Earth tracking stopps before closest approach
tracking resumes after tbd hours after closest approach
=> data gap of tbd hours

21. Ground station visibility

22. Requirements & Recommendations
Stop HGA tracking before closest approach as late as feasible
Recommendation: cover the closest approach
Resume HGA tracking after closest approach within 2 hours
Keep 3000 km closest approach distance; distance is an issue for this flyby-geometry !
Entire flyby visible from Europe: keep one ground station for the flyby
use DSN for X & S-band reception (CEB no S-band)
Recommendation: use 70-m DSN Madrid for improved SNR

23. Comparison 35-m and 70-m ground station
Mars Express MaRS radio occultation (X-band)
35-m ground station
1-sigma: 32 mHz
70-m ground station
1-sigma: 3 mHz