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

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

geometry

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

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

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

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

MEX/Phobos flyby, 17th July 2008 f = -35.03 ± 0.06 mHz GM = 0.7120 ± 0.0006 x10-3 km3/sec2 (error 0.08%) (1) Based on JPL Phobos ephemeris from Jacobson, 2008

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°

simulated flyby: parameter

Simulation: dependence on mass

Simulation: dependence on mass Simulation performed with: Bulk density 2000 kg/m3 Frequency noise (@10s): 12 mHz (1s)

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

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

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

HGA stopps tracking 20 min before c.a.

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

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

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

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

Ground station visibility

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

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