1. Prepared by: M. Marabucci, L. Iess M. Di Benedetto, S. Finocchiaro, A.Genova, R. Meriggiola, P. Racioppa, G.Rapino Progress Meeting 15 October 2009 Simulations of the impact of the RW maneuvers on MORE experiment

2. MORE Progress Meeting – October 2009 Summary SECTION 1: Comparison between settings with different value of residual DeltaVs SECTION 2: Comparison between a Ka configuration and a putative X-Ka configuration SECTION 3: Preliminary analysis of the impact of the accelerometer noise in the estimation of the gravity field

3. MORE Progress Meeting – October 2009 SECTION 1 - Configurations BOT EOT BOT EOT 0h 24h Ka DSM 1 DSM 2 0h 24h BOT EOT BOT EOT Ka DSM 1 DSM 2 General setup: - 88 arcs each lasting 24 hours -Gravitational field up to the degree 30 - The onboard accelerometer allows a complete knowledge of non- gravitational accelerations, therefore they are not included in the model - WGN Allan deviation = 10 -14 @ 1000s

4. MORE Progress Meeting – October 2009 SECTION 1 - Cases Solve-for parameters (all cases): State vector A priori covariance matrix by propagation from previous arc Coefficients of gravity field A priori uncertainties following Kaula’s rule Case A Residual DeltaVs1mm/s Solved-forYES Case B Residual DeltaVs1mm/s Solved-forNO Case C Residual DeltaVs0.15mm/s Solved-forYES Case D Residual DeltaVs0.15mm/s Solved-forNO

5. MORE Progress Meeting – October 2009 SECTION 1 - Multiarc estimate Case ACase B Case C Case D

6. MORE Progress Meeting – October 2009 SECTION 2 - Configurations BOT EOT BOT EOT 0h 24h Ka DSM 1 DSM 2 BOT EOT BOT EOT 0h 24h Ka DSM 1 DSM 2 XX General setup: - 88 arcs each lasting 24 hours -Gravitational field up to the degree 30 - The onboard accelerometer allows a complete knowledge of non- gravitational accelerations, therefore they are not included in the model - WGN Allan deviation = 10 -14 @ 1000s

7. MORE Progress Meeting – October 2009 SECTION 2 - Cases Solve-for parameters (all cases): State vector A priori covariance matrix by propagation from previous arc Coefficients of gravity field A priori uncertainties following Kaula’s rule Residual DeltaVs A priori uncertainties proportional to the value Case A Residual DeltaVs1mm/s TrackingKa Case B Residual DeltaVs1mm/s TrackingX-Ka Case C Residual DeltaVs0.15mm/s TrackingKa Case D Residual DeltaVs0.15mm/s TrackingX-Ka

8. MORE Progress Meeting – October 2009 SECTION 2 - Multiarc estimate Case ACase B Case C Case D

9. MORE Progress Meeting – October 2009 Case A – Ellipsoid and Geoid

10. MORE Progress Meeting – October 2009 Case A – Second iteration Multiarc estimate Corrected value of coefficients of gravity field Associated formal uncertainties Nominal value of coefficients of gravity field A priori formal uncertainties Multiarc estimate Second iteration

11. MORE Progress Meeting – October 2009 Case A – Second iteration - Results km (log) km/s (log)

12. MORE Progress Meeting – October 2009 SECTION 3 - Accelerometer noise From “Gravity field and rotation state of Mercury from the BepiColombo Radio Science Experiments”, Milani et al., 2001

13. MORE Progress Meeting – October 2009 Periodic acceleration (ODP model) Let r and v denote the spacecraft position and velocity θ denote the angle from the ascending node of the spacecraft orbit on the planet equatorial plane to the spacecraft: where :

14. MORE Progress Meeting – October 2009 Periodic acceleration - Settings

15. MORE Progress Meeting – October 2009 Multiarc estimate Estimated parameters:A priori uncertainties: State vectorPropagation of previous arc covariance matrix Constant coefficients of periodic accelerations1.000E-11 km/s 2 Cosine coefficients of periodic accelerations1.000E-11 km/s 2 Impulsive burns (1mm/s)5.000E-06 km/s Gravity field coefficients up to degree 29≈ Kaula’s rule Love number6.000E-02

16. MORE Progress Meeting – October 2009 Conclusions - In a Ka configuration, the gravity field is correctly recovered if residual DeltaVs of 0.15mm/s are considered. On the other hand, if the residual DeltaVs of 1mm/s are considered, it is necessary to include the impulsive burns in the solve-for parameters, but estimation errors larger than 3 sigma occur for degree higher than 18. Impulsive maneuvers of 1mm/s, not included in the solve-for parameter, jeopardize the recovering of the gravity field. - If an additional X band ground station is available, the gravity field can be correctly estimated also if residual DeltaVs of 1mm/s are considered. - The current Ka configuration with residual DeltaVs of 1mm/s (case A) shows error of few centimeters in the geoid radius (considering a gravity field up to degree 10) and will allow, at the end of the mission, to reconstruct the trajectory with accuracies compliant with altimeter requirements. - The preliminary analysis of the accelerometer noise provide information about a possible worsening of the estimation of the gravity field and make necessary an in-depth study of the impact of accelerometer noise and residual DeltaVs.

17. MORE Progress Meeting – October 2009

18. Case A – Ellipsoid and Geoid