1. Report of work at ROB within the MAGE European Training Network Véronique Dehant

2. Participant NamePositionResearch activity EffectiveExpected 8. ROB-BrusselsVéronique DehantProfessor70 Tim Van HoolstProfessor8570 Pascale Defraigne Senior Scientist 3050 René Warnant Senior Scientist 550 Fabian Roosbeek Senior Scientist 550 Marie YseboodtScientist100 Pascal RosenblattScientist1000 Ellen Van den Acker/ Ozgur Karatekin Scientist100 Laurent Morel/ Mikael Beuthe Scientist100 Attilio RivoldiniPhD student100 Jean-Francois Bodart/ Julien Duron PhD student100 Jacques Sleewaegen/ Olivier Verhoeven/ Gregor Pfyffer Scientist/ PhD student 100 Total ROB- Brussels 995990 + Valery Lainey MAGE Postdoc PHOBOS/DEIMOS

3. Parameters : Temperature profile Bulk iron and olivine weight fraction Pressure gradient. Modeling of the Martian mantle Recently taken into account : The effect of iron concentration in the respective minerals on the electrical conductivity The possible presence of partial melting in the upper mantle Empirical relation between olivine and the non-olivine mineralogical system.

4. Direct Problem Inversion : Marginal density for temperature

5. Collaboration with U Nantes, CETP, IPGP, OMP

6. Doppler simulation Analytical simulations of the Doppler and Range observables between Martian landers and an orbiter, extraction of the Martian orientation parameters + comparison with a direct lander-Earth link Effect of the network geometry and lander position on the parameters uncertainties (via analytical and numerical simulations) …

7. jours 700 0 0 0 0

8. GINS : For accurate S/C Orbit Determination DYNAMO : For Geophysical Parameters Determination S/C Tracking data from:  the Earth  the planetary surface S/C Tracking data sets:  Doppler & Ranging (corrected from propagation effect)  “Angular” position of S/C w.r.t. planetary surface (MPO) DYNAMO Normal matrices Stacking + Resolution Physical & Dynamics parameters: gravity field, K2 Love number, station positions, … A PRIORI ORBIT ( numerical integration of S/C motion ) Gravity field + DE406 ephemeris (Sun, Mercury, Earth, …) + relativistic corrections + K2 Love Number + Librations + Desaturation (epoch, intensity) + Non-gravitational accelerations (or modeling) + State Vector (from navigation or previous adjustment) ADJUSTED ORBIT: State Vector, Desaturation Data biases, modeling of non-gravitational forces Predicted S/C Tracking data (given positions of the tracking stations) Least Squares Adjustment on TRACKING MEASUREMENTS GINS Accelerometer data (or attitude mode: Quaternions) Normal matrices: physical & dynamics information MEASUREMENTS

9. Effect of inertial desaturation on the orbit determination When all the desaturation events are tracked from the Earth, only 15-20 minutes of lander-orbiter tracking per week allows recovering of Mars’ orientation parameters with a precision of a few milli-arc-seconds When all desaturation events are tracked from the Earth: RMS of the residual positions of the orbiter : 4.8 cm Recovery of residual accelerations 6 events a day, 1 mm/s of velocity variation and 2 DSN antennas for tracking When half of the desaturation events are tracked from the Earth: RMS of the residual positions of the orbiter: 155 cm Recovery of residual accelerations 6 events a day, 1 mm/s of velocity variation and 1 DSN antenna for tracking

10. Variations of the low degree zonal (J2 to J5) coefficients of Mars’ gravity field Strong seasonal variation of gravity field due to sublimation/condensation of the atmospheric CO2 To constrain CO2 seasonal mass variations between polar caps and the atmosphere Prediction of changes of the first zonal terms of the gravity field provided by GCM (Global Circulation Model) simulations of the atmosphere Ls (Solar Longitude) From Laboratoire de Météorologie Dynamique (LMD), France From NASA

11. An improved strategy to estimate the zonal coefficients of the Martian gravity field : Numerical simulations of a global geodetic experiment Satellite ORBITS : - orbiter 1 (as part of a Mars Network Science Experiment : NEIGE) : i = 93.2°, e = 0.001 - orbiter 2 : i = 50°, e = 0.0206 Earth-based tracking of the two orbiters by 3 DSN stations Mars-based tracking of the near-polar orbiter (1) by 4 stations (dual frequency UHF/S-band)

12. Martian lithosphere and wavelets Aim: lithosphere thickness on Mars Method: 1.Input data : topography 2.Model : flexure of a thin elastic spherical shell 3.Output : predicted gravity anomalies 4.Localization of anomalies with spherical wavelets 5.Comparison of predicted/observed gravity anomalies Conclusion: large thickness at Tharsis, small at Hellas

13. Flexure model

14. Topography and gravity anomalies: the case of Mars MGS RS and MOLA Science Teams: Zuber et al., 2000, Science 287, 1788.  Different mechanisms at work at different places: Ex1: isostatic compensation at Hellas (no lithosphere resistance) Ex2: little compensation at Tharsis (high lithosphere rigidity, or high loading density) Ex3: internal loading at Isidis

15. Martian gravitational field analyzed with spherical wavelets

16. Martian gravity anomalies from Mars Express data Collaboration with: 1.Jean-Pierre Barriot (CNES/Toulouse) for the software 2.Martin Paetzold (PI of MaRS) for the data Input data: line-of-sight Doppler residuals in areas of interest (poles…) Method: Least-squares inversion of residuals with a priori knowledge Result: local maps of gravity anomalies Work in progress: data is coming!

17. Radio science data on particular targets ROB determination of gravity anomalies ROB+OMP Knowledge of Phobos ephemerides ROB+BdL Interpretation in terms of properties of the interior of Phobos ROB Quality factor of Mars ROB+IPGP Study of lithosphere properties IPGP Work in progress! Thanks to MAGE!