1. Geodesy with Mars lander Network V. Dehant, J.-P. Barriot, and T. Van Hoolst Royal Observatory of Belgium Observatoire Midi-Pyrénées

2. Topics Rotation variations –Orientation in space: precession/nutation –Orientation in planet: polar motion –Rotation speed: length-of-day variations Gravity Field Modeling of –Interior of planets –Atmosphere dynamics  =  0 +  X ecliptic Y ecliptic Z ecliptic I = I 0 +  I Rotation Axis Precession-Nutation

3. Overview of the presentation Amplitudes of rotation variations of Mars Relation to interior structure and atmosphere of Mars Simulations of rotation variations and expected precisions (importance of landers) Gravity field: seasonal gravity variations

4. r : 230 m after 700 days  Moment of inertia of Mars ( C ) Precession of Mars

6. r : 15 m (main term: semi-annual) Precession and nutation of Mars

8. Nutation and interior structure Most important and geophysically interesting influence: existence of a liquid core Nutational motion of core differs from that of the mantle (if sphere: no core nutation). Core’s nutational effect : amplification of nutation with respect to rigid planet Main effect: resonance due to the existence of a free rotational mode related to the core

9. Free Core Nutation Rotation axis of the core Rotation axis of the mantle n close to resonant frequency: large core nutational motion in opposite direction of mantle nutation, which can then largely be amplified n Restoring forces depend on flattening of core Flattening mainly depends on core density FCN Period  core density, core radius ROB Relative rotation of axes Retrograde long period in space Close to main nutations

10. Amplification due to liquid core: 5mas or more

11. Variations of the rotation speed (  r : 10 m )

12. Polar motion (  r : 10 to over 100 cm)

13. Measuring Doppler shifts on Lander-Orbiter link ≈ Projection of relative velocity on line-of-sight Lander-Orbiter

15. days 7000 0 0 0 Error: centimeter level

16. Number of landers

17. Lander-Earth link

18. Graphes de resultats

19. Low degree zonal gravity coefficients and rotation rate Variations in C 20 give information about the CO 2 cycle. But strongly linked LOD (mass redistribution is main factor). Doppler shifts between landers – orbiter (LOD) and orbiter – Earth (C 20 ) Previous results assume a perfectly known orbit Numerical simulations with GINS (Géodésie par Intégrations Numériques Simultanées, CNES) software

20. Time-Varying Gravity Field C 20 C 30 The precision of current gravity observations are not sufficient enough to provide additional constrains to C0 2 cycle Gravity observation from SC, High Electron detector observation,GCM

21. Simulations with MGS (I=93°, e=0.01) & MEX (I=86°, e=0.6)

22. Simulations with two orbiters MGS (I=93°, e=0.01) +MEX (I=86°, e=0.6) The error is reduced by a factor of about 2 C40C50 C20C30

23. Effect of a Lander Network (single orbiter) Landers help to resolve the LOD, to determine better the orbit ascending node hence the even coefficients

24. Conclusions An additional lander – orbiter link improves the determination of rotation variations and gravity variations and makes it possible to extract information on Mars’ interior and atmosphere/polar caps CO 2 cycle

25. C DARGAUD v.dehant@oma.be ROB

26. Signature of MOPs Change in lander velocity due to MOP Geometric effect = change in direction lander-orbiter due to MOP Large effect for low altitude satellite |  V| : velocity différence between landers and orbiter (~3 km/s), |  V MOP | : change in |  V| due to (~ mm/s),  : angle between |  V| and line-of-sight lander-orbiter,   MOP : change in  due to MOP (~ 10 -7 rad).

27. Effect of the Landers-orbiter Doppler tracking on the J2 determination : model C 20 +: DSN, fixed ΔLOD but modified ----: DSN, fixed ΔLOD O: DSN + lander data

28. Landers-Orbiter Doppler tracking and seasonal gravity field : model C l0 o: near polar, DSN x: near polar DSN + lander tracking +: near polar + Starlette like orbiter, DSN tracking

29. Landers-Orbiter Doppler tracking and seasonal gravity field : Formal error o: near polar, DSN x: near polar DSN + lander tracking +: near polar + Starlette like orbiter, DSN tracking

30. Lander-Orbiter Doppler tracking and rotation rate determination Simulation of Mars’ Rotation rate determination From the Landers-orbiter Doppler-link (four landers and one near-polar orbiter).