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Geodesy with Mars lander Network

Geodesy with Mars lander Network. V. Dehant, J.-P. Barriot, and T. Van Hoolst Royal Observatory of Belgium Observatoire Midi-Pyrénées. Precession-Nutation. Z ecliptic. Rotation Axis. I = I 0 + I. Y ecliptic.  =  0 + . X ecliptic. Topics. Rotation variations

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Geodesy with Mars lander Network

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

  2. Precession-Nutation Zecliptic Rotation Axis I = I0 + I Yecliptic  = 0 +  Xecliptic 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

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

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

  6. 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

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

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

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

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

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

  12. Error: centimeter level days 0 700 700 0 0 700 0 700 700

  13. Number of landers

  14. Lander-Earth link

  15. Graphes de resultats

  16. Low degree zonal gravity coefficients and rotation rate • Variations in C20 give information about the CO2 cycle. But strongly linked LOD (mass redistribution is main factor). • Doppler shifts between landers – orbiter (LOD) and orbiter – Earth (C20) • Previous results assume a perfectly known orbit • Numerical simulations with GINS (Géodésie par Intégrations Numériques Simultanées, CNES) software

  17. Time-Varying Gravity Field Gravity observation from SC, High Electron detector observation,GCM C20 C30 The precision of current gravity observations are not sufficient enough to provide additional constrains to C02 cycle

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

  19. Simulations with two orbiters MGS (I=93°, e=0.01)+MEX (I=86°, e=0.6) C40 C50 C20 C30 The error is reduced by a factor of about 2

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

  21. 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 CO2 cycle

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

  23. Signature of MOPs Geometric effect= change in direction lander-orbiter due to MOP Large effect for low altitude satellite Change in lander velocity due to MOP |V| : velocity différence between landers and orbiter (~3 km/s), |VMOP| : 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).

  24. Effect of the Landers-orbiter Doppler tracking on the J2 determination : model C20 +: DSN, fixed ΔLOD but modified ----: DSN, fixed ΔLOD O: DSN + lander data

  25. Landers-Orbiter Doppler tracking and seasonal gravity field : model Cl0 o: near polar, DSN x: near polar DSN + lander tracking +: near polar + Starlette like orbiter, DSN tracking

  26. 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

  27. 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).

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