1. 3MS 3 – Session 9: New projects and instruments October 11 th 2012 – Moscow, Russia Belgium-Geodesy experiment using Direct-To-Earth Radio-link: Application to Mars and Phobos Rosenblatt P., Le Maistre S., M. Mitrovic, and Dehant V. ROYAL OBSERVATORY OF BELGIUM

2. Overview  Why a Geodesy experiment in the Martian system? Scientific rationale: Mars’ deep interior (size, inner core?)  core evolution Phobos’ interior (internal mass distribution)  origin of the Martian moons Goals: Precise measurements of the rotational state (Mars’ nutation, Phobos’ librations) Using dedicated payload: X-band coherent transponder (LaRa, Lander Radioscience, developed by Belgium)

3. crust mantle outer core (radius 3480 km) inner core (radius 1221 km) Probing Earth’s interior In the absence of seismic data, geodesy brings precious information on deep interior of terrestrial planets Measurements of tides and rotation variations

4. Current knowledge of the Martian core from geodesy JPL solution ROB/CNES solution Tidal Love number 250 km Core radius estimates given possible mantle temperature end-members, mantle rheology, and crust density and thickness range (Rivoldini et al., 2010).  Liquid core inside Mars (k 2 > 0.08), but large discrepancies (+/- 250 km).  Better core radius estimate is required to better constrain other core parameters (sulfur content, solid inner core…), which drive its thermal evolution.  More data are needed. Space geodesy can play an important role by measuring nutations of the rotation axis of Mars (  Lander(s) on Mars). k 2 tidal Love number determined from orbiters (Yoder et al., 2003; Konopliv et al., 2006; Marty et al., 2009)

5.  Mars’ nutation have not been measured so far, but they can be precisely computed considering Mars’ interior is rigid.  If the core is liquid, nutation amplitudes can be amplified w.r.t. “rigid nutations”. Precise measurements of nutations  Information on the deep interior structure Nutations of the planet Mars Measured nutation - rigid nutation = Constraint on deep interior solid core liquid core

6. retrograde ter- annual nutation retrograde semi- annual nutation retrograde 1/4 year nutation prograde semi- annual nutation transfer function 250 days Amplitudes rigid Mars’ nutations non-rigid Mars’ nutations IMPORTANT FOR: ROB Free core nutation and transfer function

7. Rigid nutation amplification → core dimension & moment of inertia Core moment of inertia  Constraint on core size and shape observations Known from theory  Resonance Large amplification Rigid nutation Transfer function Free core nutation and transfer function

8. Amplification of rigid Mars’ nutation due to a liquid core... prograde semi-annual nutation 1.5% to 3% > 20% retrograde ter-annual nutation  Primary effect on retrograde ter-annual and prograde semi-annual nutations Resonance Amplification at ~3% of rigid nutation amplitude of 500 mas  ~15 mas for the liquid core signature. Amplification at >20% of rigid nutation amplitude of 10 mas  >2 mas for the liquid core signature. But it can be much more if FCN period ~Ter-annual period 1 mas = 1.6 cm at Mars’ equator

9. ROB Ter-annual nutation (period of 229 days) amplification depends on liquid core size (i.e. FCN period).  Improvement of core size determination.

10. Amplification of rigid Mars’ nutation due to a liquid core... prograde semi-annual nutation 1.5% to 3% > 20% retrograde ter-annual nutation  Effect of an inner core on nutation amplification. Resonance The existence of an inner core is expected to remove FCN semi-annual prograde amplification  detection of inner core if it does exist

11. X-band radiolink Uplink in [7.145,7.190] GHz Downlink in [8.400,8.450] GHz Coherent transponder maser Geodesy experiment to monitor Mars’ spin axis nutation Coherent transponder (LaRa) initially designed and constructed by Belgium: TRL-5 Mass: 850 grams. Power peak consumption (20 W). Direct-To-Earth (DTE) radio-link between Mars and tracking stations on Earth X-band 2-way Doppler shift measurements: Precision 0.1 mm/s  Monitoring of the rotational motion of Mars LaRa electronic box

12. Milli-acr seconds (mas) Mission duration (days) Semi-annual prograde nutation amplitude Milli-acr seconds (mas) Mission duration (days) 1/3 annual retrograde nutation amplitude Direct-to-Earth radio-link (with one Lander) Numerical simulations (1) ! Predictions of precision and accuracy on the retrieval of nutation amplitude  Nutation amplitude can be retrieved with enough precision to detect liquid core especially when the FCN period is close to the ter-annual period (229 days). FCN=230 days FCN=240 days Le Maistre et al., 2012 (Planet. Space Sci.)

13. Direct-to-Earth radio-link (with one Lander) Numerical simulations (2) !  Determining transfer function parameters with one Lander at Mars’ surface  Challenging task ! (because of non-linearity).  Use of more Landers  Network Le Maistre et al., 2012 (Planet. Space Sci.)

14. Opportunity of pre-network experiment INSIGHT + ExoMars NASA-INSIGHT scout mission due to land on Mars in 2016. Radioscience experiment with US instrument. If Radioscience transponder (possibly LaRa) onboard ExoMars (2018) we may perform Single Beam Interferometry (SBI) experiment.  Lander relative position known at the sub-cm precision level. Improvement of the determination of the Mars’ spin axis nutations.

15. ‘Puzzling’ Phobos (and Deimos) In Situ formation PROS: Current moon orbits Highly porous. Additional argument: A silicate composition. CONS: No modelling yet (Rosenblatt and Charnoz, Accepted in Icarus, 2012) All model of origin are flawed MEX/HRSC image Capture scenario: PROS: Shape, ViS/NIR spectra  Carbonaceous asteroid. CONS: Ambiguous surface composition from remote sensing data. Current orbit requires high tidal dissipation rate inside Phobos. Phobos Interior relevant to the origin: composition, mass distribution, dissipative properties … See recent review: Rosenblatt P., A&A Rev., vol. 19, 2011.

16. Which ‘Bulk interior’ for Phobos ? Murchie et al. (1991) From Fanale and Salvail (1989) From Rambaux et al., accepted in A&A, 2012 See also, PD1 Poster Session Rock+ice Blocks of rocks Stickney-induced fractures Highly porous rocky body (Rubble Pile) From Andert et al. (2010) No monolithic Phobos ! Compositional and/or structural heterogeneities inside Phobos. Principal moments of inertia to constrain it.

17. Internal mass distribution through geodetic parameters  Internal mass distribution related to principal moments of inertia (A<B<C).  Principal moments of inertia also related to quadrupole gravity coefficients C 20 and C 22 and the libration amplitudes θ Where M is the mass of Phobos, r 0 is the mean radius of Phobos and e is the ellipticity of its orbit around Mars.  Modeling internal mass distribution  Constraining those models by measurements: Geodetic experiment

18.  Monitoring of control points network (Willner et al., 2010) θ = 1.2° +/- 0.15 ° (12.5%) (Homogeneous value from the shape = 1.1°)  Updated shape model (Nadezhdina et al., EPSC, 2012): θ = 1.09° +/- 0.1 ° (9%) (Homogeneous = 0.93°)  Homogeneous/Heterogeneous …  Gravity field C 20  heterogeneity but error bar ~50% ( Andert et al., EPSC, 2011 ) (Willner et al., 2010) Mars Express: Libration/gravity measurement Shape model

19. Modeling heterogeneity inside Phobos Porosity: 10% 30% 40% Water ice: 23% 7% 0% Probability density functions of the quadrupole gravity coefficients C 20 and C 22  Geodetic parameters of heterogeneous interior departs by a few percent (<10%) from the homogeneous interior  Precise measurement is required (geodetic experiment) From Rivoldini et al., 2011 Expected C 20 value Expected C 22 value Red line homogeneous Heterogeneous models: rock+ice+porosity which fit the observed libration within its error bar.

20. X-band radiolink Uplink in [7.145,7.190] GHz Downlink in [8.400,8.450] GHz Coherent transponder maser Radio-science instrumentation Coherent transponder (LaRa) initially designed by Belgium for Martian Lander experiment Direct-To-Earth (DTE) radio-link between Phobos Lander/Orbiter on Phobos and tracking stations on Earth (DSN, ESTRACK and VLBI) X-band 2-way Doppler shift measurements: Precision 0.1 mm/s  Monitoring of the rotational and orbital motion of Phobos LaRa electronic box

21. Phobos libration from future Phobos Lander: Numerical simulations (1) !  Phobos’ rotational model: rich spectrum of libration (Rambaux et al., 2012)  Short periods contain information on the interior: Relative moments of inertia.  Numerical simulations of geodesy experiment with a Lander on Phobos show:  Short-periodic libration with a precision < 1% after a few weeks of operation  Knowledge of quadrupole gravity coefficients is also required Uncertainty on C versus uncertainty on C 20 (or C 22 ) Relative moments of inertia

22. Additional constraint from Tides  Phobos’ surface displacement due to Tides raised by Mars inside Phobos (up to 5 cm), depending on its interior structure (« rubble-pile » vs monolith)  Precise monitoring of Lander (transponder) position  interior Le Maistre et al., 2012 Predictions of formal error and accuracy Expected constraint on the interiorAmplitude of periodic tidal displacement

23. CONCLUSION & PERSPECTIVES  A geodesy (radio-science) with one (or more) Lander will provide constraints on the Martian core, (i.e. light elements content, inner core, …), therewith on its evolution.  Same experiment on Phobos (one Lander) will provide constraints on its bulk interior structure (i.e. water-ice/porosity content), therewith on its origin.  Radioscience instrument: X-band coherent transponder LaRa (TRL 5) easy to implement on Landing platform of future missions to Mars, Phobos, the Moon, Ganymede, … (ExoMars, INSPIRE, PHOOTPRINT, GETEMME, Phobos-Soil-2, JUICE …)  Radio-science instrument part of the ‘core package’ to probe in-situ the bulk interior structure of solar system bodies.

24. Lander network experiment

25. Core moment factor Nutation parameters are recovered (case where a liquid core is considered). Same results for Polar Motion and Lentgh-Of-Day variations. The effect of desaturation on the orbiter motion have been taken into account and the tracking is assumed to be as continuous as possible (from Rosenblatt et al., Planet. Space Sci., 2004). Landers (network) orbiter radio-link Numerical simulations ! Core momentum factor: Free core nutation period:

26. Acknowledgements This work was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office.