Gravimetry Geodesy Rotation ROB

rotation nutation ROB

Interior structure Mars-Earth MMars= 6.4185 1023 kg  0.1MEarth (orbits) RMars = 3390 km  0.5 Rearth (occultation) gMars = 3.7 m/s2  0.4 gEarth (M/R2) Mars = 3.93 g/cm3  0.8 Earth (M/R3) ROB

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Many questions for Mars (size, state) MARS INTERIOR Core: Many questions for Mars (size, state) Important for the understanding of origin, evolution, and dynamics of terrestrial planets ROB

Gravimetry Geodesy Rotation ROB

Static gravity field The gravity field presents spatial variations on the surface, reflecting the mass distribution on and in the planet. Analysis of the spatial variation of the gravity field is a powerful tool to get information on the internal structure: crustal thickness, mantle inhomogeneities, core size, non-hydrostatic anomalies Gravity field variations extracted from their effect on the satellite motion

Global and local gravity fields 2 approaches: global gravity field: spherical harmonic coefficients estimated from the data (GINS/DYNAMO software); resolution up to degree 25, i.e. 300km. line-of-sight method: Doppler residuals interpreted in terms of difference with respect to long wavelength gravity; 200km resolution for well-covered areas.

Physical insights from gravity Present knowledge on crust and lithosphere from study of gravity above particular targets; of Global gravity field + topography provide - map of crustal thickness variations (all gravity anomalies interpreted in terms of crustal thickness) - lithospheric thickness : flexure model

Flexure model

Global admittance analysis Crustal density Admittance: Cl depends on the rigidity of the lithosphere, Cl = 1 for rigidity=0, perfect compensation, isostasy = 0 for an infinite flexural rigidity, no compensation Fit Cl to observations to extract global rigidity topography gravity anomaly ~ internal mass load degree of compensation density jump rm-rc

Local admittance analysis Local model: characteristics of the lithosphere differ from place to place: rigidity, loading density, crustal thickness, crust density. use a different set of parameters for each site Local data: windowing of global data with Fourier window or wavelet analysis or use line-of-sight method

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

Gravimetry Geodesy Rotation ROB

Mars’ response to external forcing Mars rotation nutations equilibrium polar motion International Celestial Reference Frame deformations ROB

Comparison Earth/Mars no tectonic/mono-plate plate tectonic outer core lower mantle crust upper inner geoid large ondulations large topography (Tharsis) crust upper mantle lower mantle ? outer core inner core? liquid/solid? ROB

Strategy for Geodesy rotation rate/ variations of polar precession/ length-of-day inertial reference frame precession/ nutations polar motion reference frame tied to Mars Mars’ interior core: liquid/solid? atmosphere ice cap ROB

Precession and nutation of Mars ROB

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Nutations of the planet Mars Solid or liquid core? Existence of the FCN? Existence of an inner core? Dimension of the core? NEtlander Ionosphere and Geodesy Experiment NEIGE nutations Information about planet interior ROB

Definition of the FCN This mode does only exist if the core is liquid Rotation axis of the core of the mantle This mode does only exist if the core is liquid ROB

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

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... prograde semi-annual nutation ROB

annual nutation semi-annual nutation 1/3-annual nutation ROB

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Nutation Amplitudes could be infinitely high if close to FCN (if core liquid) ROB

Residuals between solid Nutation Amplitudes Residuals between solid and liquid case solid core liquid core in Dy in De De (in meter) meter Dy (in meter) ROB

1) liquid/solid core? SEIS: NEIGE: PKP, PcP, effect of FCN shadow zone, tides, normal modes NEIGE: effect of FCN on nutation ROB

Computation of the Atmospheric angular momentum Matter term : rigid rotation of the atmosphere with the solid Mars Motion term Matter term Motion term Motion term : relative angular momentum of the atmosphere Matter term ROB

Wind and matter term in angular momentum of the atmosphere => change in Mars’ rotation & polar motion ROB

General circulation Global circulation ROB

Torque between Mars and its fluid layer Pressure torque ROB

Torque between Mars and its fluid layer Gravitational torque ROB

Torque between Mars and its fluid layer Friction torque ROB

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Length-Of-Day (LOD) Variations meter ROB

Length-Of-Day (LOD) Variations ROB

This mode does only exist if the planet is ellipsoidal Definition of the CW Instantaneous rotation axis of the mantle Figure axis of the mantle This mode does only exist if the planet is ellipsoidal ROB

Polar Motion ROB

Polar Motion cm cm ROB

Rotation of Mars Network of landers fixed to the surface: frame Radio links between landers-orbiter-Earth Rotation variations: precession and nutation  internal structure polar motion and variations in rotation speed (LOD)  atmosphere-polar ice caps

Link between rotation and gravimetry When on computes the gravitational potential coefficients in a reference frame affected by polar motion, on obtains:

SUN SET AT THE PATHFINDER SITE ROB