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Gravimetry Geodesy Rotation
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rotation nutation ROB
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Interior structure Mars-Earth
MMars= 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
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Gravimetry Geodesy Rotation
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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
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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.
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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
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Flexure model
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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
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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
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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
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Gravimetry Geodesy Rotation
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Mars’ response to external forcing
Mars rotation nutations equilibrium polar motion International Celestial Reference Frame deformations ROB
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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
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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
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Precession and nutation of Mars
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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
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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
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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
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annual nutation semi-annual nutation 1/3-annual nutation
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Nutation Amplitudes could be infinitely high if close to FCN
(if core liquid) ROB
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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
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1) liquid/solid core? SEIS: NEIGE: PKP, PcP, effect of FCN
shadow zone, tides, normal modes NEIGE: effect of FCN on nutation ROB
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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
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Wind and matter term in angular momentum of the atmosphere
=> change in Mars’ rotation & polar motion ROB
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General circulation Global circulation ROB
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Torque between Mars and its fluid layer
Pressure torque ROB
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Torque between Mars and its fluid layer
Gravitational torque ROB
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Torque between Mars and its fluid layer
Friction torque ROB
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Length-Of-Day (LOD) Variations
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Length-Of-Day (LOD) Variations
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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
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Polar Motion ROB
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Polar Motion cm cm ROB
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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
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Link between rotation and gravimetry
When on computes the gravitational potential coefficients in a reference frame affected by polar motion, on obtains:
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SUN SET AT THE PATHFINDER SITE
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