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Gravimetry Geodesy Rotation

ROB. Gravimetry Geodesy Rotation. ROB. rotation nutation. ROB. Interior structure Mars-Earth. M Mars = 6.4185 10 23 kg  0.1 M Earth (orbits) R Mars = 3390 km  0.5 R earth (occultation) g Mars = 3.7 m/s 2  0.4 g Earth (M/R 2 )

yvonne-austin
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Gravimetry Geodesy Rotation

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  1. ROB Gravimetry GeodesyRotation

  2. ROB rotation nutation

  3. 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)

  4. ROB

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

  6. ROB GravimetryGeodesyRotation

  7. Static gravity field Thegravity 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

  8. 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.

  9. 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

  10. Flexure model

  11. 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

  12. 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

  13. 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

  14. ROB GravimetryGeodesyRotation

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

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

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

  18. ROB Precession and nutation of Mars

  19. ROB

  20. nutations Information about planet interior ROB 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

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

  22. rigid Mars’ nutations Amplitudes 250 days transfer function 250 days non-rigid Mars’ nutations Amplitudes 250 days ROB IMPORTANTFOR: • retrograde ter-annual nutation • retrograde semi-annual nutation • retrograde 1/4 year nutation • prograde semi-annual nutation

  23. ROB

  24. ... prograde semi-annual nutation ROB

  25. ROB annual nutation semi-annual nutation 1/3-annual nutation 1/4 annual nutation

  26. ROB

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

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

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

  30. 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

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

  32. ROB General circulation Global circulation

  33. ROB Torque between Mars and its fluid layer Pressure torque

  34. ROB Torque between Mars and its fluid layer Gravitational torque

  35. ROB Torque between Mars and its fluid layer Friction torque

  36. ROB

  37. ROB Length-Of-Day (LOD) Variations meter

  38. ROB Length-Of-Day (LOD) Variations

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

  40. ROB Polar Motion

  41. ROB Polar Motion cm cm

  42. 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

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

  44. ROB SUN SET AT THE PATHFINDER SITE

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