1. Gravimetry Geodesy Rotation
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2. rotation
nutation
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3. 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)
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4. ROB

5. 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
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6. Gravimetry Geodesy Rotation
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7. 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

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.

10. 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

11. Flexure model

12. 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

13. 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

14. 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

15. Gravimetry Geodesy Rotation
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16. Mars’ response to external forcing
Mars rotation
nutations
equilibrium
polar motion
International
Celestial
Reference
Frame
deformations
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18. 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?
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20. 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
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21. Precession and nutation of Mars
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23. ROB

24. 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
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25. 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
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26. 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
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27. ROB

28. ...
prograde semi-annual
nutation
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29. annual nutation semi-annual nutation 1/3-annual nutation
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30. ROB

31. Nutation Amplitudes could be infinitely high if close to FCN
(if core liquid)
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32. 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)
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33. 1) liquid/solid core? SEIS: NEIGE: PKP, PcP, effect of FCN
shadow zone,
tides,
normal modes
NEIGE:
effect of FCN
on nutation
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34. 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
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35. Wind and matter term in angular momentum of the atmosphere
=> change in Mars’ rotation & polar motion
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36. General circulation
Global circulation
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37. Torque between Mars and its fluid layer
Pressure torque
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38. Torque between Mars and its fluid layer
Gravitational torque
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39. Torque between Mars and its fluid layer
Friction torque
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41. ROB

42. Length-Of-Day (LOD) Variations
meter
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43. Length-Of-Day (LOD) Variations
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44. 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
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45. Polar Motion
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46. Polar Motion cm cm
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47. 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

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

49. SUN SET AT THE PATHFINDER SITE
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