Gravimetry Geodesy Rotation ROB
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Gravimetry GeodesyRotation
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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)
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MARS INTERIOR
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Core:– Many questions for
Mars (size, state)– Important for the
understanding of origin, evolution, and dynamics of terrestrial planets
Gravimetry GeodesyRotation
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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
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
• 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
lmlc
lm hCg
gravity anomaly~ internal mass load
Crustal density
density jump m-c
topography
degree of compensation
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 GeodesyRotation
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Mars’ response to external forcing
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Comparison Earth/Mars
outercore
lowermantle
crust uppermantle
innercore
crust uppermantle
lowermantle ?outer
core innercore?
large topography (Tharsis)
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liquid/solid?
geoid large ondulations
no tectonic/mono-plate
plate tectonic
Strategy for Geodesy
reference frametied to Mars
inertialreference frame
precession/nutations
rotation rate/variations oflength-of-day
polarmotion
atmosphereice cap
Mars’ interiorcore: liquid/solid?
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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
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Information about planet interior
Definition of the FCN
This mode does only exist if the core is liquid
Rotation axisof the core
Rotation axisof the mantle
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• retrograde ter-annual nutation• retrograde semi-annual nutation• retrograde 1/4 year nutation• prograde semi-annual nutation
transfer function
250 days
250 days
250 days
Am
plit
udes
Am
plit
udes
rigid Mars’ nutations
non-rigid Mars’ nutations
IMPORTANT FOR:
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...
prograde semi-annualnutation
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annual nutationsemi-annual nutation1/3-annual nutation1/4 annual nutation
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period(day)
rigid Marsamplitude
(mas)
solid/liquidcontribution
(mas)prograde1/2-yr
343 499.5 5.2
retrograde1 yr
687 136.5 1.4
retrograde1/2-yr
343 18.0 0.6
retrograde1/3-yr
229 4.7 0.5
retrograde1/4-yr
172 0.8 0.3
Nutation Amplitudes
could beinfinitelyhigh if close to FCN (if core liquid)
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Nutation Amplitudes
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(in meter)
(
in m
eter
)
ininliquid core
solid coreResiduals between solid
and liquid case
met
er
1) liquid/solid core?
NEIGE:effect of FCN
on nutation
SEIS:PKP, PcP,
shadow zone,tides,
normal modes
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Matter term : rigid rotationof the atmosphere withthe solid Mars
Motion term : relative angular momentum of the atmosphere
Computation of the Atmospheric angular momentum
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Wind and matter term in angular momentumof the atmosphere
=> change in Mars’ rotation & polar motion
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Global circulationGeneral circulation
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Torque between Mars and its fluid layer
Pressure torque
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Gravitational torque
Torque between Mars and its fluid layer
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Torque between Mars and its fluid layer
Friction torqueROB
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Length-Of-Day (LOD) Variations
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met
er
Length-Of-Day (LOD) Variations
ice cap &atmosphere
annualsignal onequator
7.6 m
semi-annualsignal onequator
4.9 m
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Definition of the CW
This mode does only exist if the planet is ellipsoidal
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Instantaneous rotation axis of the mantle
Figure axisof the mantle
Polar Motion
atmosphere & ice cap(sublimation/condensation)
annual polar motioncomponent
10 cm
semi-annual polarmotion component
10 cm
Chandler WobbleQ=[50, 300]
[50 cm, 150 cm]
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Polar Motion
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cm
cm
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:
PP
PP
P
P
PP
yxCS
CyxC
yCS
xCC
CyxC
2022
2022
22
2021
2021
2022
20
3
2
3
3
3
2
3
SUN SET AT THE PATHFINDER SITE
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