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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