Geodesy with Mars lander Network

V. Dehant, J.-P. Barriot, and T. Van Hoolst

Royal Observatory of BelgiumObservatoire Midi-Pyrénées

Topics• Rotation variations

– Orientation in space: precession/nutation– Orientation in planet:

polar motion– Rotation speed: length-of-day

variations

• Gravity Field

• Modeling of – Interior of planets– Atmosphere dynamics = 0 +

Xecliptic

Yecliptic

Zecliptic

I = I0 + I

Rotation Axis

Precession-Nutation

Overview of the presentation

• Amplitudes of rotation variations of Mars

• Relation to interior structure and atmosphere of Mars

• Simulations of rotation variations and expected precisions (importance of landers)

• Gravity field: seasonal gravity variations

r : 230 m after 700 days Moment of inertia of Mars ( C )

Precession of Mars

r : 15 m (main term: semi-annual)

Precession and nutation of Mars

Nutation and interior structure

• Most important and geophysically interesting influence: existence of a liquid core

• Nutational motion of core differs from that of the mantle (if sphere: no core nutation).

• Core’s nutational effect : amplification of nutation with respect to rigid planet

• Main effect: resonance due to the existence of a free rotational mode related to the core

LdtdH

Free Core NutationRotation axisof the core

Rotation axisof the mantle

close to resonant frequency: large core close to resonant frequency: large core nutational motion in opposite direction of mantle nutational motion in opposite direction of mantle nutation, which can then largely be amplifiednutation, which can then largely be amplified

Restoring forces depend on flattening of coreRestoring forces depend on flattening of core

Flattening mainly depends on core density Flattening mainly depends on core density

FCN Period FCN Period core density, core radius core density, core radius

ROB

Relative rotation of axesRetrograde long period in spaceClose to main nutations

Amplification due to liquid core: 5mas or more

Variations of the rotation speed

(r : 10 m)

Polar motion (r : 10 to over 100 cm)

Measuring Doppler shifts on Lander-Orbiter link

R

RV

Dop.

≈ Projection of relative velocity on line-of-sight Lander-Orbiter

days 7000700 700 700 7000 0 0

Error: centimeter level

Number of landers

Lander-Earth link

Graphes de resultats

Low degree zonal gravity coefficients and rotation rate

• Variations in C20 give information about the CO2

cycle. But strongly linked LOD (mass redistribution is main factor).

• Doppler shifts between landers – orbiter (LOD) and orbiter – Earth (C20)

• Previous results assume a perfectly known orbit• Numerical simulations with GINS (Géodésie par

Intégrations Numériques Simultanées, CNES) software

Time-Varying Gravity Field

C20 C30

The precision of current gravity observations are not sufficient enough to provide additional constrains to C02 cycle

Gravity observation from SC, High Electron detector observation,GCM

Simulations with MGS (I=93°, e=0.01) & MEX (I=86°, e=0.6)

Simulations with two orbiters MGS (I=93°, e=0.01)+MEX (I=86°, e=0.6)

The error is reduced by a factor of about 2

C40 C50

C20 C30

Effect of a Lander Network(single orbiter)

Landers help to resolve the LOD, to determine better the orbit ascending node hence the even coefficients

Conclusions

• An additional lander – orbiter link improves the determination of rotation variations and gravity variations

• and makes it possible to extract information on Mars’ interior and atmosphere/polar caps CO2 cycle

C DARGAUD

v.dehant@oma.be

ROB

Signature of MOPs

Change in lander velocity due to MOP

Geometric effect= change in direction lander-orbiter due to MOP

Large effect for low altitude satellite

cosMOPV

sinVMOP

|V| : velocity différence between landers and orbiter (~3 km/s), |VMOP| : change in |V| due to (~ mm/s), : angle between |V| and line-of-sight lander-orbiter, MOP : change in due to MOP (~ 10-7 rad).

Effect of the Landers-orbiter Doppler tracking on the J2 determination

: model C20

+: DSN, fixed ΔLOD but modified

----: DSN, fixed ΔLOD

O: DSN + lander data

Landers-Orbiter Doppler tracking and seasonal gravity field

: model Cl0

o: near polar, DSN

x: near polar DSN + lander tracking

+: near polar + Starlette like orbiter, DSN tracking

Landers-Orbiter Doppler tracking and seasonal gravity field : Formal error

o: near polar, DSN

x: near polar DSN + lander tracking

+: near polar + Starlette like orbiter, DSN tracking

Lander-Orbiter Doppler tracking and rotation rate determination

Simulation of Mars’Rotation rate determination From the Landers-orbiter Doppler-link (four landers and one near-polar orbiter).