Report of work at ROB within the MAGE European Training Network

Véronique Dehant

Participant Name Position Research activity

Effective Expected

8. ROB-Brussels Véronique Dehant Professor 70 70

  Tim Van Hoolst Professor 85 70

  Pascale Defraigne Senior Scientist

30 50

  René Warnant Senior Scientist

5 50

  Fabian Roosbeek Senior Scientist

5 50

  Marie Yseboodt Scientist 100 100

  Pascal Rosenblatt Scientist 100 0

  Ellen Van den Acker/Ozgur Karatekin

Scientist 100 100

  Laurent Morel/Mikael Beuthe

Scientist 100 100

  Attilio Rivoldini PhD student 100 100

  Jean-Francois Bodart/Julien Duron

PhD student 100 100

  Jacques Sleewaegen/ Olivier Verhoeven/ Gregor Pfyffer

Scientist/PhD student

100 100

Total ROB-Brussels

    995 990

+ Valery LaineyMAGE Postdoc

PHOBOS/DEIMOS

Parameters :

•Temperature profile

•Bulk iron and olivine weight fraction

•Pressure gradient.

Modeling of the Martian mantle

Recently taken into account :•The effect of iron concentration in the respective minerals on the electrical conductivity

•The possible presence of partial melting in the upper mantle

• Empirical relation between olivine and the non-olivine mineralogical system.

Direct Problem

Direct Problem Inversion : Marginal density for temperature

Collaboration with U Nantes, CETP, IPGP, OMP

Doppler simulation

• Analytical simulations of the Doppler and Range observables between Martian landers and an orbiter, extraction of the Martian orientation parameters + comparison with a direct lander-Earth link

• Effect of the network geometry and lander position on the parameters uncertainties (via analytical and numerical simulations)

…

jours 7000700 700 700 7000 0 0

GINS : For accurate S/C Orbit DeterminationDYNAMO : For Geophysical Parameters Determination

S/C Tracking data from: the Earth the planetary surface

S/C Tracking data sets: Doppler & Ranging(corrected from propagation effect) “Angular” position of S/C w.r.t. planetary surface (MPO)

DYNAMONormal matrices

Stacking + Resolution

Physical & Dynamics parameters:gravity field, K2 Love number, station positions, …

A PRIORI ORBIT (numerical integration of S/C motion)

Gravity field + DE406 ephemeris (Sun, Mercury, Earth, …) + relativistic corrections + K2 Love Number + Librations+ Desaturation (epoch, intensity)+ Non-gravitational accelerations (or modeling)+ State Vector (from navigation or previous adjustment)

ADJUSTED ORBIT:State Vector, DesaturationData biases, modeling of non-gravitational forces

Predicted S/C Tracking data(given positions of the tracking stations)

Least Squares Adjustment onTRACKING MEASUREMENTS

GINS

Accelerometer data(or attitude mode: Quaternions)

Normal matrices:physical & dynamics information

MEASUREMENTS

Effect of inertial desaturation on the orbit determination

When all the desaturation events are tracked from the Earth, only 15-20 minutes of lander-orbiter tracking per week allows recovering of Mars’ orientation

parameters with a precision of a few milli-arc-seconds

When all desaturation events are tracked from the Earth: RMS of the residual positions of the orbiter : 4.8 cm

Recovery of residual accelerations6 events a day, 1 mm/s of velocity variation

and 2 DSN antennas for tracking

When half of the desaturation events are tracked from the Earth: RMS of the residual positions of the orbiter: 155 cm

Recovery of residual accelerations6 events a day, 1 mm/s of velocity variation

and 1 DSN antenna for tracking

Variations of the low degree zonal (J2 to J5) coefficients of Mars’

gravity field

Strong seasonal variation of gravity field due to sublimation/condensation of

the atmospheric CO2

To constrain CO2 seasonal mass variations

between polar caps and the atmosphere

Prediction of changes of the first zonal terms of the gravity field provided by

GCM (Global Circulation Model) simulations of the atmosphere

Ls (Solar Longitude)From Laboratoire de Météorologie

Dynamique (LMD), France

From NASA

An improved strategy to estimate the zonal coefficients of the Martian gravity field : Numerical simulations of a global geodetic

experiment • Satellite ORBITS : - orbiter 1 (as part of a Mars Network Science Experiment : NEIGE) : i = 93.2°, e = 0.001

- orbiter 2 : i = 50°, e = 0.0206• Earth-based tracking of the two orbiters by 3 DSN stations• Mars-based tracking of the near-polar orbiter (1) by 4 stations (dual frequency UHF/S-band)

Martian lithosphere and wavelets

• Aim: lithosphere thickness on Mars• Method:1. Input data : topography2. Model : flexure of a thin elastic spherical shell3. Output : predicted gravity anomalies4. Localization of anomalies with spherical wavelets5. Comparison of predicted/observed gravity

anomalies• Conclusion: large thickness at Tharsis, small at

Hellas

Flexure model

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

Martian gravitational field analyzed with spherical wavelets

Martian gravity anomalies from Mars Express data

Collaboration with:1. Jean-Pierre Barriot (CNES/Toulouse) for the software2. Martin Paetzold (PI of MaRS) for the data• Input data: line-of-sight Doppler residuals in areas

of interest (poles…)• Method: Least-squares inversion of residuals with a

priori knowledge • Result: local maps of gravity anomalies• Work in progress: data is coming!

Radio science dataon particular targets

ROB

determination of gravity anomalies

ROB+OMP

Knowledge of Phobos ephemerides

ROB+BdL

Interpretation in terms of properties of the interior of Phobos

ROB

Quality factor of MarsROB+IPGP

Study of lithosphere propertiesIPGP

Work in progress!Thanks to MAGE!