ASSESSMENT OF THE MARS EXPRESS ORBIT DETERMINATION FOR THE IMPROVEMENT OF MARS’ GRAVITY FIELD

P. ROSENBLATT(1), J.C. MARTY(3), M. PÄTZOLD(2), V. DEHANT(1), G. BALMINO(3), S. LE MAISTRE(1), J. DURON(1), T. VAN HOOLST(1), B. HÄUSLER(4)

(1)Royal Observatory of Belgium, Av. Circulaire 3, B-1180 Brussels, Belgium, rosenb@oma.be; (2)Insitut für Geophysik und Meteorologie, Universität zu Köln, Albertus-Magnus Platz, D-50923, Köln, Germany(3)Observatoire Midi-Pyrénées/CNES/GRGS, 14 Av. E. Belin, F-31400, Toulouse, France; (4)Institute for Space Technology, Universität der Bundeswehr München, Werner-Heisenberg, Weg 39, D-85577 Neubiberg, Germany

This work was supported by the European Community’s Improving Human Potential Programme under contract RTN2-2001-00414, MAGE

Improving the time-variable gravity using MGS & MEX tracking data:

With tracking data of only one orbiter it is not possible to separate the contribution on the orbit of each even (J2, J4, …) and odd (J3, J5, …) zonal term (e.g. Yoder et al., 2003; Karatekin et al., 2005).

The orbit eccentricity of MGS and MEX are quite different, offering the opportunity to separate the contributions of J2 and J3 from higher order zonal terms (Rosenblatt et al., 2004a).

The expected results will depend on the accuracy of the orbit determination of both spacecrafts.

The ESOC flight dynamics center provides ephemeris of MEX but without estimates of dynamical parameters (among them, time-variable gravity coefficients). Therefore we have to re-compute the orbit.

Estimation of Mars’ time-variable gravity to constrain the seasonal CO2 mass budget

Strong seasonal variation of gravity field due to sublimation/condensation of the atmospheric CO2

From NASA

The time variations of the zonal terms (J2 & J3) are estimated to constrain the mass budget of the CO2 cycle. The figures show results from tracking data of MGS (Smith et al.; Yoder et al.),

HEND data (Mars Odyssey) and Global Circulation Models (Ames, LMD) of Mars’ atmosphere.

Input for data-arcs :

Duration : It depends on available tracking dataInitial state vector of MEX : Orbit data files (ESOC)Attitude mode of MEX : Quaternions data files (ESOC)Epoch of wheel offloading : Event data files (ESOC)Tracking data : 2-way Doppler & Range (NNO + DSN)

Output of data-arcs as adjusted values of :

Initial state vector & ephemeris.Scale factor “FD” for atmospheric drag acceleration and“FS” for Solar radiation pressure acceleration.Frequency bias.Residual accelerations at epochs of wheel offloading events.

Normal matrix containing the information on the time-variable gravity field.

INTRODUCTIONINTRODUCTION

Objective : To improve the determination of J2 & J3 by using the MaRS experiment onboard Mars Express

From ESA

  Mars Global Surveyor (MGS)

Mars Express (MEX)

Semi-major axis (km)

3796 9355

Eccentricity 0.01 0.6

Inclination (°) 92.9 86.5

From Mars Global surveyor (MGS):

•Smith et al. (2001), (J1, J2, J3)

•Yoder et al. (2003), (J2, J3)

Precision of only 50 %

From NASA

Numerical simulations predict an improvement by up to a factor of 2

From Rosenblatt et al., 2004aComparison between MGS and MEX orbital parameters

METHODOLOGY OF ORBIT DETERMINATIONMETHODOLOGY OF ORBIT DETERMINATION

Forces acting on the MEX spacecraft:

Mars’ gravity field GMM-2B (Lemoine et al., 2001) & mass point representation of the Sun and other planets (JPL DE405 ephemeris).Non-gravitational forces : atmospheric drag (atmospheric density from Stewart, 1987), solar radiation pressure, surface albedo and thermal infra-red emission (from Lemoine et al. 2001).Residual accelerations induced by each inertial wheel offloading event (or angular momentum desaturation).

Modeling of non-gravitational forces uses :

• “Macro-model” of MEX which represents the spacecraft as flat plates (6 for the bus + 4 for the solar panels) with known area and optical properties (Morley T., 2003).

• The orientation of the model w.r.t. an inertial frame follows from the attitude mode as given by the quaternions of the bus.

• A fixed value is taken for the offset between the High Gain Antenna (HGA) center of phase and the MEX center of mass.

GINS

Iterative least-squares fit of the MEX dynamical model

on the tracking data

Least-squares adjustment procedure :

The orbit is determined as segmented-arcs

ASSESSMENT OF ORBIT COMPUTATIONASSESSMENT OF ORBIT COMPUTATION

CONCLUSIONS:

Our orbit computation yields Doppler residuals (a few tenths of mm/s) similar to those obtained with the ESOC flight dynamics computation for short arcs (one orbit).

Longer arcs increase the residuals most likely due to the partial coverage of the tracking data. In this case, some pericenter passes and wheel offloading events can occur outside of the tracking periods, thus affecting the orbit determination (Rosenblatt et al., 2004b).

Short arc computation should be used to estimate the time-variable gravity coefficients.

OBSERVATOIREMIDI-PYRÉNÉES

ROYAL OBSERVATORYOF BELGIUM

References:Karatekin et al., JGR, in press, 2005; Morley T., Private Communication, October, 2003Lemoine et al., JGR, Vol., 106, pp. 23,759, 2001; Rosenblatt et al., AGU Fall Meeting, 2004aRosenblatt et al., PSS, vol. 52, pp. 965, 2004b; Smith et al., Science, vol. 294, pp. 2141, 2001Stewart, Report JPL PO NQ-802429, 1987; Yoder et al., Science, vol. 300, pp. 299, 2003

Bus

Solar Panel Solar Panel

For each flat plate :• Its area• Its specular & diffusive reflectivy• Its emissivity coefficient• Its temperature

“Macro-Model” of MEX

Attitude mode of MEX Variations of quaternions occur, generally, near pericenter or apocenter passes when MEX is oriented toward Mars or the Earth.When they are steady MEX takes a fixed inertial

attitude.

Long arc (3days) computation:

•For 3-days data-arcs our residuals (RMS of 0.85 mm/s) are larger than those obtained with ESOC’s orbit (RMS of 0.6 mm/s). Our atmospheric drag model needs to be rescaled (FD parameter estimated as -3.8). •When considering a fixed atmospheric drag model (FD=1), our RMS residuals increase only to 0.9-0.95 mm/s. •Estimating more FD parameters (one per orbit) doesn’t change significantly the results.

Short arc (one orbit) computation:

For short data-arcs (one orbit) our residuals (RMS of 0.19 mm/s) are similar to those obtained with the ESOC’s orbit (RMS of 0.22 mm/s). Our atmospheric drag and solar pressure models don’t need to be rescaled (FD and FS parameters adjusted to ~ 1).

We use a computer code (Géodésie par Intégrations Numériques Simultanées, GINS) primarily developed by CNES (Centre National d’Etude Spatiale) and further adapted at the Royal Observatory of Belgium (ROB) for planetary geodesy applications.

We model all the forces acting on the MEX spacecraft and numerically integrate the motion equations to obtain positions and velocities of MEX.

We then calculate the associated predicted tracking data in order to perform an iterative least-squares adjustment on the tracking data of MEX. During this process several parameters are adjusted, which are related to the data and to the dynamical model of the MEX motion.

The results are new ephemeris of MEX based on the adjusted dynamical model and normal matrices which contain the information about the time-variable zonal coefficients of Mars’ gravity field

NEXT STEPS:

Our results can be improved by adding the available range data to account for biases in our dynamical model

We can estimate the errors on our MEX positions by performing “orbit overlap” tests (Lemoine et al., 2001)

The normal matrix obtained from each data arc will be stacked to produce monthly normal matrices

These matrices will be stacked with those obtained from tracking data of MGS in order to obtain new solutions for the J2 and J3 seasonal variations