Update of seasonal gravity field and k2 love number of Mars from MGS, Mars Odyssey and MRO radio science

The Mars Global Surveyor (MGS), Mars Odyssey (MO), and Mars reconnaissance Orbiter (MRO) Doppler tracking data from 1999 to end of 2021 have been reprocessed, offering the longest time series ever obtained for the gravity field of a planet.

 

The process, called Precise Orbit Determination (POD), uses the Doppler radio-tracking data acquired at the Deep Space Network (DSN) ground stations, and an accurate dynamical model for each spacecraft. This model employs identical up-to-date standards and state-of-the-art of the force models, both surface forces and gravitational forces. A macromodel of each spacecraft (surface area and optical properties of the faces of the probe) is taken into account. It is oriented in space at any time given telemered quaternions. This attitude information of the bus of the spacecraft is completed by the attitude of the articulated solar array and of the steerable high gain antenna with respect to the spacecraft body. In addition, the  self-shadowing effect is introduced for each surface force, atmospheric drag and radiation pressure form the Sun and the planet (albedo and infra-red emission). The angular momentum desaturation maneuvers are taken into account by solving for empirical accelerations at the epoch of each maneuver.

 

This force model allows to compute theoretical Doppler tracking data, then the difference of these predicted data with the tracking data collected at ground stations is computed. Least square fit of this difference is processed over successive data-arcs with a duration of 4 days for each spacecraft. This least squares filter allows to adjust a scale factor of the drag and solar pressure force for each data-arc as well as residual accelerations at each angular momentum desaturation event. The least squares fit results in normal matrices for each data-arc and for each spacecraft. It contains partial derivatives for each coefficient of the force model (scale factors, residual accelerations) as well as for the time series the first zonal gravity field coefficients and for the degree 2 tidal Love number, k2. All the normal matrices are stacked together in order to retrieve a time series of the gravity field from 1999 to 2021 (about 10 Martian year), which has never been obtained before. The k2 Love number solution is also re-estimated.  We analyze the error on the obtained solution depending on the number of satellite we used (1 to 3) and the data timespan used.

 

The retrieved time-varying gravity coefficients and the Love number k2 are then use to tightly constrain the seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively