Relativistic contributions to the rotation of Mars

Abstract

Context. The orientation and rotation of Mars can be described by a set of Euler angles (longitude, obliquity, and rotation angles) and estimated from radioscience data (tracking of orbiters and landers), which can then be used to infer the planet's internal properties. The data are analyzed using a modeling expressed within the barycentric celestial reference system (BCRS). This modeling includes several relativistic contributions that need to be properly taken into account to avoid any misinterpretation of the data. Aims. We provide new and more accurate (to the 0.1 mas level) estimations of the relativistic corrections to be included in the BCRS model of the orientation and rotation of Mars. Methods. There are two types of relativistic contributions with regard to Mars's rotation and orientation: (i) those that directly impact the Euler angles and (ii) those resulting from the time transformation between a local Mars reference frame and BCRS. The former contribution essentially corresponds to the geodetic effect, as well as to the smaller Lense-Thirring and Thomas precession effects, and we computed their values assuming that Mars evolves on a Keplerian orbit. As for the latter contribution, we computed the effect of the time transformation and compared the rotation angle corrections obtained, based on the assumption that the planets evolve on Keplerian orbits, with the corrections obtained, based on realistic orbits as described by the ephemerides. Results. The relativistic correction in longitude mainly comes from the geodetic effect and results in a geodetic precession (6.754 mas yr−1) and geodetic annual nutation (0.565 mas amplitude). For the rotation angle, the correction is dominated by the effect of the time transformation. The main annual, semiannual, and terannual terms display amplitudes of 166.954 mas, 7.783 mas, and 0.544 mas, respectively. The amplitude of the annual term differs by about 9 mas from the estimate usually considered by the community. We identified new terms at the Mars-Jupiter and Mars-Saturn synodic periods (0.567 mas and 0.102 mas amplitude) that are relevant considering the current level of uncertainty of the measurements, as well as a contribution to the rotation rate (7.3088 mas day−1). There is no significant correction that applies to the obliquity.