The precession and nutations of a rigid Mars
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(2020) 132:47
ORIGINAL ARTICLE
The precession and nutations of a rigid Mars Rose-Marie Baland1 · Marie Yseboodt1 · Sébastien Le Maistre1 · Attilio Rivoldini1 · Tim Van Hoolst1 · Véronique Dehant1 Received: 13 January 2020 / Revised: 13 June 2020 / Accepted: 28 August 2020 © Springer Nature B.V. 2020
Abstract The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and nutation model for a rigidly behaving Mars is needed. Here, we develop such a model with adequate accuracy based on the Torque approach and compare it to previous models. We include in the model the forcings by the Sun, Phobos, Deimos, and the other planets of the solar system. We also include the geodetic precession and nutations. We use semi-analytical developments for the solar and planetary torques, and analytical solutions for the effect of Phobos and Deimos and for the geodetic precession and nutations. With a truncation criterion of 0.025 milliarcseconds in prograde and/or retrograde amplitude, we identify 43 nutation terms. The uncertainty on our solution mainly derives from the observational uncertainty on the current determination of the precession rate of Mars. Uncertainties related to our modeling choices are negligible in comparison. Given the current determination of the precession rate (7608.3 ± 2.1 mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02.052), our model predicts a dynamical flattening H D = 0.00538017 ± 0.00000148 and a normalized polar moment of inertia C/MR2 = 0.36367 ± 0.00010 for Mars. Keywords Nutation · Precession · Mars
1 Introduction The geodesy experiments Rotation and Interior Structure Experiment (RISE, Folkner et al. 2018) and Lander Radioscience (LaRa, Dehant et al. 2020) on InSight and ExoMars 2022 measure the rotation of Mars by tracking the respective lander on its surface. From the measurements, important orientation parameters of Mars are determined. These are the length-of-day variations, the polar motion of the spin axis with respect to a crust-fixed frame, and the precession/nutation of the spin axis in space.
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Rose-Marie Baland [email protected] Royal Observatory of Belgium, Ringlaan 3, 1180 Brussels, Belgium 0123456789().: V,-vol
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Fig. 1 Precession and nutations of the spin axis about the orbit pole. Adapted from Lowrie (2011)
The precession is the slow uniform circular retrograde motion of the spin axis about the perpendicular to the orbital plane induced mainly by the gravitational torque exerted by the Sun on Mars, which reacts as a spinning top (see Fig. 1). The aperture of the precession cone is about 25◦ and the precession period is about 170,000 years, corr
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