Yseboodt, M. ; Baland, R.-M. ; Le Maistre, S.

Talk presented at Complex Planetary Systems II Kavli-IAU Symposium 382, Namur, Belgium on 2023-07-05

Abstract: In order to describe the orientation of the spin axis of Mars, the radioscience community commonly uses Euler angles, with obliquity and node longitude defined with respect to the planet mean orbit at epoch. The IAU Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) uses the right ascension and declination angles, the equatorial coordinates orienting the planet with respect to the Earth equator in J2000. In both sets of coordinates, a third angle, which has a diurnal periodicity, is used to position the prime meridian. The usual way to transform Euler angles into IAU angles is to numerically evaluate the IAU angles over a given time interval with the help of spherical geometry, then to perform a frequency analysis on the so-obtained time series (e.g. Jacobson 2010, Kuchynka et al. 2014 and Jacobson et al. 2018 for Mars). Unfortunately, such a method does not take into account the physical meaning of the planet’s rotational dynamics, which relies on well-known periodicities governed by the celestial mechanics. We explain the analytical expressions to precisely transform one set of angles into the other in the case of Mars. Each angle is modeled by the sum of a quadratic polynomial, a periodic series (nutation or rotation variations) and a Poisson series (a periodic series with amplitudes changing linearly with time). The targeted precision of the transformation is 0.1 mas for each angle on an interval of about 30 years before and after J2000. Even when no quadratic terms exist in a Mars rotation model expressed with Euler angles, the corresponding model with IAU angles does have quadratic terms coming from the transformation. Current IAU-like solutions present very long period signals that result from the absence of a quadratic term in the model used. Such a long period signal has an amplitude, a phase and a frequency specifically chosen to mimic the quadratic behavior over an interval of a few decades around J2000. Adding a long period modulation instead of a quadratic term largely and artificially alters the angle values at J2000 as well as their rates. We compare the solutions of different authors, including the change in the rotation angle value.

Keyword(s): Mars ; Rotation
Links: link
Funding: 3PRODPLANINT/3PRODPLANINT/3PRODPLANINT