Mars orientation and rotation angles

• Published in: Celestial mechanics and dynamical astronomy Vol. 135; no. 5; p. 50
• Main Authors: Yseboodt, Marie, Baland, Rose-Marie, Le Maistre, Sébastien
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2023; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Astrophysics and Astroparticles; Classical Mechanics; Data acquisition; Declination; Dynamical Systems and Ergodic Theory; Equator; Euler angles; Geophysics/Geodesy; Mars; Mars surface; Modelling; Orientation; Original Article; Physics; Physics and Astronomy; Polynomials; Rotation; Space missions; Transformations; Mars; IAU recommendations; Analytical method; Rotation model
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-023-10159-y

The rotation and orientation of Mars is commonly described using two different sets of angles, namely (1) the Euler angles with respect to the Mars orbit plane and (2) the right ascension, declination, and prime meridian location angles with respect to the Earth equator at J2000 (as adopted by the IAU). We propose a formulation for both these sets of angles, which consists of the sum of a second degree polynomial and of periodic and Poisson series. Such a formulation is shown here to enable accurate (and physically sound) transformation from one set of angles to the other. The transformation formulas are provided and discussed in this paper. In particular, we point that the quadratic and Poisson terms are key ingredients to reach a transformation precision of 0.1 mas, even 30 years away from the reference epoch of the rotation model (e.g., J2000). Such a precision is required to accurately determine the smaller and smaller geophysical signals observed in the high-accuracy data acquired from the surface of Mars. In addition, we present good practices to build an accurate Martian rotation model over a long time span ( ± 30 years around J2000) or over a shorter one (e.g., lifetime of a space mission). We recommend to consider the J2000 mean orbit of Mars as the reference plane for Euler angles. An accurate rotation model should make use of up-to-date models for the rigid (this study) and liquid (Le Maistre et al., Nature 619, 733–737 (2023)) nutations, relativistic corrections in rotation (Baland et al., Astron. Astrophys. 670, A29 (2023)), and polar motion induced by the external torque (this study). Our transformation model and recommendations can be used to define the future IAU solution for the rotation and orientation of Mars using right ascension, declination, and prime meridian location. In particular, thanks to its quadratic terms, our transformation model does not introduce arbitrary and non-physical terms of very long period and large amplitudes, thus providing unbiased values of the rates and epoch values of the angles.