Mars orientation and rotation angles

TL;DR

This paper introduces a precise mathematical formulation for Mars rotation and orientation angles, enabling accurate transformations between different angle sets crucial for high-precision planetary geophysics.

Contribution

It proposes a novel polynomial and series-based formulation for Mars angles, improving long-term transformation accuracy and physical consistency.

Findings

Achieves 0.1 mas transformation precision over 30 years.

Highlights importance of quadratic and Poisson terms for accuracy.

Provides best practices for long-term Mars rotation modeling.

Abstract

The rotation and orientation of Mars is commonly described using two different sets of angles, namely the Euler angles wrt the Mars orbit plane and the right ascension, declination, and prime meridian location angles wrt 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 and liquid nutations, relativistic corrections in rotation, and polar motion induced by the external torque. 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.