Numerical model of Phobos' motion incorporating the effects of free rotation

TL;DR

This paper develops a comprehensive numerical model of Phobos' orbit and rotation, integrating Euler's equations to improve understanding of its physical behavior and refine gravitational parameters.

Contribution

It introduces a fully dynamical model that simultaneously considers Phobos' rotation and orbit, differing from previous models that did not incorporate rotation explicitly.

Findings

Confirmed latitude libration of Phobos.

Gravity field coefficients need re-examination.

Difficulty in determining k_2 with current data.

Abstract

High-precision ephemerides are not only useful in supporting space missions, but also in investigating the physical nature of celestial bodies. This paper reports an update to the orbit and rotation model of the Martian moon Phobos. In contrast to earlier numerical models, this paper details a dynamical model that fully considers the rotation of Phobos. Here, Phobos' rotation is first described by Euler's rotational equations and integrated simultaneously with the orbital motion equations. We discuss this dynamical model, along with the differences with respect to the model now in use. We present the variational equation for Phobos' rotation employing the symbolic \emph{Maple} computation software. The adjustment test simulations confirm the latitude libration of Phobos, suggesting gravity field coefficients obtained using a shape model and homogeneous density hypothesis should be re-examined in the future in the context of dynamics. Furthermore, the simulations with different $k_2$ values indicate that it is difficult to determine k_2 efficiently using the current data.