Transformation of orientation and rotation angles of synchronous satellites: Application to the Galilean moons

TL;DR

This paper develops second-order analytical formulas to transform the orientation and rotation angles of synchronous satellites between different reference frames, applying them to the Galilean moons to improve understanding and interpretation of observational data.

Contribution

It introduces a new analytical transformation method for satellite orientation angles that preserves physical meaning and applies it to the Galilean moons, enhancing geophysical and observational analysis.

Findings

Derived second-order analytical expressions for angle transformations.

Provided tables for satellite coordinates assuming solid interiors.

Proposed an updated IAU solution improving zero obliquity models.

Abstract

The orientation and rotation of a synchronous satellite can be referred to both its Laplace plane and the ICRF equatorial plane, in terms of Euler angles or spin axis Cartesian coordinates and Earth equatorial coordinates, respectively. We computed second-order analytical expressions to make the transformation between the two systems and applied them to the Galilean satellites (Io, Europa, Ganymede, and Callisto). If one term of the spin axis Cartesian coordinates series is dominant, trigonometric series can be generated for the inertial and orbital obliquities, node longitude and offset with respect to the Cassini plane. Since the transformation does not require any fit of amplitudes and frequencies on numerical series, the physical meaning of the frequencies is preserved from the input series and the amplitudes can be directly related to the geophysical parameters of interest. We provide tables for the coordinates and angles' series assuming that the satellites are entirely solid, and considering two different orbital theories. The possible amplitude ranges for the main terms are also examined in the case where a liquid layer is assumed in the interior model. We use our transformation method to propose an updated IAU WG solution which would result in an improvement with respect to zero obliquity models used so far. This method will also be useful for the interpretation of future Earth-based radar observations or JUICE data.