Some Aspects of the Relativistic Rotation of Solar System Bodies using the Example of Jupiter and its Galilean Satellites

Abstract

This paper is devoted to some aspects of the study of relativistic effects (geodetic precession and geodetic nutation, which together constitute geodetic rotation) in the rotation of celestial bodies of the Solar System using the example of Jupiter and its Galilean satellites (Io, Europa, Ganymede, and Callisto). The difference in the angular velocity vectors of geodetic rotation is shown depending on the choice of reference frame. Thus, the absolute value of the angular velocity vector of the geodetic rotation of the satellite under study relative to the barycenter of the Solar System will not coincide with the absolute value of a similar vector of the satellite under study relative to the barycenter of the planet’s satellite system. As a result, the most significant secular and periodic terms of geodetic rotation were determined for the first time: a) of Jupiter and its Galilean satellites in terms of the Euler angles, in the perturbing terms of physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the body under study relative to the barycenter of the Solar System and the plane of the mean orbit of Jupiter of the epoch J2000.0; b) of Galilean satellites of Jupiter in the perturbing terms of physical libration and the absolute value of the angular rotation vector of the geodetic rotation of the studied body relative to the barycenter of the Galilean satellite system of Jupiter and the mean orbit plane of the studied Galilean satellite of the epoch J2000.0. The obtained analytical values of the geodetic rotation of the studied objects can be used for a numerical study of their rotation in the relativistic approximation, and also used to evaluate the influence of relativistic effects on the orbital–rotational dynamics of bodies of exoplanetary systems.