The dependence of geodetic precession on the choice of coordinate system using the example of the Galilean moons of Jupiter

The relativistic effect of geodetic precession in the rotation of Jupiter and its Galilean moons (Io, Europa, Ganymede and Callisto) are investigated. For this purpose, the method developed in (Pashkevich, 2016) was modified, which is applicable for studying any bodies of the Solar System that have long-term ephemeris. As a result of its application, the most significant secular terms of geodetic precession were determined. In this study, the values of the angular velocity vectors of the geodetic rotation of the Galilean satellites of Jupiter relative to the barycenter of the Solar System and relative to the barycenter of the system of Jupiter satellites were calculated. Their differences are shown depending on the choice of coordinate reference system due to the asymmetry of the formula for the angular velocity vector of geodetic rotation for any solar system bodies used for these calculations. The obtained analytical values of the geodetic precession of the rotation parameters of the studied objects can be used for the numerical study of their rotation in the relativistic approximation.