Geodetic nutation of Jupiter and its Galilean moons

Abstract

In the article, the relativistic effect of geodetic nutation in the rotation of Jupiter and its Galilean moons (Io, Europa, Ganymede and Callisto) was investigated in two ways over an 800-year time interval. As a result, for the first time, the most significant periodic terms of the geodetic rotation of these celestial bodies relative to: a) the barycenter of the Solar system and the plane of the mean orbit of Jupiter of the epoch J2000.0 in the Euler angles, in the disturbing terms of the physical libration and in the absolute magnitude of the angular rotation vector of the geodetic rotation of the body under study; b) (with the exception of Jupiter) the barycenter of the Jupiter satellite system and the mean orbit of the studied satellite of the epoch J2000.0 in the disturbing terms of the physical libration and in the absolute magnitude of the angular rotation vector of the geodetic rotation of the body under study. It is shown that the use of Way II in this study, which uses the numerical integration procedure, is more preferable, and the values of the geodetic nutation terms obtained by this way are more accurate. The accuracy level of calculating the parameters (obtained by Way II) for the geodetic nutation values of the studied celestial bodies was 0.1 microarcseconds. The obtained analytical values of geodetic nutation of the studied celestial bodies can be used for numerical investigation of the rotation of these bodies in the relativistic approximation.