Geodetic Nutation of Celestial Bodies in the Jovian Satellite System

We investigate the relativistic effect of geodetic nutation in the rotation of Jupiter and its 94 satellites, for which the ephemerides are known, around their axes on an 800-year time interval. The most significant periodic terms of the geodetic rotation of these celestial bodies have been determined for the first time: (1) for Jupiter relative to the Solar System Barycenter and the plane of the mean orbit of Jupiter at epoch J2000.0 in the Euler angles, in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the body under study; (2) for eight regular (four inner (Metis J16, Adrastea J15, Amalthea J5, Thebe J14) and four Galilean (Io J1, Europa J2, Ganymede J3, Callisto J4)) satellites of Jupiter relative to: (a) the Solar System Barycenter and the plane of the mean orbit of the satellite under study at epoch J2000.0 in the Euler angles, in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the body under study; (b) the Solar System Barycenter and the plane of the mean orbit of the Jovian System Barycenter at epoch J2000.0 in the Euler angles, in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the body under study; (c) the Jovian System Barycenter and the plane of the mean orbit of the satellite under study at epoch J2000.0 in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the body under study; (3) for 86 irregular satellites (J6–J13, J17–J72, J5501–J5507, J5509–J5523) of Jupiter in the absolute value of the angular rotation vector of the geodetic rotation of the body under study relative to: (a) the Solar System Barycenter; (b) the Jovian System Barycenter. The calculated analytical values of the geodetic nutation of the celestial bodies under study can be used to numerically study the rotation of these bodies in the relativistic approximation.