Secular geodetic rotation of celestial bodies in the system of Jupiter’s moons

This article studies the relativistic effect of geodetic precession in the rotation around their axes of Jupiter and its 94 satellites for which ephemerides are known. As a result, the most significant secular terms of the geodetic rotation of these celestial bodies were determined for the first time: 1. for Jupiter relative to the barycenter of the Solar System and the plane of the mean orbit of Jupiter at the epoch J2000.0 in Euler angles, in the perturbing terms of physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; 2. for 8 regular (4 inner (Metis J16, Adrastea J15, Amalthea J5 and Thebe J14)) and 4 Galilean (Io J1, Europa J2, Ganymede J3 and Callisto J4))) satellites of Jupiter relative to: a) the barycenter of the Solar system and the plane of the mean orbit of the satellite under study at epoch J2000.0 in Euler angles, in the perturbing terms of the physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; b) the barycenter of the Solar system and the plane of the mean orbit of the barycenter of the Jovian system at epoch J2000.0 in Euler angles, in the perturbing terms of the physical libration and in the absolute value of the vector of angular rotation of the geodetic rotation of the body under study; c) the barycenter of the Jupiter satellite system and the plane of the mean orbit of the studied satellite of the J2000.0 epoch in the perturbing terms of the physical libration and in the absolute value of the angular rotation vector of the geodetic rotation of the studied body; 3. for 86 irregular satellites (J6–J13, J17–J72, J5501–J5507, J5509–J5523) of Jupiter relative to: a) the barycenter of the Solar system in the absolute value of the angular rotation vector of the geodetic rotation of the studied body; b) the barycenter of the Jupiter satellite system in the absolute value of the angular rotation vector of the geodetic rotation of the studied body. For the J2000.0 epoch, the mean orbits of the studied celestial bodies and the mean orbit of the barycenter of the Jovian system were calculated. For regular satellites, the values of the angles of inclination of their equator to their own orbits were determined. The obtained analytical values of the geodetic precession of the studied celestial bodies can be used for a numerical study of the rotation of these bodies in the relativistic approximation.