On Saturn’s rotation relative to a center of mass under the action of the gravitational moments of the Sun and Jupiter

Abstract

Saturn’s rotation relative to a center of mass is considered within an elliptic restricted three-body problem. It is assumed that Saturn is a solid under the action of gravity of the Sun and Jupiter. The motions of Saturn and Jupiter are considered elliptic with small eccentricities eS and eJ, respectively; the mean motion of Jupiter nJ is also small. We obtain the averaged Hamiltonian function for a small parameter of e = nJ and integrals of evolution equations. The main effects of the influence of Jupiter on Saturn’s rotation are described: (α) the evolution of the constant parameters of regular precession for the angular momentum vector I2; (β) the occurrence of new libration zones of oscillations I2 near the plane of the celestial equator parallel to the plane of the Jupiter’s orbit; (γ) the occurrence of additional unstable equilibria of vector I2 at the points of the north and south poles of the celestial sphere and, as a result, the existence of homoclinic trajectories; and (δ) the existence of periodic trajectories with arbitrarily large periods near the homoclinic trajectory. It is shown that the effects of (β), (γ), and (δ) are caused by the eccentricity e of the Jupiter’s orbit and are practically independent of Jupiter’s mass (within satellite approximation).