On the exoplanet obliquity variations in planetary four – body problem with evolving satellite’s orbit

Abstract

The evolution of the obliquity (the axial tilt) of a hypothetical exoEarth under the influence of gravitational moments from a star, a planet’s satellite in evolving orbit, and an outer exoplanet Evolution was investigated analytically. The exoEarth is assumed to be rigid, axially symmetric and almost spherical. The case where the orbits of two planets and satellite are given Keplerian ellipses while the satellite’s ellipse evolves on the lunar type was considered. The canonical equations describing the oscillations of spin axis of exoEarth were obtained. These equations contain one parameter (the longitude of the ascending node of the satellite’s orbit) slowly changing in time. Using the theory of the adiabatic invariant, approximate formulas for the precession angle and obliquity in time are obtained.