Impact of a moon on the evolution of a planet’s rotation axis: a non-resonant case

We investigate how the variation of obliquity (the axial tilt) a hypothetical exo-Earth is effected by presence satellite, an exo-Moon. Namely, we study analytically and numerically range changes if exo-Moon added to system comprised exo-Sun, exo-planets. say that impact stabilising upon addition decreases, while call destabilising increases as system. The problem considered in general setup. assumed be rigid, axially symmetric almost spherical, difference between largest smallest principal moments inertia being small parameter problem. Assuming orbits celestial bodies quasiperiodic, apply time averaging rotation at times large compared respective periods. Non-resonant frequencies are assumed. identify class systems for which prove where it destabilising. also particular star two planets varies on modifying geometry second planet initial obliquity.