Steady state obliquity of a rigid body in the spin-orbit resonant problem: application to Mercury

摘要: We investigate the stable Cassini state 1 in p : q spin–orbit resonant problem. Our study includes effect of gravitational potential up to degree and order 4 resonances with \(p,q\le 8\) \(p\ge q\). derive new formulae that link field coefficients its secular orbital elements rotational parameters. The can be used predict orientation spin axis necessary angular momentum at exact resonance. also develop a simple pendulum model approximate dynamics close resonance make use it libration periods widths oscillatory regime motions phase space. analytical results are based on averaging theory we confirm by means numerical simulations dynamical equations. applied possible history Mercury.