Spin-orbit gravitational locking - an effective potential approach

Abstract The objective of this paper is to study the tidally locked 3:2 spin–orbit resonance Mercury around Sun. In order achieve goal, effective potential energy that determines spinning motion an ellipsoidal planet its axis considered. By studying rotational orbiting a spherical star on elliptic orbit with fixed eccentricity and semi-major axis, it shown system presents infinite number metastable equilibrium configurations. These states correspond local minima averaged over orbit, where ratio between period revolution fixed. configurations in which integer or half are particular interest. Among these configurations, deepest minimum average corresponds situation orbital synchronous, locked. next-to-the case rotates three times time needs complete two orbits latter indeed describes Mercury's motion. method discussed work allows one identify half-integer ratios spin-orbit resonances describe resonant orbit.