On the problem of stability of Mercury's rotation about its center of mass (Q735711)

The author analyses the fact that planet Mercury has a rotation period which is in \(3:2\) resonance with its orbital period. He uses a model of planet Mercury representing it as an ellipsoid, and calculates the elliptic motion about the sun in dependence of the moments of inertia of that ellipsoid. Using the Lyapunov exponents, the author also estimates under which circumstances such resonance motion is stable. He gets, as expected from observations, stability for the case of Mercury.