Second-Order Perturbation Theory for Spin-Orbit Resonances

We implement Lie transform perturbation theory to second order for the planarspin-orbit problem. The perturbation parameter is the asphericity of the body,with the orbital eccentricity entering as an additional parameter. We studyfirst and second order resonances for different values of these parameters. Fornearly spherical bodies like Mercury and the Moon first order perturbationtheory is adequate, whereas for highly aspherical bodies like Hyperion the spinis mostly chaotic and perturbation theory is of limited use. However, inbetween, we identify a parameter range where second order perturbation theoryis useful and where as yet unidentified objects may be in second orderresonances.Comment: To appear in A