  We implement Lie transform perturbation theory to second order for the planar
spin-orbit problem. The perturbation parameter is the asphericity of the body,
with the orbital eccentricity entering as an additional parameter. We study
first and second order resonances for different values of these parameters. For
nearly spherical bodies like Mercury and the Moon first order perturbation
theory is adequate, whereas for highly aspherical bodies like Hyperion the spin
is mostly chaotic and perturbation theory is of limited use. However, in
between, we identify a parameter range where second order perturbation theory
is useful and where as yet unidentified objects may be in second order
resonances.
