  Solar radiation pressure can have a substantial long-term effect on the
orbits of high area-to-mass ratio spacecraft, such as solar sails. We present a
study of the coupling between radiation pressure and the gravitational
perturbation due to polar flattening. Removing the short-period terms via
perturbation theory yields a time-dependent two-degree-of-freedom Hamiltonian,
depending on one physical and one dynamical parameter. While the reduced model
is non-integrable in general, assuming coplanar orbits (i.e., both Spacecraft
and Sun on the equator) results in an integrable invariant manifold. We discuss
the qualitative features of the coplanar dynamics, and find three regions of
the parameters space characterized by different regimes of the reduced flow.
For each regime, we identify the fixed points and their character. The fixed
points represent frozen orbits, configurations for which the long-term
perturbations cancel out to the order of the theory. They are advantageous from
the point of view of station keeping, allowing the orbit to be maintained with
minimal propellant consumption. We complement existing studies of the coplanar
dynamics with a more rigorous treatment, deriving the generating function of
the canonical transformation that underpins the use of averaged equations.
Furthermore, we obtain an analytical expression for the bifurcation lines that
separate the regions with different qualitative flow.
