  We study how the curvature of spacetime, in conjunction with solar radiation
pressure (SRP), affects the bound orbital motion of solar sails. While neither
the curvature of spacetime nor the SRP alter the form of Kepler's third law by
themselves, their simultaneous effects lead to deviations from this law. We
also study deviations from Keplerian motion due to frame dragging, the
gravitational multipole moments of the sun, a possible net electric charge on
the sun, and a positive cosmological constant. The presence of the SRP tends to
increase these deviations by several orders of magnitude, possibly rendering
some of them detectable. As for non-circular bound orbits, the SRP dampens the
rate at which the perihelion is shifted due to curved spacetime, while the
perihelion shift due to the oblateness of the sun is increased. With regards to
the Lense-Thirring effect, the SRP increases the angle of precession of polar
orbits during one orbital period, although the precession frequency is not
actually altered. We also consider non-Keplerian orbits, which lie outside of
the plane of the sun. In particular, we investigate how the pitch angle of the
solar sail is affected by the partial absorption of light by the sail, general
relativistic effects, and the oblateness of the sun. Non-Keplerian orbits
exhibit an analog of the Lense-Thirring effect, in that the orbital plane
precesses around the sun. A near-solar mission for observations of these
effects could provide an interesting confirmation of these phenomena.
