Bound Orbits of Solar Sails and General Relativity

Abstract

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.