The Poynting-Robertson Effect on Solar Sails

We consider a special relativistic effect, known as the Poynting-Robertson effect, on various types of trajectories of solar sails. Since this effect occurs at order $v^{\phi}/c$, where $v^{\phi}$ is the tangential speed relative to the sun, it can dominate over other special relativistic effects, which occur at order $v^2/c^2$. While solar radiation can be used to propel the solar sail, the absorbed portion of it also gives rise to a drag force in the tangential direction. For escape trajectories, this diminishes the cruising velocity, which can have a cumulative effect on the heliocentric distance. For a solar sail directly facing the sun in a bound orbit, the Poynting-Robertson effect decreases its orbital speed, thereby causing it to slowly spiral towards the sun. We also consider this effect for non-Keplerian orbits in which the solar sail is tilted in the azimuthal direction. While in principle the drag force could be counter-balanced by an extremely small tilt of the solar sail in the polar direction, periodic adjustments are more feasible.