Lightsails using Earth-based lasers for propulsion require passive stabilization to stay within the beam. This can be achieved through the sail's scattering properties, creating optical restoring forces and torques. Undamped restoring forces produce uncontrolled oscillations, which could jeopardize the mission, but it is not obvious how to achieve damping in the vacuum of space. Using a simple two-dimensional model we show that the Doppler effect and relativistic aberration of the propelling laser beam create damping terms in the optical forces and torques. The effect is similar to the Poynting-Robertson effect causing loss of orbital momentum of dust particles around stars, but can be enhanced by design of the sail's geometry.
