Quantify Doppler-effect impact on velocity amplitude of lightsail oscillations

Determine quantitatively the reduction in the velocity amplitude of transverse oscillations in passively stabilized laser beam–driven lightsails that is attributable to the Doppler-effect–induced frequency shift modifying the sail’s reflectivity and, consequently, the optical restoring force, as in the scenario analyzed by Salary (2020).

Background

Passive optical stabilization of laser-driven lightsails uses spatially varying reflectivity to produce restoring forces and torques that keep the sail centered in the beam. Prior simulations (Salary 2020) reported a reduction in the spatial amplitude of oscillations due to the Doppler shift changing reflectivity, thereby altering the restoring force (effectively the stiffness). However, reducing spatial amplitude via stiffness change does not necessarily imply a reduction in kinetic energy or velocity amplitude.

The authors explicitly note that the magnitude of any velocity-amplitude reduction due to this Doppler-induced reflectivity change is unclear. Their paper introduces an alternative damping mechanism based on relativistic aberration and Doppler effects (Poynting-Robertson–like damping), but does not resolve how much the earlier Doppler-reflectivity mechanism alone reduces velocity amplitude, leaving this as an open quantitative question.