Reflection from Inclined, Relativistic Light Sails

TL;DR

This paper derives a new formula for relativistic sunlight reflection from inclined light sails, extending previous models and applicable to various angles and energy calculations.

Contribution

It introduces an elementary two-body analysis to derive a general relativistic reflection formula for inclined light sails, unifying previous special cases.

Findings

Derived a new general formula for relativistic reflection at arbitrary angles.

Showed the formula reduces to classical and relativistic limits.

Potential extension to calculate energy gain of inclined light sails.

Abstract

Kipping (2017) discusses relativistic reflection from light sails. As an extension to this work, we present a new formula for relativistic reflection of sunlight from a light sail moving at a velocity inclined at an arbitrary angle, using an elementary two-body analysis. The formula is shown to reduce to the formulas of Euclid, Einstein, and Gjurchinovski in the relevant limits. This calculation may be extended to calculate the kinetic energy gained by a relativistic light sail inclined at an arbitrary angle.