Energy needed to propel a tiny spacecraft to Proxima Centauri,and, an unstated assumption in Einstein's 1905 paper

TL;DR

This paper calculates the laser energy needed for a tiny spacecraft to reach Proxima Centauri and clarifies a subtle assumption in Einstein's 1905 paper that has caused confusion in recent literature.

Contribution

It presents two derivations of the laser energy requirement for interstellar propulsion and clarifies an unstated assumption in Einstein's 1905 paper affecting current research.

Findings

Two methods to estimate laser energy for spacecraft propulsion

Identification of a limited validity condition in Einstein's 1905 formula

Clarification of confusion in Breakthrough Starshot literature

Abstract

The Breakthrough Starshot project aims to send a tiny 2 gram spacecraft to Proxima Centauri propelled by a light sail and powerful Earth-based lasers. We provide two derivations of the laser energy required to propel the spacecraft and give the reader the opportunity to decide which one is correct before providing the answer. In the second part of this paper we point out that one of the formulae in Einstein's amazing 1905 paper is correct only in certain limits, but Einstein fails to mention that. This has caused some confusion in the Breakthrough Starshot literature.