Energy needed to propel a tiny spacecraft to Proxima Centauri

Conventional chemical rockets enable exploration of the entire solar system. However, exploration beyond the solar system on a human time scale requires new technology. The goal of the Breakthrough Starshot project, and one of the goals of the Starlight project, is to send a tiny 2 g spacecraft to the nearest star, Proxima Centauri, propelled by a light sail and powerful Earth-based lasers. We provide simple derivations of two different expressions for the laser energy required to propel the spacecraft, both of which have been published in the literature. One of these expressions is relevant to the mission and the other is not, and we invite the reader to think of the reason before providing the answer. In the appendix 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. Although Einstein's formula results in a completely negligible error in the energy estimate for the Starshot/Starlight project, it has been incorrectly blamed for the differences in the published energy estimates.