http://arxiv.org/abs/1704.04310
One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or beamed lasers. This idea constitutes the thesis behind the Breakthrough Starshot Initiative, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light towards Proxima Centauri. For such a case, the spacecraft’s low mass and relativistic terminal velocity render classical treatments invalid. To address this, we present formulae for a sail’s acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail’s motion in response to an ensemble of incident photons is well-described by that of a single high energy photon for both elastic and inelastic collisions, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot, we estimate that a classical treatment would overestimate the spacecraft’s terminal velocity by ~10% for the same incident energy. Additionally, we use a simple model to predict to the temperature of the sail during the laser firing period, allowing us to estimate that for firing times less than 4 hours and operating temperatures below $300^{\circ}$C ($573^{\circ}$K), Starshot will require a sail of reflectivity better than 99.99%.
D. Kipping
Mon, 17 Apr 17
24/24
Comments: Submitted to AAS Journals. Comments welcome!
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