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Title: Relativistic Light Sails

Abstract

One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. 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 equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot , we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffractionmore » beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.« less

Authors:
 [1]
  1. Department of Astronomy, Columbia University, 550 W. 120th St., New York, NY 10027 (United States)
Publication Date:
OSTI Identifier:
22663536
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (Online); Journal Volume: 153; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; DIAGRAMS; DIFFRACTION; LASERS; MASS; MIRRORS; PHOTONS; RADIATION PRESSURE; RELATIVISTIC RANGE; RELATIVITY THEORY; SAILS; SOLAR RADIATION; SPACE; SPACE VEHICLES; STARS; VELOCITY; VISIBLE RADIATION

Citation Formats

Kipping, David, E-mail: dkipping@astro.columbia.edu. Relativistic Light Sails. United States: N. p., 2017. Web. doi:10.3847/1538-3881/AA729D.
Kipping, David, E-mail: dkipping@astro.columbia.edu. Relativistic Light Sails. United States. doi:10.3847/1538-3881/AA729D.
Kipping, David, E-mail: dkipping@astro.columbia.edu. Thu . "Relativistic Light Sails". United States. doi:10.3847/1538-3881/AA729D.
@article{osti_22663536,
title = {Relativistic Light Sails},
author = {Kipping, David, E-mail: dkipping@astro.columbia.edu},
abstractNote = {One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. 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 equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot , we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.},
doi = {10.3847/1538-3881/AA729D},
journal = {Astronomical Journal (Online)},
number = 6,
volume = 153,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}