December 16, 2011

Fig. 1: Solar sail with sails fully deployed.
Source: Wikimedia
Commons. (Courtesy of NASA) |

Solar sails (also known as light sails and photon sails) have been long proposed as an alternative propulsion mechanism for space applications. Russian astronautic theorist Konstantin Tsiolkovsky and astronautical engineer Friedrich Zander theorized the idea early in the 20th century. [1] In the present-day, these ideas have cemented into successful spacecrafts which have begun to pave the way for major investments into their research and use. The Japan Aerospace Exploration Agency (JAXA) launched its IKAROS spacecraft (a fitting acronym for Interplanetary Kite-craft Accelerated by Radiation Of the Sun) in 2010. NASA also deployed its NanoSail-D2 in early 2011, and The Planetary Society (TPS) successfully launched its first of a series of solar sail-propelled CubeSats called the LightSail-1. [1]

These launches, all of which are experimental CubeSats, are important first steps in probing the plausibility of interstellar travel, manned and unmanned. They provide an alternative means of propulsion, much like a sailboat on the sea versus engine-powered ships. This uniqueness and importance of solar sails to the future of space exploration will be highlighted here.

The propulsive means of a solar sail is different than other historically-used propulsion systems in many ways. Unlike chemical, ion, and nuclear rockets, the solar sail system does not carry with it any fuel to produce thrust. [2] Instead, it essentially uses large sails made of very thin aluminized BoPET (Mylar) or aluminized Kapton film that receives a transfer of momentum from the photon pressure of a star or laser source. This transfer of momentum from the photons increases the acceleration and thereby speed of the satellite. [3]

Therefore, the momentum of an absorbed photon can be found through relavistic mechanics to be

where E is the energy of the photon, P is the momentum, c is the speed of light in a vacuum, and m is the photon mass, which is zero. The equation reduces to E = P c, and furthermore pressure, p, can be derived as

p = | F A |
= | 1 A |
( | dp dt |
) | = | 1 A c |
( | dE dt |
) |

where F is the force generated by the momentum change, and A is the surface area. However, since the sail material is highly reflective, it's reasonable to assume that all of the light is reflected, thereby doubling the momentum gained (and subsequently pressure) such that p = 2 (dE/dt) / (A c). Therefore, the solar radiation pressure can be expressed as twice the energy flux density divided by the speed of light in a vacuum.

In terms of the solar sail launched from Earth, the
effective pressure experienced by the sails depends on two things: the
energy flux density from the Sun at the distance of the satellite and
the sail area. At Earth's distance of 1 AU from the Sun, recent
recordings have show the energy flux density to be 1.36
kW/(m^{2}). [4] This means that for even a sail area of 1 square
kilometer, the force on the sail would be: F = 2 (dE/dt) / (A c) = 2
× ((1360 W/(m^{2}))/(3 × 10^{8} m/s)) ×
(1000 m)^{2} = 9 N, which is effectively the thrust generated by
the sunlight at Earth's distance away.

This means that, once past Earth's escape velocity, the spacecraft gains seemingly perpetual thrust so long as there's solar light radiation. Although the impulse depends on the square inverse of the craft's distance relative to the star, the specific impulse - if even quantifiable - is infinite. There's no fuel mass needed for this ever-lasting acceleration.

The uses for this kind of propulsion and spacecraft system are numerous. One such use could be as replacements for conventional telecommunications satellites. These types of satellites orbit Earth in a geostationary orbit (GEO) around the equatorial plane such that their period is in line with Earth's rotation period (24 hours), and thus they are always located at the same point in the sky to the ground observer. However, future congestion of the equatorial GEO plane can be alleviated by the use of hybrid solar sails (solar sails that combine their inherit propulsion mechanism with that of solar electric (ion) propulsion. [5] This dual propulsion system allows for continuous acceleration that counteracts the gravitational force and allows the spacecraft to orbit in a displaced non-Keplerian orbit. Effectively, solar sails can be used to help establish another geostationary ring displaced above and below the equatorial plane, thereby reducing overcrowding in the future. Research has shown that such a system could maintain payloads of up to 450 kg in a 35 km-displaced orbit for 10-15 years. [5]

Using these sails also inherently decreases the need for fuel consumption during orbit transfers. At the end of a satellite's service life, the craft is usually intended to be transferred into a larger radius orbit known colloquially as a graveyard orbit. The transfer itself usually requires two boosts of thrust at key orbital points, but with the continuous acceleration that a solar sail has, it can transfer itself to outer orbits without needing extra thruster fuel. Despite the low thrust from the light, it has been calculated that a transfer into an outer orbit can be made within less than half a year's time given optimal sail acceleration values. [6] Moreover, the spacecraft is much lighter during the transfer due to reduced fuel and engine weight.

While the technology is still at the early stages of
practical use, solar sails have a bright outlook in future spacecraft
applications. The replacement of conventional geostationary
telecommunication satellites is only one them. Solar sails can use the
accumulated acceleration over time to reach very high speeds, if for
instance one were launched toward the sun in an attempt to use the
increased solar radiation pressure to create an assistive effect (much
like gravity assists). Nearing the sun at a distance of about 0.004 AU, solar radiation
power density can be estimated using the Stefan-Boltzmann law and the inverse square law.
The power density, then reaches 64 MW/(m^{2}), which is forty-seven thousand
times the energy at the Earth's surface. For an arbitrary sail with
a square kilometer of reflective surface area, then the resulting thrust
would be 427,000 N. Although this is a very generous approximation since
actual crafts will not reach that close to the Sun, this is a massive
jump from 9 N. It can accelerate a 500 kg spacecraft at 853
m/(s^{2}). Withstanding such massive acceleration (86 times
Earth's gravity force) is not feasible for humans, but reaching distant
celestial bodies can be feasible for an exploratory spacecraft nearing
those acceleration values.

© Nghia Nguyen. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] H. Furuya, Y. Inoue and T. Masuoka, "Deployment Characteristics of Rotationally Skew Fold Membrane for Spinning Solar Sail," 46th AIAA/ASME/ASCEA/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA 2005-2045, 18 Apr 05.

[2] R. H. Frisbee, "Advanced Space Propulsion for the
21st Century," California Institute of Technology Jet Propulsion
Laboratory," J. Propulsion and Power **19**, 1129 (2003).

[3] P. K. Kundu and I. M. Cohen, *Fluid
Mechanics*, (Academic Press, 2008), p. 731.

[4] G. Kopp and J. L. Lean, "A New, Lower Value of
Total Solar Irradiance: Evidence and Climate Significance,"
Geophys. Res. Lett. **38**, L01706 (2011).

[5] J. Heiligers *et al.*, "Displaced
Geostationary Orbit Design Using Hybrid Sail Propulsion," J. Guidance,
Control, and Dynamics **34**, 1852 (2011).

[6] V. L. Coverstone and J. E. Prussing, "Technique
for Escape from Geosynchronous Transfer Orbit Using a Solar Sail," J.
Guidance, Control, and Dynamics **26**, 628 (2003).