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Solar sail

## Summary

Solar sails (also known as light sails and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. A number of spaceflight missions to test solar propulsion and navigation have been proposed since the 1980s. The first spacecraft to make use of the technology was IKAROS, launched in 2010.

IKAROS space-probe with solar sail in flight (artist's depiction) showing a typical square sail configuration

A useful analogy to solar sailing may be a sailing boat; the light exerting a force on the mirrors is akin to a sail being blown by the wind. High-energy laser beams could be used as an alternative light source to exert much greater force than would be possible using sunlight, a concept known as beam sailing. Solar sail craft offer the possibility of low-cost operations combined with long operating lifetimes. Since they have few moving parts and use no propellant, they can potentially be used numerous times for delivery of payloads.

Solar sails use a phenomenon that has a proven, measured effect on astrodynamics. Solar pressure affects all spacecraft, whether in interplanetary space or in orbit around a planet or small body. A typical spacecraft going to Mars, for example, will be displaced thousands of kilometers by solar pressure, so the effects must be accounted for in trajectory planning, which has been done since the time of the earliest interplanetary spacecraft of the 1960s. Solar pressure also affects the orientation of a spacecraft, a factor that must be included in spacecraft design.[1]

The total force exerted on an 800 by 800 metre solar sail, for example, is about 5 N (1.1 lbf) at Earth's distance from the Sun,[2] making it a low-thrust propulsion system, similar to spacecraft propelled by electric engines, but as it uses no propellant, that force is exerted almost constantly and the collective effect over time is great enough to be considered a potential manner of propelling spacecraft.

## History of concept

Johannes Kepler observed that comet tails point away from the Sun and suggested that the Sun caused the effect. In a letter to Galileo in 1610, he wrote, "Provide ships or sails adapted to the heavenly breezes, and there will be some who will brave even that void." He might have had the comet tail phenomenon in mind when he wrote those words, although his publications on comet tails came several years later.[3]

James Clerk Maxwell, in 1861–1864, published his theory of electromagnetic fields and radiation, which shows that light has momentum and thus can exert pressure on objects. Maxwell's equations provide the theoretical foundation for sailing with light pressure. So by 1864, the physics community and beyond knew sunlight carried momentum that would exert a pressure on objects.

Jules Verne, in From the Earth to the Moon,[4] published in 1865, wrote "there will some day appear velocities far greater than these [of the planets and the projectile], of which light or electricity will probably be the mechanical agent ... we shall one day travel to the moon, the planets, and the stars."[5] This is possibly the first published recognition that light could move ships through space.

Pyotr Lebedev was first to successfully demonstrate light pressure, which he did in 1899 with a torsional balance;[6] Ernest Nichols and Gordon Hull conducted a similar independent experiment in 1901 using a Nichols radiometer.[7]

Svante Arrhenius predicted in 1908 the possibility of solar radiation pressure distributing life spores across interstellar distances, providing one means to explain the concept of panspermia. He apparently was the first scientist to state that light could move objects between stars.[8]

Konstantin Tsiolkovsky first proposed using the pressure of sunlight to propel spacecraft through space and suggested, "using tremendous mirrors of very thin sheets to utilize the pressure of sunlight to attain cosmic velocities".[9]

Friedrich Zander (Tsander) published a technical paper in 1925 that included technical analysis of solar sailing. Zander wrote of "applying small forces" using "light pressure or transmission of light energy to distances by means of very thin mirrors".[10]

JBS Haldane speculated in 1927 about the invention of tubular spaceships that would take humanity to space and how "wings of metallic foil of a square kilometre or more in area are spread out to catch the Sun's radiation pressure".[11]

J. D. Bernal wrote in 1929, "A form of space sailing might be developed which used the repulsive effect of the Sun's rays instead of wind. A space vessel spreading its large, metallic wings, acres in extent, to the full, might be blown to the limit of Neptune's orbit. Then, to increase its speed, it would tack, close-hauled, down the gravitational field, spreading full sail again as it rushed past the Sun."[12]

Carl Sagan, in the 1970s, popularized the idea of sailing on light using a giant structure which would reflect photons in one direction, creating momentum. He brought up his ideas in college lectures, books, and television shows. He was fixated on quickly launching this spacecraft in time to perform a rendezvous with Halley's Comet. Unfortunately, the mission didn't take place in time and he would never live to finally see it through.[13]

The first formal technology and design effort for a solar sail began in 1976 at Jet Propulsion Laboratory for a proposed mission to rendezvous with Halley's Comet.[2]

In 2018, diffraction was proposed as a related solar sail propulsion mechanism with the advantage of less waste heat.[14]

## Physical principles

The force imparted to a solar sail arises from the momentum of photons. The momentum of a photon or an entire flux is given by Einstein's relation:[15][16]

${\displaystyle p=E/c}$

where p is the momentum, E is the energy (of the photon or flux), and c is the speed of light. Specifically, the momentum of a photon depends on its wavelength p = h/λ

Solar radiation pressure can be related to the irradiance (solar constant) value of 1361 W/m2 at 1 AU (Earth-Sun distance), as revised in 2011:[17]

• perfect absorbance: F = 4.54 μN per square metre (4.54 μPa) in the direction of the incident beam (a perfectly inelastic collision)
• perfect reflectance: F = 9.08 μN per square metre (9.08 μPa) in the direction normal to surface (an elastic collision)

An ideal sail is flat and has 100% specular reflection. An actual sail will have an overall efficiency of about 90%, about 8.17 μN/m2,[16] due to curvature (billow), wrinkles, absorbance, re-radiation from front and back, non-specular effects, and other factors.

Force on a sail results from reflecting the photon flux

The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the Sun (unless extremely close to the Sun[18]), and by the square of the cosine of the angle between the sail force vector and the radial from the Sun, so

${\displaystyle F=F_{0}\cos ^{2}(\theta )/R^{2}}$  (for an ideal sail)

where R is distance from the Sun in AU. An actual square sail can be modelled as:

${\displaystyle F=F_{0}(0.349+0.662\cos(2\theta )-0.011\cos(4\theta ))/R^{2}}$

Note that the force and acceleration approach zero generally around θ = 60° rather than 90° as one might expect with an ideal sail.[19]

If some of the energy is absorbed, the absorbed energy will heat the sail, which re-radiates that energy from the front and rear surfaces, depending on the emissivity of those two surfaces.

Solar wind, the flux of charged particles blown out from the Sun, exerts a nominal dynamic pressure of about 3 to 4 nPa, three orders of magnitude less than solar radiation pressure on a reflective sail.[20]

### Sail parameters

Sail loading (areal density) is an important parameter, which is the total mass divided by the sail area, expressed in g/m2. It is represented by the Greek letter σ (sigma).

A sail craft has a characteristic acceleration, ac, which it would experience at 1 AU when facing the Sun. Note this value accounts for both the incident and reflected momentums. Using the value from above of 9.08 μN per square metre of radiation pressure at 1 AU, ac is related to areal density by:

ac = 9.08(efficiency) / σ mm/s2

Assuming 90% efficiency, ac = 8.17 / σ mm/s2

The lightness number, λ, is the dimensionless ratio of maximum vehicle acceleration divided by the Sun's local gravity. Using the values at 1 AU:

λ = ac / 5.93

The lightness number is also independent of distance from the Sun because both gravity and light pressure fall off as the inverse square of the distance from the Sun. Therefore, this number defines the types of orbit maneuvers that are possible for a given vessel.

The table presents some example values. Payloads are not included. The first two are from the detailed design effort at JPL in the 1970s. The third, the lattice sailer, might represent about the best possible performance level.[2] The dimensions for square and lattice sails are edges. The dimension for heliogyro is blade tip to blade tip.

Type σ (g/m2) ac (mm/s2) λ Size (km2)
Square sail 5.27 1.56 0.26 0.820
Heliogyro 6.39 1.29 0.22 15
Lattice sailer 0.07 117 20 0.840

### Attitude control

An active attitude control system (ACS) is essential for a sail craft to achieve and maintain a desired orientation. The required sail orientation changes slowly (often less than 1 degree per day) in interplanetary space, but much more rapidly in a planetary orbit. The ACS must be capable of meeting these orientation requirements. Attitude control is achieved by a relative shift between the craft's center of pressure and its center of mass. This can be achieved with control vanes, movement of individual sails, movement of a control mass, or altering reflectivity.

Holding a constant attitude requires that the ACS maintain a net torque of zero on the craft. The total force and torque on a sail, or set of sails, is not constant along a trajectory. The force changes with solar distance and sail angle, which changes the billow in the sail and deflects some elements of the supporting structure, resulting in changes in the sail force and torque.

Sail temperature also changes with solar distance and sail angle, which changes sail dimensions. The radiant heat from the sail changes the temperature of the supporting structure. Both factors affect total force and torque.

To hold the desired attitude the ACS must compensate for all of these changes.[21]

### Constraints

In Earth orbit, solar pressure and drag pressure are typically equal at an altitude of about 800 km, which means that a sail craft would have to operate above that altitude. Sail craft must operate in orbits where their turn rates are compatible with the orbits, which is generally a concern only for spinning disk configurations.

Sail operating temperatures are a function of solar distance, sail angle, reflectivity, and front and back emissivities. A sail can be used only where its temperature is kept within its material limits. Generally, a sail can be used rather close to the Sun, around 0.25 AU, or even closer if carefully designed for those conditions.[2]

## Applications

Potential applications for sail craft range throughout the Solar System, from near the Sun to the comet clouds beyond Neptune. The craft can make outbound voyages to deliver loads or to take up station keeping at the destination. They can be used to haul cargo and possibly also used for human travel.[2]

## In popular culture

Cordwainer Smith gives a description of solar-sail-powered spaceships in "The Lady Who Sailed The Soul", published first in April 1960.

Jack Vance wrote a short story about a training mission on a solar-sail-powered spaceship in "Sail 25", published in 1961.

Arthur C. Clarke and Poul Anderson (writing as Winston P. Sanders) independently published stories featuring solar sails, both stories titled "Sunjammer," in 1964. Clarke retitled his story "The Wind from the Sun" when it was reprinted, in order to avoid confusion.[105]

In Larry Niven and Jerry Pournelle's 1974 novel The Mote in God's Eye, aliens are discovered when their laser-sail propelled probe enters human space.

A similar technology was the theme in the Star Trek: Deep Space Nine episode "Explorers". In the episode, Lightships are described as an ancient technology used by Bajorans to travel beyond their solar system by using light from the Bajoran sun and specially constructed sails to propel them through space ("Explorers". Star Trek: Deep Space Nine. Season 3. Episode 22.).[106][non-primary source needed]

In the 2002 Star Wars film Attack of the Clones, the main villain Count Dooku was seen using a spacecraft with solar sails.[107]

In the third season of Apple TV+'s alternate history TV show For All Mankind, the fictional NASA spaceship Sojourner 1 utilises solar sails for additional propulsion on its way to Mars.

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## Bibliography

• G. Vulpetti, Fast Solar Sailing: Astrodynamics of Special Sailcraft Trajectories, ;;Space Technology Library Vol. 30, Springer, August 2012, (Hardcover) https://www.springer.com/engineering/mechanical+engineering/book/978-94-007-4776-0, (Kindle-edition), ASIN: B00A9YGY4I
• G. Vulpetti, L. Johnson, G. L. Matloff, Solar Sails: A Novel Approach to Interplanetary Flight, Springer, August 2008, ISBN 978-0-387-34404-1
• J. L. Wright, Space Sailing, Gordon and Breach Science Publishers, London, 1992; Wright was involved with JPL's effort to use a solar sail for a rendezvous with Halley's comet.
• NASA/CR 2002-211730, Chapter IV— presents an optimized escape trajectory via the H-reversal sailing mode
• G. Vulpetti, The Sailcraft Splitting Concept, JBIS, Vol. 59, pp. 48–53, February 2006
• G. L. Matloff, Deep-Space Probes: To the Outer Solar System and Beyond, 2nd ed., Springer-Praxis, UK, 2005, ISBN 978-3-540-24772-2
• T. Taylor, D. Robinson, T. Moton, T. C. Powell, G. Matloff, and J. Hall, "Solar Sail Propulsion Systems Integration and Analysis (for Option Period)", Final Report for NASA/MSFC, Contract No. H-35191D Option Period, Teledyne Brown Engineering Inc., Huntsville, AL, May 11, 2004
• G. Vulpetti, "Sailcraft Trajectory Options for the Interstellar Probe: Mathematical Theory and Numerical Results", the Chapter IV of NASA/CR-2002-211730, The Interstellar Probe (ISP): Pre-Perihelion Trajectories and Application of Holography, June 2002
• G. Vulpetti, Sailcraft-Based Mission to The Solar Gravitational Lens, STAIF-2000, Albuquerque (New Mexico, USA), 30 January – 3 February 2000
• G. Vulpetti, "General 3D H-Reversal Trajectories for High-Speed Sailcraft", Acta Astronautica, Vol. 44, No. 1, pp. 67–73, 1999
• C. R. McInnes, Solar Sailing: Technology, Dynamics, and Mission Applications, Springer-Praxis Publishing Ltd, Chichester, UK, 1999, ISBN 978-3-540-21062-7
• Genta, G., and Brusa, E., "The AURORA Project: a New Sail Layout", Acta Astronautica, 44, No. 2–4, pp. 141–146 (1999)
• S. Scaglione and G. Vulpetti, "The Aurora Project: Removal of Plastic Substrate to Obtain an All-Metal Solar Sail", special issue of Acta Astronautica, vol. 44, No. 2–4, pp. 147–150, 1999