# Solar sail

(Redirected from Solar sails)
IKAROS spaceprobe with solar sail in flight (artist's depiction) showing a typical square sail configuration

Solar sails (also called light sails or photon sails) are a form of spacecraft propulsion using the radiation pressure (also called solar pressure) of a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds. Light sails could also be driven by energy beams to extend their range of operations, which is strictly beam sailing rather than solar 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 spacecraft. 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 by more than 1,000 km 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 attitude of a craft, a factor that must be included in spacecraft design.[1]

The total force exerted on a solar sail may be around 1 newton or less,[2] making it a low-thrust spacecraft, along with spacecraft propelled by electric engines.

## 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 1861-64, 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, 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." This is possibly the first published recognition that light could move ships through space. Given the date of his publication and the widespread, permanent distribution of his work, it appears that he should be regarded as the originator of the concept of space sailing by light pressure, although he did not develop the concept further. Verne probably got the idea directly and immediately from Maxwell's 1864 theory (although it cannot be ruled out that Maxwell or an intermediary recognized the sailing potential and became the source for Verne).[4]

Pyotr Lebedev was first to successfully demonstrate light pressure, which he did in 1899 with a torsional balance;[5] Ernest Nichols and Gordon Hull conducted a similar independent experiment in 1901 using a Nichols radiometer.[6]

Albert Einstein provided a different formalism by his recognizing the equivalence of mass and energy. We can now write simply p = E/c as the relationship between momentum, energy, and speed of light.

Svante Arrhenius predicted in 1908 the possibility of solar radiation pressure distributing life spores across interstellar distances, the concept of panspermia. He apparently was the first scientist to state that light could move objects between stars.[7]

Friedrich Zander (Tsander) published a technical paper that included technical analysis of solar sailing. Zander wrote of "using tremendous mirrors of very thin sheets" and "using the pressure of sunlight to attain cosmic velocities".[8]

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."[9]

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]

## Physical principles

Solar radiation exerts a pressure on the sail due to reflection and a small fraction that is absorbed. The absorbed energy heats the sail, which re-radiates that energy from the front and rear surfaces.

The momentum of a photon or an entire flux is given by p = E/c,[10][11] where E is the photon or flux energy, p is the momentum, and c is the speed of light. At 1 AU the solar power flux density is about 1370 W/m2, resulting in a pressure under:

perfect absorbance: F = 4.57 μN per square metre (4.57 μPa)

perfect reflectance: F = 9.13 μN per square metre (9.13 μPa)

A perfect sail is flat and has 100% specular reflection. An actual sail will have an overall efficiency of about 90%, about 8.22 μN/m2,[12] due to curvature (billow), wrinkles, absorbance, re-radiation from front and back, non-specular effects, and other factors.

The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the sun (unless close to the sun[13]), and by the square of the cosine of the angle between the sail force vector and the radial from the sun, so

```F = F0 cos2 θ / R2 (ideal sail)
```

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

```F = F0 (0.349 + 0.662 cos 2θ - 0.011 cos 4θ) / R2
```

Note that the force and acceleration approach zero generally around θ = 60° rather than 90° as one might expect with an ideal sail.[14]

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.[15]

### 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.

A sail craft has a characteristic acceleration, ac, which it would experience at 1 AU when facing the sun. It is related to areal density by:

```ac = 8.22 / σ, in 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 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]

Type   σ    ac    λ   Size
Square sail 5.27 1.56 0.26 820 m
Heliogyro 6.39 1.29 0.22 15 km
Lattice sailer 0.07 117 20 1 km

### Sailing techniques

Sailing operations are simplest in interplanetary orbits, where attitude changes are done at low rates. For outward bound trajectories, the sail force vector is oriented forward of the sun line, which increases orbital energy and angular momentum, resulting in the craft moving farther from the sun. For inward trajectories, the sail force vector is oriented behind the sun line, which decreases orbital energy and angular momentum, resulting in the craft moving in toward the sun. To change orbital inclination, the force vector is turned out of the plane of the velocity vector.

In orbits around planets or other bodies, the sail is oriented so that its force vector has a component along the velocity vector, either in the direction of motion for an outward spiral, or against the direction of motion for an inward spiral.

### 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.

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.

The ACS must compensate for all of these changes for it to hold the desired attitude.[16]

### 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

### Satellites

Robert L. Forward pointed out that a solar sail could be used to modify the orbit of a satellite around the Earth. In the limit, a sail could be used to "hover" a satellite above one pole of the Earth. Spacecraft fitted with solar sails could also be placed in close orbits about the Sun that are stationary with respect to either the Sun or the Earth, a type of satellite named by Forward a statite. This is possible because the propulsion provided by the sail offsets the gravitational potential of the Sun. Such an orbit could be useful for studying the properties of the Sun over long durations.[citation needed]

Such a spacecraft could conceivably be placed directly over a pole of the Sun, and remain at that station for lengthy durations. Likewise a solar sail-equipped spacecraft could also remain on station nearly above the polar terminator of a planet such as the Earth by tilting the sail at the appropriate angle needed to just counteract the planet's gravity.[citation needed]

In his book, The Case for Mars, Robert Zubrin points out that the reflected sunlight from a large statite placed near the polar terminator of the planet Mars could be focussed on one of the Martian polar ice caps to significantly warm the planet's atmosphere. Such a statite could be made from asteroid material.[citation needed]

### Trajectory corrections

The MESSENGER probe orbiting Mercury used light pressure on its solar panels to perform fine trajectory corrections on the way to Mercury.[17] By changing the angle of the solar panels relative to the Sun, the amount of solar radiation pressure was varied to adjust the spacecraft trajectory more delicately than possible with thrusters. Minor errors are greatly amplified by gravity assist maneuvers, so using radiation pressure to make very small corrections saved large amounts of propellant.

### Interstellar flight

In the 1970s, Robert Forward proposed two beam-powered propulsion schemes using either lasers or masers to push giant sails to a significant fraction of the speed of light.[18]

In The Flight of the Dragonfly, Forward described a light sail propelled by superlasers. As the starship neared its destination, the outer portion of the sail would detach. The outer sail would then refocus and reflect the lasers back onto a smaller, inner sail. This would provide braking thrust to stop the ship in the destination star system.

Both methods pose monumental engineering challenges. The lasers would have to operate for years continuously at gigawatt strength. Forward's solution to this requires enormous solar panel arrays to be built at or near the planet Mercury. A planet-sized mirror or fresnel lens would be needed several dozen astronomical units from the Sun to keep the lasers focused on the sail. The giant braking sail would have to act as a precision mirror to focus the braking beam onto the inner "deceleration" sail.

A potentially easier approach would be to use a maser to drive a "solar sail" composed of a mesh of wires with the same spacing as the wavelength of the microwaves, since the manipulation of microwave radiation is somewhat easier than the manipulation of visible light. The hypothetical "Starwisp" interstellar probe design would use a maser to drive it. Masers spread out more rapidly than optical lasers owing to their longer wavelength, and so would not have as long an effective range.

Masers could also be used to power a painted solar sail, a conventional sail coated with a layer of chemicals designed to evaporate when struck by microwave radiation.[19] The momentum generated by this evaporation could significantly increase the thrust generated by solar sails, as a form of lightweight ablative laser propulsion.

To further focus the energy on a distant solar sail, designs have considered the use of a large zone plate. This would be placed at a location between the laser or maser and the spacecraft.[clarification needed] The plate could then be propelled outward using the same energy source, thus maintaining its position so as to focus the energy on the solar sail.[citation needed]

Additionally, it has been theorized by da Vinci Project contributor T. Pesando that solar sail-utilizing spacecraft successful in interstellar travel could be used to carry their own zone plates or perhaps even masers to be deployed during flybys at nearby stars. Such an endeavor could allow future solar-sailed craft to effectively utilize focused energy from other stars rather than from the Earth or Sun, thus propelling them more swiftly through space and perhaps even to more distant stars. However, the potential of such a theory remains uncertain if not dubious due to the high-speed precision involved and possible payloads required.[citation needed]

Another more physically realistic approach would be to use the light from the home star to accelerate. The ship would first orbit continuously away around the home star until the appropriate starting velocity is reached, then the ship would begin its trip away from the system using the light from the star to keep accelerating. Beyond some distance, the ship would no longer receive enough light to accelerate it significantly, but would maintain its course due to inertia. When nearing the target star, the ship could turn its sails toward it and begin to orbit inward to decelerate. Additional forward and reverse thrust could be achieved with more conventional means of propulsion such as rockets.

Similar solar sailing, such launch and capture were suggested for directed panspermia to expand life in other solar systems. Velocities of 0.0005 c could be obtained by solar sails carrying 10 kg payloads, using thin solar sail vehicles with effective areal densities 0.0001 kg/m^2 with thin sails of thickness of 0.1 microns and sizes on the order of one square km. Alternatively, swarms of 1 mm capsules can be launched on solar sails with radii of 42 cm, each carrying 10,000 capsules of a hundred million extremophile microorganism to seed life in diverse target environments.[20][21]

## Sail configurations

NASA illustration of the unlit side of a half-kilometre solar sail, showing the struts stretching the sail.
An artist's depiction of a Cosmos 1 type spaceship in orbit

Parachutes have very low mass, but a parachute is not a workable configuration for a solar sail. Analysis shows that a parachute configuration would collapse from the forces exerted by shroud lines, since radiation pressure does not behave like aerodynamic pressure, and would not act to keep the parachute open.[22]

Eric Drexler[23] proposed very high thrust-to-mass solar sails, and made prototypes of the sail material. His sail would use panels of thin aluminium film (30 to 100 nanometres thick) supported by a tensile structure. The sail would rotate and would have to be continually under thrust. He made and handled samples of the film in the laboratory, but the material was too delicate to survive folding, launch, and deployment. The design planned to rely on space-based production of the film panels, joining them to a deployable tension structure. Sails in this class would offer high area per unit mass and hence accelerations up to "fifty times higher" than designs based on deployable plastic films.[23]

The highest thrust-to-mass designs for ground-assembled deployable structures are square sails with the masts and guy lines on the dark side of the sail. Usually there are four masts that spread the corners of the sail, and a mast in the center to hold guy-wires. One of the largest advantages is that there are no hot spots in the rigging from wrinkling or bagging, and the sail protects the structure from the Sun. This form can therefore go close to the Sun for maximum thrust. Most designs steer with small sails on the ends of the spars.[24]

In the 1970s JPL studied many rotating blade and ring sails for a mission to rendezvous with Halley's Comet. The intention was to stiffen the structures using angular momentum, eliminating the need for struts, and saving mass. In all cases, surprisingly large amounts of tensile strength were needed to cope with dynamic loads. Weaker sails would ripple or oscillate when the sail's attitude changed, and the oscillations would add and cause structural failure. The difference in the thrust-to-mass ratio between practical designs was almost nil, and the static designs were easier to control.[24]

JPL's reference design was called the "heliogyro." It had plastic-film blades deployed from rollers and held out by centrifugal forces as it rotated. The spacecraft's attitude and direction were to be completely controlled by changing the angle of the blades in various ways, similar to the cyclic and collective pitch of a helicopter. Although the design had no mass advantage over a square sail, it remained attractive because the method of deploying the sail was simpler than a strut-based design.[24]

JPL also investigated "ring sails" (Spinning Disk Sail in the above diagram), panels attached to the edge of a rotating spacecraft. The panels would have slight gaps, about one to five percent of the total area. Lines would connect the edge of one sail to the other. Masses in the middles of these lines would pull the sails taut against the coning caused by the radiation pressure. JPL researchers said that this might be an attractive sail design for large manned structures. The inner ring, in particular, might be made to have artificial gravity roughly equal to the gravity on the surface of Mars.[24]

A solar sail can serve a dual function as a high-gain antenna.[25] Designs differ, but most modify the metallization pattern to create a holographic monochromatic lens or mirror in the radio frequencies of interest, including visible light.[25]

Pekka Janhunen from FMI has invented a type of solar sail called the electric solar wind sail.[26] Mechanically it has little in common with the traditional solar sail design. The sails are replaced with straightened conducting tethers (wires) placed radially around the host ship. The wires are electrically charged to create an electric field around the wires. The electric field extends a few tens of metres into the plasma of the surrounding solar wind. The solar electrons are reflected by the electric field (like the photons on a traditional solar sail). The radius of the sail is from the electric field rather than the actual wire itself, making the sail lighter. The craft can also be steered by regulating the electric charge of the wires. A practical electric sail would have 50-100 straightened wires with a length of about 20 km each.[citation needed]

A magnetic sail would also employ the solar wind. However, the magnetic field deflects the electrically charged particles in the wind. It uses wire loops, and runs a static current through them instead of applying a static voltage.[27]

All these designs maneuver, though the mechanisms are different. Magnetic sails bend the path of the charged protons that are in the solar wind. By changing the sails' attitudes, and the size of the magnetic fields, they can change the amount and direction of the thrust. Electric solar wind sails can adjust their electrostatic fields and sail attitudes.

## Sail making

### Materials

NASA engineer Les Johnson views interstellar sail material

The material developed for the Drexler solar sail was a thin aluminum film with a baseline thickness of 0.1 micrometres, to be fabricated by vapor deposition in a space-based system. Drexler used a similar process to prepare films on the ground. As anticipated, these films demonstrated adequate strength and robustness for handling in the laboratory and for use in space, but not for folding, launch, and deployment.

The most common material in current designs is aluminized 2 µm Kapton film. It resists the heat of a pass close to the Sun and still remains reasonably strong. The aluminium reflecting film is on the Sun side. The sails of Cosmos 1 were made of aluminized PET film (Mylar).

Research by Dr. Geoffrey Landis in 1998-9, funded by the NASA Institute for Advanced Concepts, showed that various materials such as alumina for laser lightsails and carbon fiber for microwave pushed lightsails were superior sail materials to the previously standard aluminium or Kapton films.[28]

In 2000, Energy Science Laboratories developed a new carbon fiber material which might be useful for solar sails.[29] The material is over 200 times thicker than conventional solar sail designs, but it is so porous that it has the same mass. The rigidity and durability of this material could make solar sails that are significantly sturdier than plastic films. The material could self-deploy and should withstand higher temperatures.

There has been some theoretical speculation about using molecular manufacturing techniques to create advanced, strong, hyper-light sail material, based on nanotube mesh weaves, where the weave "spaces" are less than half the wavelength of light impinging on the sail. While such materials have so far only been produced in laboratory conditions, and the means for manufacturing such material on an industrial scale are not yet available, such materials could mass less than 0.1 g/m²,[30] making them lighter than any current sail material by a factor of at least 30. For comparison, 5 micrometre thick Mylar sail material mass 7 g/m², aluminized Kapton films have a mass as much as 12 g/m²,[24] and Energy Science Laboratories' new carbon fiber material masses 3 g/m².[29]

## Sail testing in space

### IKAROS

The model of IKAROS at the 61st International Astronautical Congress in 2010

Japan's JAXA successfully tested IKAROS in 2010. The goal was to deploy and control the sail and for the first time determining the minute orbit perturbations caused by light pressure. Orbit determination was done by the nearby AKATSUKI probe from which IKAROS detached after both had been brought into a transfer orbit to Venus. The total effect over the six month' flight was 100 m/s.[31]

Until 2010, no solar sails had been successfully used in space as primary propulsion systems. On 21 May 2010, the Japan Aerospace Exploration Agency (JAXA) launched the “IKAROS” (Interplanetary Kite-craft Accelerated by Radiation Of the Sun) spacecraft, which deployed a 200 m2 polyimide experimental solar sail on June 10.[32][33][34] In July, the next phase for the demonstration of acceleration by radiation began. On 9 July 2010, it was verified that IKAROS collected radiation from the Sun and began photon acceleration by the orbit determination of IKAROS by range-and-range-rate (RARR) that is newly calculated in addition to the data of the relativization accelerating speed of IKAROS between IKAROS and the Earth that has been taken since before the Doppler effect was utilized.[35] The data showed that IKAROS appears to have been solar-sailing since 3 June when it deployed the sail.

IKAROS has a diagonal spinning square sail 20 m (66 ft) made of a 7.5-micrometre (0.0075 mm) thick sheet of polyimide. A thin-film solar array is embedded in the sail. Eight LCD panels are embedded in the sail, whose reflectance can be adjusted for attitude control.[36][37] IKAROS spent six months traveling to Venus, and then began a three-year journey to the far side of the Sun.[38]

### Attitude (orientation) control

Both the Mariner 10 mission, which flew by the planets Mercury and Venus, and the MESSENGER mission to Mercury demonstrated the use of solar pressure as a method of attitude control in order to conserve attitude-control propellant.

Hayabusa also used solar pressure as a method of attitude control to compensate for broken reaction wheels and chemical thruster.

### Sail deployment tests

Full-scale (20mx20m) deployment test by DLR/ESA in 1999

NASA has successfully tested deployment technologies on small scale sails in vacuum chambers.[39]

On February 4, 1993, the Znamya 2, a 20-meter wide aluminized-mylar reflector, was successfully deployed from the Russian Mir space station. Although the deployment succeeded, propulsion was not demonstrated. A second test, Znamya 2.5, failed to deploy properly.

In 1999, a full-scale deployment of a solar sail was tested on the ground at DLR/ESA in Cologne.[40]

On August 9, 2004, the Japanese ISAS successfully deployed two prototype solar sails from a sounding rocket. A clover-shaped sail was deployed at 122 km altitude and a fan-shaped sail was deployed at 169 km altitude. Both sails used 7.5-micrometer film. The experiment purely tested the deployment mechanisms, not propulsion.[41]

### Solar sail propulsion attempts

NanoSail-D of LightSail-1 with sail deployed

A joint private project between Planetary Society, Cosmos Studios and Russian Academy of Science made two sail testing attempts: in 2001 a suborbital prototype test failed because of rocket failure; and in June 21, 2005, Cosmos 1 launched from a submarine in the Barents Sea, but the Volna rocket failed, and the spacecraft failed to reach orbit. They intended to use the sail to gradually raise the spacecraft to a higher Earth orbit over a mission duration of one month. On Carl Sagan's 75th birthday (November 9, 2009) the same group announced plans[42] to make three further attempts, dubbed LightSail-1, -2, and -3.[43] The new design will use a 32-square-meter Mylar sail, deployed in four triangular segments like NanoSail-D.[43] The launch configuration is that of three adjacent CubeSats, and as of 2011 was waiting for a piggyback launch opportunity.[44]

A 15-meter-diameter solar sail (SSP, solar sail sub payload, soraseiru sabupeiro-do) was launched together with ASTRO-F on a M-V rocket on February 21, 2006, and made it to orbit. It deployed from the stage, but opened incompletely.[45]

### NanoSail-D

A team from the NASA Marshall Space Flight Center (Marshall), along with a team from the NASA Ames Research Center, developed a solar sail mission called NanoSail-D which was lost in a launch failure aboard a Falcon 1 rocket on 3 August 2008.[46][47] The second backup version, NanoSail-D2, also sometimes called simply NanoSail-D,[48] was launched with FASTSAT on a Minotaur IV on November 19, 2010, becoming NASA's first solar sail deployed in low earth orbit. The objectives of the mission were to test sail deployment technologies, and to gather data about the use of solar sails as a simple, "passive" means of de-orbiting dead satellites and space debris.[49] The NanoSail-D structure was made of aluminium and plastic, with the spacecraft massing less than 10 pounds (4.5 kg). The sail has about 100 square feet (9.3 m2) of light-catching surface. After some initial problems with deployment, the solar sail was deployed and over the course of its 240 day mission reportedly produced a "wealth of data" concerning the use of solar sails as passive deorbit devices.[50]

### Future solar sail propulsion tests

NASA researchers are developing a technology demonstration Mission known as "In-Space Demonstration of a Mission-Capable Solar Sail" with the intent to prove the viability and value of the technology just a few short years from now. The Solar Sail Demonstration will launch on a Falcon 9 as early as 2014.[51]

## Future approaches

Despite the losses of Cosmos 1 and NanoSail-D (which were due to failure of their launchers), scientists and engineers around the world remain encouraged and continue to work on solar sails. While most direct applications created so far intend to use the sails as inexpensive modes of cargo transport, some scientists are investigating the possibility of using solar sails as a means of transporting humans. This goal is strongly related to the management of very large (i.e. well above 1 km²) surfaces in space and the sail making advancements. Thus, in the near/medium term, solar sail propulsion is aimed chiefly at accomplishing a very high number of non-crewed missions in any part of the solar system and beyond.[citation needed] Manned space flight utilizing solar sails is still in the development state of infancy.

### Solar sail launching projects in 2010 and 2011

On 21 May 2010, Japan Aerospace Exploration Agency (Jaxa) launched the world's first interplanetary solar sail spacecraft "IKAROS" (Interplanetary Kite-craft Accelerated by Radiation Of the Sun) to Venus.[52] NASA launched the second NanoSail-D unit stowed inside the FASTSAT satellite on the Minotaur IV on November 19, 2010. The ejection date from the FASTSAT microsatellite was planned for December 6, 2010 but deployment only occurred on January 20, 2011.[53] The Planetary Society of the United States plans to launch an artificial satellite "LightSail-1" onto the Earth's orbit in 2011.[54]

## Mathematical survey

Solar sail vessels are classified by their lightness number which is the ratio of the acceleration due to the light force on the sail to the force of gravity. (These both vary with the inverse square of distance, so the ratio is constant for any vehicle.) A typical reflective surface needs to provide about 4 square meters of reflective area for every 5 grams of vehicle weight to have a lightness factor of 1.[55]

The light force can be separated into the normal force (away from the light source) and the tangential force as a function of the angle A of the sail face to the light. The Normal Force per area = 8/9 $cos^2 A$ + 1/9 $cos A$. The Tangential Force per area = 4/9 $sin 2A$.

### Extended heliocentric reference frame

• In 1991-92 the classical equations of solar sail motion in the solar gravitational field were written using a different mathematical formalism, namely the lightness vector, fully characterizing the sailcraft dynamics. In addition, a solar sail spacecraft has been supposed to be able to reverse its motion (in the solar system) provided that its sail is sufficiently light that sailcraft sail loading (σ) is not higher than 2.1 g/m². This value entails a very high-performance technology, but probably within the capabilities of emerging technologies.
• For describing the concept of fast sailing and some related items, we need to define two frames of reference. The first is an inertial Cartesian coordinate system centred on the Sun or a heliocentric inertial frame (HIF, for short). For instance, the plane of reference, or the XY plane, of HIF can be the mean ecliptic at some standard epoch such as J2000. The second Cartesian reference frame is the so-called heliocentric orbital frame (HOF, for short) with the origin in the sailcraft barycenter. The x-axis of HOF is the direction of the Sun-to-sailcraft vector, or position vector, the z-axis is along the sailcraft orbital angular momentum, whereas the y-axis completes the counterclockwise triad. Such a definition can be extended to sailcraft trajectories, including both counterclockwise and clockwise arcs of motion, in such a way that HOF is always a continuous positively oriented triad. The sail orientation unit vector (defined in sailcraft), say, n can be specified in HOF by a pair of angles, e.g. the azimuth α and the elevation δ. Elevation is the angle that n forms with the xy-plane of HOF (-90° ≤ δ ≤ 90°). Azimuth is the angle that the projection of n onto the HOF xy-plane forms with the HOF x-axis (0 ≤ α < 360 °). In HOF, azimuth and elevation are equivalent to longitude and latitude, respectively.
• The sailcraft lightness vector L = [λr, λt, λn] depends on α and δ (non-linearly) and the thermo-optical parameters of the sail materials (linearly). Neglecting a small contribution coming from the aberration of light, one has the following particular cases (irrespective of the sail material):
1. α = 0, δ = 0 ⇔ [λr, 0, 0] ⇔ λ=|L|=λr
2. α ≠ 0, δ = 0 ⇔ [λr, λt, 0]
3. α = 0, δ ≠ 0 ⇔ [λr, 0, λn].

### Flight example

#### Conventional strategy

• Suppose a sailcraft is built with an all-metal sail of aluminium and chromium such that σ = 2 g/m². A launcher delivers the (packed) sailcraft at some million kilometers from the Earth. There, the whole sailcraft is deployed and begins its flight in the solar system (here, for the sake of simplicity, any gravitational perturbation from planets is neglected). A conventional spacecraft would move approximately in a circular orbit at about 1 AU from the Sun. In contrast, a sailcraft like this one is sufficiently light to be able to escape the solar system or to point to some distant object in the heliosphere. If the direction that sail's surface faces, represented by surface normal vector n, is parallel to the local sunlight direction (i.e. the sail faces toward the Sun), then λr = λ = 0.725 (i.e. 1/2 < λ < 1); as a result, this sailcraft moves on a hyperbolic orbit. Its speed at infinity is equal to 20 km/s. Strictly speaking, this potential solar sail mission would be faster than the current record speed for missions beyond the planetary range, that of Voyager 1, which is 17 km/s or about 3.6 AU/yr (1 AU/yr = 4.7404 km/s). However, three kilometers per second are not meaningful in the context of very deep space missions.
• As a consequence, one has to resort to some L having more than one component different from zero. The classical way to gain speed is to tilt the sail at some suitable positive α. If α= +21°, then the sailcraft begins by accelerating; after about two months, it achieves 32 km/s. However, this is a speed peak inasmuch as its subsequent motion is characterized by a monotonic speed decrease towards an asymptotic value, or the cruise speed, of 26 km/s. After 18 years, the sailcraft is 100 AU away from the Sun. This would mean a pretty fast mission. However, considering that a sailcraft with 2 g/m² is technologically advanced, is there any other way to increase its speed significantly? Yes, there is. Let us try to explain this effect of non-linear dynamics.

#### Optimal strategy

• The above figures show that spiralling out from a circular orbit is not a convenient mode for a sailcraft to be sent away from the Sun since it would not have a high enough excess speed. On the other hand, it is known from astrodynamics that a conventional Earth satellite has to perform a rocket maneuver at/around its perigee for maximizing its speed at "infinity". Similarly, one can think of delivering a sailcraft close to the Sun to get much more energy from the solar photon pressure that scales as 1/R2. (Inverse-square law) For instance, suppose one starts from a point at 1 AU on the ecliptic and achieves a perihelion distance of 0.2 AU in the same plane by a two-dimensional trajectory. In general, there are three ways to deliver a sailcraft, initially at R0 from the Sun, to some distance R < R0:
• using an additional propulsion system to send the folded-sail sailcraft to the perihelion of an elliptical orbit; there, the sail is deployed with its axis parallel to the sunlight for getting the maximum solar flux at the chosen distance;
• spiralling in by α slightly negative, namely, via a slow deceleration;
• strongly decelerating by a "sufficiently large" sail-axis angle negative in HOF.
The first way - although usable as a good reference mode - requires another high-performance propulsion system.
The second way is ruled out in the present case of σ = 2 g/m²; as a matter of fact, a small α < 0 entails a λr too high and a negative λt too low in absolute value: the sailcraft would go far from the Sun with a decreasing speed (as discussed above).
In the third way, there is a critical negative sail-axis angle in HOF, say, αcr such that for sail orientation angles α < αcr the sailcraft trajectory is characterized as follows:
1. the distance (from the Sun) first increases, achieves a local maximum at some point M, then decreases. The orbital angular momentum (per unit mass), say, H of the sailcraft decreases in magnitude. It is suitable to define the scalar H = Hk, where k is the unit vector of the HIF Z-axis;
2. after a short time (few weeks or less, in general), the sailcraft speed V = |V| achieves a local minimum at a point P. H continues to decrease;
3. past P, the sailcraft speed increases because the total vector acceleration, say, A begins by forming an acute angle with the vector velocity V; in mathematical terms, dV / dt = AV / V > 0. This is the first key-point to realize: the orbital velocity having been largely neutralized, the sailcraft is falling nearly straight toward the Sun under the influence of its gravity, gaining velocity in that direction;
4. eventually, the sailcraft achieves a point Q where H = 0; here, the sailcraft's total energy (per unit mass), say, E (including the contribution of the solar pressure on the sail) shows a (negative) local minimum. This is the second key-point: in the absence of continued light pressure, the craft would fall directly into the Sun;
5. past Q, the sailcraft - keeping the negative value of the sail orientation - regains angular momentum by reversing its original motion (that is H is oriented downward in the diagram and H < 0 means the trajectory is now clockwise or retrograde motion, the opposite of normal planetary orbits). R (distance from Sun) decreases rapidly while dV/dt (acceleration) increases. This is the third key-point;
6. the sailcraft energy continues to increase and a point S is reached where E=0, namely, the escape condition is satisfied (V is greater than solar escape velocity); the sailcraft continues accelerating. S is located before the perihelion. The (negative) H becomes increasingly negative (retrograde);
7. if the sail attitude α has been chosen appropriately (about -25.9 deg in this example), the sailcraft flies-by the Sun at the desired (0.2 AU) perihelion, say, U; however, differently from a Keplerian orbit (for which the perihelion is the point of maximum speed), past the perihelion, V increases further while the sailcraft rapidly accelerates away from the Sun due to the much stronger photon pressure at small distances from the Sun;
8. past U, the sailcraft is very fast and passes through a point, say, W of local maximum for the speed, since λ < 1. Thus, speed decreases but, at a few AU from the Sun (about 2.7 AU in this example), both the (positive) E and the (negative) H begin a plateau or cruise phase; V becomes practically constant and, the most important thing, takes on a cruise value considerably higher than the speed of the circular orbit of the departure planet (the Earth, in this case). This example shows a cruise speed of 14.75 AU/yr or 69.9 km/s. At 100 AU, the sailcraft speed is still 69.6 km/s. The net effect is a powered slingshot maneuver utilizing the Oberth effect to achieve a much higher final velocity than would otherwise be possible.

#### H-reversal Sun flyby trajectory

The figure below shows the optimal sailcraft trajectory mentioned above. Only the initial arc around the Sun has been plotted. The remaining part is rectilinear, in practice, and represents the cruise phase of the spacecraft. The sail is represented by a short segment with a central arrow that indicates its direction of thrust. Note that the complicated change of sail direction in HIF is very simply achieved by a constant attitude in HOF. That brings about a net non-Keplerian feature to the whole trajectory.
• As mentioned in point-3, past P the strong sailcraft speed increase is due to both the solar-light thrust (reducing the residual orbital angular momentum) and gravity (towards the Sun) acceleration vectors. In particular, dV / dt, or the along-track (sunward) component of the total acceleration, is positive and particularly high from the point-Q to the point-U. This suggests that if a quick sail attitude maneuver is performed just before H vanishes, α → -α, the sailcraft motion continues to be a direct motion with a final cruise velocity equal in magnitude to the total velocity reversal (because the above maneuver keeps the perihelion value unchanged). The basic principle may be summarised as follows: a sufficiently light sailcraft, by losing most of its initial energy, subsequently achieves the absolute maximum of energy compliant with its given technology.
• The above 2D class of new trajectories represents an ideal case. The realistic 3D fast sailcraft trajectories are considerably more complicated than the 2D cases. However, the general feature of producing a fast cruise speed can be further enhanced. Some of the enclosed references[clarification needed] contain strict mathematical algorithms for dealing with this topic. Recently (July 2005), in an international symposium an evolution of the above concept of fast solar sailing has been discussed.[clarification needed] A sailcraft with σ = 1 g/m² could achieve over 30 AU/yr (0.000474 c) in cruise (by keeping the perihelion at 0.2 AU), namely, well beyond the cruise speed of any nuclear-electric spacecraft (at least as conceived today). Such paper has been published on the Journal of the British Interplanetary Society (JBIS) in 2006.[clarification needed]

The complete (2D and 3D) theory of the theory of the sailcraft reverse motion has been developed only in the last five years, and can be found in a very recent book from Springer (August 2012) (see Bibliography).

## In science fiction

The earliest reference to solar sailing was in Jules Verne's 1865 novel From the Earth to the Moon, coming only a year after Maxwell's equations were published. The next known publication came more than 20 years later when Georges Le Faure and Henri De Graffigny published a four-volume science fiction novel in 1889, The Extraordinary Adventures of a Russian Scientist, which included a spacecraft propelled by solar pressure. B. Krasnogorskii published On the Waves of the Ether in 1913. In his story backed by technical calculations, a small, bullet-shaped capsule is surrounded by a circular mirror 35 meters in diameter. It travels through space by means of solar pressure on the mirror.

One of the earliest American stories about light sails is "The Lady Who Sailed the Soul" by Cordwainer Smith, which was published in 1960. In it, a tragedy results from the slowness of interstellar travel by this method. Another example is the 1962 story "Gateway to Strangeness" (also known as "Sail 25") by Jack Vance, in which the outward direction of propulsion poses a life-threatening dilemma. Also in early 20th century literature, Pierre Boulle's Planet of the Apes starts with a couple floating in space on a ship propelled and maneuvered by light sails. In Larry Niven and Jerry Pournelle's The Mote in God's Eye, a sail is used as a brake and a weapon. Author and scientist Arthur C. Clarke depicted a "yacht race" between solar sail spacecraft in the 1964 short story "Sunjammer". In "Flight of the Dragonfly", Robert Forward (who also proposed the microwave-pushed Starwisp design) described an interstellar journey using a light driven propulsion system, wherein a part of the sail was broken off and used as a reflector to slow the main spacecraft as it approached its destination. In the 1982 film Tron, a "Solar Sailer" was an inner spacecraft with butterfly like sails moved along focused beam of light. The 1983 episode "Enlightenment" of Doctor Who featured sailing ships in space which used solar wind to fly. In the episode "Explorers" of Star Trek: Deep Space Nine that aired in 1995, a "light ship" was featured. It was designed to use solar wind to fly out of a solar system with no engine.[56] In the film Star Wars Episode II: Attack of the Clones one is used by Count Dooku to propel himself across space. A solar sail was also used in James Cameron's Avatar. In the Disney film Treasure Planet, solar sails are used literally as sails for interstellar travel of a steampunk-styled masted sailing ship capable of traveling through space.

## References

1. ^ R.M. Georgevic (1973) "The Solar Radiation Pressure Forces and Torques Model", The Journal of the Astronautical Sciences, Vol. 27, No. 1, Jan-Feb. First known publication describing how solar radiation pressure creates forces and torques that affect spacecraft.
2. ^ a b c d Jerome Wright (1992), Space Sailing, Gordon and Breach Science Publishers
3. ^ Johannes Kepler (1604) Ad vitellionem parali pomena , Frankfort; ( 1619) De cometis liballi tres , Augsburg
4. ^ Jules Verne (1865) De la Terre à la Lune (From the Earth to the Moon)
5. ^ P. Lebedev, 1901, "Untersuchungen über die Druckkräfte des Lichtes", Annalen der Physik, 1901
6. ^ Lee, Dillon (2008). "A Celebration of the Legacy of Physics at Dartmouth". Dartmouth Undergraduate Journal of Science. Dartmouth College. Retrieved 2009-06-11.
7. ^ Svante Arrhenius (1908) Worlds in the Making
8. ^ Friedrich Zander‘s 1925 paper, “Problems of flight by jet propulsion: interplanetary flights,” was translated by NASA. See NASA Technical Translation F-147 (1964)
9. ^ J.D. Bernal (1929) The World, the Flesh & the Devil: An Enquiry into the Future of the Three Enemies of the Rational Soul
10. ^
11. ^ Wright, ibid, Appendix A
12. ^ Wright, ibid., Appendix A
13. ^ McInnes, C.R. and Brown, J.C. (1989) Solar Sail Dynamics with an Extended Source of Radiation Pressure, International Astronautical Federation, IAF-89-350, October.
14. ^ Wright, ibid, Appendix B.
15. ^
16. ^ Wright, ibid., Ch 6 and Appendix B.
17. ^ "MESSENGER Sails on Sun's Fire for Second Flyby of Mercury". 2008-09-05. "On September 4, the MESSENGER team announced that it would not need to implement a scheduled maneuver to adjust the probe's trajectory. This is the fourth time this year that such a maneuver has been called off. The reason? A recently implemented navigational technique that makes use of solar-radiation pressure (SRP) to guide the probe has been extremely successful at maintaining MESSENGER on a trajectory that will carry it over the cratered surface of Mercury for a second time on October 6."
18. ^ Forward, R.L. (1984). "Roundtrip Interstellar Travel Using Laser-Pushed Lightsails". J Spacecraft 21 (2): 187–195. Bibcode:1984JSpRo..21..187F. doi:10.2514/3.8632.
19. ^ "Earth To Mars in a Month With Painted Solar Sail". SPACE.com. 2005-02-11. Retrieved 2011-01-18.
20. ^ Gregory L., Michael N.; Matloff (1979). Journal of the British Interplanetary Society 32: 419–423 http://www.astro-ecology.com/PDFDirectedPanspermia1JBIS1997Paper.pdf `|url=` missing title (help). Unknown parameter `|first title=` ignored (help)
21. ^ Mautner, Michael N. (1995). "Directed panspermia. 2. Technological advances toward seeding other solar systems, and the foundations of panbiotic ethics". Journal of the British Interplanetary Society 48: 435–440.
22. ^ Wright, ibid., p71, last para
23. ^ a b Drexler, K.E. (1977). "Design of a High Performance Solar Sail System, MS Thesis,". Dept. of Aeronautics and Astronautics, Massachusetts Institute of Techniology, Boston.
24. "Design & Construction". NASA JPL. Archived from the original on 2005-03-11.
25. ^ a b Khayatian, Rahmatsamii, Porgorzelski, UCLA and JPL. "An Antenna Concept Integrated with Future Solar Sails".
26. ^
27. ^ Zubrin & Andrew's presentation in a pdf.
28. ^ Geoffrey A. Landis, Ohio Aerospace Institute (1999). "Advanced Solar- and Laser-pushed Lightsail Concepts".
29. ^ a b
30. ^ "Researchers produce strong, transparent carbon nanotube sheets". Physorg.com. 2005-08-18. Retrieved 2011-01-18.
31. ^ Tsuda, Yuichi (2011). "Solar Sail Navigation Technology of IKAROS". JAXA.
32. ^ "Small Solar Power Sail Demonstrator 'IKAROS' Successful Solar Sail Deployment". JAXA website press release. Japan Aerospace Exploration Agency. 2010-06-11. Retrieved 2010-06-17.
33. ^ "News briefing: 27 May 2010". NatureNEWS. 26 May 2010. Retrieved 2 June 2010.
34. ^ Samantha Harvey (21 May 2010). "Solar System Exploration: Missions: By Target: Venus: Future: Akatsuki". NASA. Retrieved 2010-05-21.
35. ^ "About the confirmation of photon acceleration of "IKAROS" the small solar-sail demonstrating craft (There is not English press release yet)". JAXA website press release. Japan Aerospace Exploration Agency. 2010-07-09. Retrieved 2010-07-10.
36. ^ "Small Solar Power Sail Demonstrator". JAXA. 11 March 2010. Retrieved 2010-05-07.
37. ^ "IKAROS Project". JAXA. 2008. Retrieved 30 March 2010.
38. ^ McCurry, Justin (2010-05-17). "Space yacht Ikaros ready to cast off for far side of the Sun". London: The Guardian Weekly. Retrieved 2010-05-18.
39. ^
40. ^
41. ^
42. ^ OVERBYE, DENNIS (November 9, 2009). "Setting Sail Into Space, Propelled by Sunshine". Retrieved 18 May 2012. "Planetary Society, ... the next three years, ... series of solar-sail spacecraft dubbed LightSails"
43. ^ a b "LightSail Mission FAQ". The Planetary Society. Retrieved 18 May 2012.
44. ^ "LightSail-1 on NASA Short List for Upcoming Launch". planetary.org. 2011-02-09. Retrieved 2012-05-18.
45. ^ "SSSat 1, 2". Space.skyrocket.de. Retrieved 2011-01-18.
46. ^
47. ^ "NASA to Attempt Historic Solar Sail Deployment". NASA. 2008-06-26.
48. ^ "NASA Chat: First Solar Sail Deploys in Low-Earth Orbit". NASA. 2011-01-27. Retrieved 18 May 2012. "Sometimes the satellite is called NanoSail-D and sometimes NanoSail-D2. ... Dean: The project is just NanoSail-D. NanoSail-D2 is the serial #2 version."
49. ^ Nasa report on mission
50. ^ Nasa report on mission
51. ^ "Nasa Solar Sail Demonstration". www.nasa.gov.
52. ^ "IKAROS Project｜JAXA Space Exploration Center". Jspec.jaxa.jp. 2010-05-21. Retrieved 2011-01-18.
54. ^ "LightSail-1- A Solar Sail Missio no fThe Planetary Society". Planetary.org. Retrieved 2011-01-18.
55. ^ http://240plan.ovh.net/~upngmmxw/projets/doc/HoustonU3P.pdf
56. ^

## Bibliography

• G. Vulpetti, Fast Solar Sailing: Astrodynamics of Special Sailcraft Trajectories, Space Technology Library Vol. 30, Springer, August 2012, (Hardcover) http://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, the chapter IV - presents the theory and the optimal NASA-ISP 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