A
celestial body (yellow) is orbited by a mass of fluid (blue) held
together by gravity, here viewed from above the orbital plane. Far from
the Roche limit (white line), the mass is practically spherical.
Closer to the Roche limit, the body is deformed by tidal forces.
Within the Roche limit, the mass's own gravity can no longer withstand the tidal forces, and the body disintegrates.
Particles closer to the primary move more quickly than particles farther away, as represented by the red arrows.
The varying orbital speed of the material eventually causes it to form a ring.
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit, material tends to coalesce. The Roche radius depends on the radius of the second body and on the ratio of the bodies' densities.
Comet Shoemaker–Levy 9 was disintegrated by the tidal forces of Jupiter into a string of smaller bodies in 1992, before colliding with the planet in 1994.
The Roche limit typically applies to a satellite's disintegrating due to tidal forces induced by its primary, the body around which it orbits.
Parts of the satellite that are closer to the primary are attracted
more strongly by gravity from the primary than parts that are farther
away; this disparity effectively pulls the near and far parts of the
satellite apart from each other, and if the disparity (combined with any
centrifugal effects due to the object's spin) is larger than the force
of gravity holding the satellite together, it can pull the satellite
apart. Some real satellites, both natural and artificial,
can orbit within their Roche limits because they are held together by
forces other than gravitation. Objects resting on the surface of such a
satellite would be lifted away by tidal forces. A weaker satellite, such
as a comet, could be broken up when it passes within its Roche limit.
Since, within the Roche limit, tidal forces overwhelm the
gravitational forces that might otherwise hold the satellite together,
no satellite can gravitationally coalesce out of smaller particles
within that limit. Indeed, almost all known planetary rings are located within their Roche limit. (Notable exceptions are Saturn's E-Ring and Phoebe ring. These two rings are formed from particles released from the moons Enceladus and Phoebe due to cryovolcanic plumes and meteoroid impacts, respectively.)
The gravitational effect occurring below the Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure, and rotational splitting are other ways for a comet to split under stress.
Determination
The limiting distance to which a satellite
can approach without breaking up depends on the rigidity of the
satellite. At one extreme, a completely rigid satellite will maintain
its shape until tidal forces break it apart. At the other extreme, a
highly fluid satellite gradually deforms leading to increased tidal
forces, causing the satellite to elongate, further compounding the tidal
forces and causing it to break apart more readily.
Most real satellites would lie somewhere between these two
extremes, with tensile strength rendering the satellite neither
perfectly rigid nor perfectly fluid. For example, a rubble-pile asteroid
will behave more like a fluid than a solid rocky one; an icy body will
behave quite rigidly at first but become more fluid as tidal heating
accumulates and its ices begin to melt.
But note that, as defined above, the Roche limit refers to a body
held together solely by the gravitational forces which cause otherwise
unconnected particles to coalesce, thus forming the body in question.
The Roche limit is also usually calculated for the case of a circular
orbit, although it is straightforward to modify the calculation to apply
to the case (for example) of a body passing the primary on a parabolic
or hyperbolic trajectory.
Rigid satellites
The rigid-body Roche limit is a simplified calculation for a spherical
satellite. Irregular shapes such as those of tidal deformation on the
body or the primary it orbits are neglected. It is assumed to be in hydrostatic equilibrium. These assumptions, although unrealistic, greatly simplify calculations.
The Roche limit for a rigid spherical satellite is the distance, ,
from the primary at which the gravitational force on a test mass at the
surface of the object is exactly equal to the tidal force pulling the
mass away from the object:
where is the radius of the primary, is the density of the primary, and is the density of the satellite. This can be equivalently written as
where is the radius of the secondary, is the mass of the primary, and
is the mass of the secondary. A third equivalent form which uses only
one property for each of the two bodies, the mass of the primary and the
density of the secondary, is
(where 0.7816 = (3/2π)^(1/3) )
These all represent the orbital distance inside of which loose material (e.g. regolith)
on the surface of the satellite closest to the primary would be pulled
away, and likewise material on the side opposite the primary will also
go away from, rather than toward, the satellite.
Fluid satellites
A
more accurate approach for calculating the Roche limit takes the
deformation of the satellite into account. An extreme example would be a
tidally locked liquid satellite orbiting a planet, where any force acting upon the satellite would deform it into a prolate spheroid.
The calculation is complex and its result cannot be represented
in an exact algebraic formula. Roche himself derived the following
approximate solution for the Roche limit:
However, a better approximation that takes into account the primary's oblateness and the satellite's mass is:
The fluid solution is appropriate for bodies that are only loosely held together, such as a comet. For instance, comet Shoemaker–Levy 9's
decaying orbit around Jupiter passed within its Roche limit in July
1992, causing it to fragment into a number of smaller pieces. On its
next approach in 1994, the fragments crashed into the planet.
Shoemaker–Levy 9 was first observed in 1993, but its orbit indicated
that it had been captured by Jupiter a few decades prior.
IKAROS,
the first space-probe with a solar sail in flight (artist's depiction),
featuring a typical square sail configuration of almost 200 m2
Solar sails (also known as lightsails, light sails, and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight
on large surfaces. A number of spaceflight missions to test solar
propulsion and navigation have been proposed since the 1980s. The two
spacecraft to successfully use the technology for propulsion were IKAROS, launched in 2010, and LightSail-2, launched in 2019.
A useful analogy to solar sailing may be a sailing boat; the light exerting a force on the large surface 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 high speeds (relative to chemical rockets)
and long operating lifetimes. Since they have few moving parts and use
no propellant, they can potentially be used numerous times for the
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.
The total force exerted on an 800 by 800 metres (2,600 by 2,600 ft) solar sail, for example, is about 5 N (1.1 lbf) at Earth's distance from the Sun, 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.
The theory of electromagnetic fields and radiation, first published by James Clerk Maxwell in 1861–1864, 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.
Pyotr Lebedev was first to successfully demonstrate light pressure, which he did in 1899 with a torsional balance; Ernest Nichols and Gordon Hull conducted a similar independent experiment in 1901 using a Nichols radiometer.
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 was apparently the first scientist to state that light could move objects between stars.
Konstantin Tsiolkovsky first proposed using the pressure of sunlight to propel spacecraft through space in 1921 and suggested "using tremendous mirrors of very thin sheets to utilize the pressure of sunlight to attain cosmic velocities".
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".
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".
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."
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.[17]
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.
Types
Reflective
Most solar sails are based on reflection. The surface of the sail is highly reflective, like a mirror, and light reflecting off of the surface imparts a force.
Pekka Janhunen from FMI has proposed a type of solar sail called the electric solar wind sail. 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.
Electric solar wind sails can adjust their electrostatic fields and sail attitudes.
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.
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.
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:
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:
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, 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), and by the square of the cosine of the angle between the sail force vector and the radial from the Sun, so
(for an ideal sail)
where R is distance from the Sun in AU. An actual square sail can be modelled as:
Note that the force and acceleration approach zero generally around θ
= 60° rather than 90° as one might expect with an ideal sail.
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.
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. 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.
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.
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.
Inner planets
For
trips within the inner Solar System, they can deliver payloads and then
return to Earth for subsequent voyages, operating as an interplanetary
shuttle. For Mars in particular, the craft could provide economical
means of routinely supplying operations on the planet. According to
Jerome Wright, "The cost of launching the necessary conventional
propellants from Earth are enormous for manned missions. Use of sailing
ships could potentially save more than $10 billion in mission costs."
Solar sail craft can approach the Sun to deliver observation
payloads or to take up station keeping orbits. They can operate at 0.25
AU or closer. They can reach high orbital inclinations, including
polar.
Solar sails can travel to and from all of the inner planets.
Trips to Mercury and Venus are for rendezvous and orbit entry for the
payload. Trips to Mars could be either for rendezvous or swing-by with
release of the payload for aerodynamic braking.
Sail size m
Mercury Rendezvous
Venus Rendezvous
Mars Rendezvous
Mars Aerobrake
days
tons
days
tons
days
tons
days
tons
800 σ = 5 g/m2 w/o cargo
600
9
200
1
400
2
131
2
900
19
270
5
500
5
200
5
1200
28
700
9
338
10
2000 σ = 3 g/m2 w/o cargo
600
66
200
17
400
23
131
20
900
124
270
36
500
40
200
40
1200
184
700
66
338
70
Outer planets
Minimum
transfer times to the outer planets benefit from using an indirect
transfer (solar swing-by). However, this method results in high arrival
speeds. Slower transfers have lower arrival speeds.
The minimum transfer time to Jupiter for ac of 1 mm/s2 with no departure velocity relative to Earth is 2 years when using an indirect transfer (solar swing-by). The arrival speed (V∞) is close to 17 km/s. For Saturn, the minimum trip time is 3.3 years, with an arrival speed of nearly 19 km/s.
Minimum times to the outer planets (ac = 1 mm/s2)
Jupiter
Saturn
Uranus
Neptune
Time, yr
2.0
3.3
5.8
8.5
Speed, km/s
17
19
20
20
Oort Cloud/Sun's inner gravity focus
The Sun's inner gravitational focus point lies at minimum distance of 550 AU from the Sun, and is the point to which light from distant objects is focused by gravity
as a result of it passing by the Sun. This is thus the distant point to
which solar gravity will cause the region of deep space on the other
side of the Sun to be focused, thus serving effectively as a very large
telescope objective lens.t has been proposed that an inflated sail, made of beryllium, that starts at 0.05 AU from the Sun would gain an initial acceleration of 36.4 m/s2,
and reach a speed of 0.00264c (about 950 km/s) in less than a day. Such
proximity to the Sun could prove to be impractical in the near term due
to the structural degradation of beryllium at high temperatures,
diffusion of hydrogen at high temperatures as well as an electrostatic
gradient, generated by the ionization of beryllium from the solar wind,
posing a burst risk. A revised perihelion of 0.1 AU would reduce the
aforementioned temperature and solar flux exposure. Such a sail would take "Two and a half years to reach the heliopause, six and a half years to reach the Sun’s inner gravitational focus, with arrival at the inner Oort Cloud in no more than thirty years." "Such a mission could perform useful astrophysical observations en
route, explore gravitational focusing techniques, and image Oort Cloud
objects while exploring particles and fields in that region that are of
galactic rather than solar origin."
Satellites
Robert L. Forward
has commented that a solar sail could be used to modify the orbit of a
satellite about 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 such that they 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 attraction of the Sun. Such an orbit could be useful
for studying the properties of the Sun for long durations. Likewise a solar sail-equipped spacecraft could also remain on station nearly above the polar solar terminator of a planet such as the Earth by tilting the sail at the appropriate angle needed to counteract the planet's gravity.
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 focused on one of
the Martian polar ice caps to significantly warm the planet's
atmosphere. Such a statite could be made from asteroid material.
A group of satellites designed to act as sails has been proposed to measure Earth's energy imbalance which is the most fundamental measure of the planet's rate of global warming. On-board state-of-the-art accelerometers would measure shifts in the pressure differential between incoming solar and outgoing thermal radiation on opposing sides of each satellite. Measurement accuracy has been projected to be better than that achievable with compact radiometric detectors.
Trajectory corrections
The MESSENGER probe orbiting Mercury used light pressure on its solar panels to perform fine trajectory corrections on the way to Mercury. 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.
In the science fiction novel Rocheworld,
Forward described a light sail propelled by super lasers. 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 need to be located at 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 directed at the sail, since
the manipulation of microwave radiation is somewhat easier than the
manipulation of visible light. The hypothetical "Starwisp" interstellar probe design would use microwaves, rather than visible light, to push it. Masers
spread out more rapidly than optical lasers owing to their longer
wavelength, and so would not have as great 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. 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, Forward proposed a lens designed as a large zone plate. This would be placed at a location between the laser or maser and the spacecraft.
Another more physically realistic approach would be to use the light from the Sun to accelerate the spacecraft. The ship would first drop into an orbit making a close pass to the Sun,
to maximize the solar energy input on the sail, then it would begin to
accelerate away from the system using the light from the Sun.
Acceleration will drop approximately as the inverse square of the
distance from the Sun, and beyond some distance, the ship would no
longer receive enough light to accelerate it significantly, but would
maintain the final velocity attained. When nearing the target star, the
ship could turn its sails toward it and begin to use the outward
pressure of the destination star to decelerate. Rockets could augment
the solar thrust.
Similar solar sailing launch and capture were suggested for directed panspermia
to expand life in other solar systems. Velocities of 0.05% the speed of
light could be obtained by solar sails carrying 10 kg payloads, using
thin solar sail vehicles with effective areal densities of 0.1 g/m2 with thin sails of 0.1 μm
thickness and sizes on the order of one square kilometer.
Alternatively, swarms of 1 mm capsules could be launched on solar sails
with radii of 42 cm, each carrying 10,000 capsules of a hundred million extremophile microorganisms to seed life in diverse target environments.
Theoretical studies suggest relativistic speeds if the solar sail harnesses a supernova.
Deorbiting artificial satellites
Small
solar sails have been proposed to accelerate the deorbiting of small
artificial satellites from Earth orbits. Satellites in low Earth orbit can use a combination of solar pressure on the sail and increased atmospheric drag to accelerate satellite reentry. A de-orbit sail developed at Cranfield University
is part of the UK satellite TechDemoSat-1, launched in 2014. The sail
deployed at the end of the satellite's five-year useful life in May
2019. The sail's purpose is to bring the satellite out of orbit over a period of about 25 years. In July 2015 British 3U CubeSat called DeorbitSail was launched into space with the purpose of testing 16 m2 deorbit structure, but eventually it failed to deploy it. A student 2U CubeSat mission called PW-Sat2, launched in December 2018 and tested a 4 m2 deorbit sail. It successfully deorbited in February 2021. In June 2017, a second British 3U CubeSat called InflateSail deployed a 10 m2 deorbit sail at an altitude of 500 kilometers (310 mi). In June 2017 the 3U Cubesat URSAMAIOR has been launched in low Earth orbit to test the deorbiting system ARTICA developed by Spacemind. The device, which occupies only 0.4 U of the cubesat, shall deploy a sail of 2.1 m2 to deorbit the satellite at the end of the operational life.
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
IKAROS,
launched in 2010, was the first practical solar sail vehicle. As of
2015, it was still under thrust, proving the practicality of a solar
sail for long-duration missions. It is spin-deployed, with tip-masses in the corners of its square sail. The sail is made of thin polyimide film, coated with evaporated aluminium. It steers with electrically controlled liquid crystal
panels. The sail slowly spins, and these panels turn on and off to
control the attitude of the vehicle. When on, they diffuse light,
reducing the momentum transfer to that part of the sail. When off, the
sail reflects more light, transferring more momentum. In that way, they
turn the sail. Thin-film solar cells
are also integrated into the sail, powering the spacecraft. The design
is very reliable, because spin deployment, which is preferable for
large sails, simplified the mechanisms to unfold the sail and the LCD
panels have no moving parts.
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.
The highest thrust-to-mass designs for ground-assembled deploy-able 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 moving sails on the ends of the
spars.
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.
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. The CubeSail (UltraSail) is an active project aiming to deploy a heliogyro sail.
Heliogyro design is similar to the blades on a helicopter. The
design is faster to manufacture due to lightweight centrifugal
stiffening of sails. Also, they are highly efficient in cost and
velocity because the blades are lightweight and long. Unlike the square
and spinning disk designs, heliogyro is easier to deploy because the
blades are compacted on a reel. The blades roll out when they are
deploying after the ejection from the spacecraft. As the heliogyro
travels through space the system spins around because of the centrifugal
acceleration. Finally, payloads for the space flights are placed in the
center of gravity to even out the distribution of weight to ensure
stable flight.
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 crewed structures. The
inner ring, in particular, might be made to have artificial gravity
roughly equal to the gravity on the surface of Mars.
A solar sail can serve a dual function as a high-gain antenna. Designs differ, but most modify the metalization pattern to create a holographic monochromatic lens or mirror in the radio frequencies of interest, including visible light.
Reflective sail making
Proposed material for the construction of solar sails - carbon fiber.
Materials
The
most common material in current designs is a thin layer of aluminum
coating on a polymer (plastic) sheet, such as aluminized 2 μm Kapton
film. The polymer provides mechanical support as well as flexibility,
while the thin metal layer provides the reflectivity. Such material
resists the heat of a pass close to the Sun and still remains reasonably
strong. The aluminum reflecting film is on the Sun side. The sails of Cosmos 1 were made of aluminized PET film (Mylar).
Eric Drexler developed a concept for a sail in which the polymer was removed. He 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 deploy-able plastic
films. The material developed for the Drexler solar sail was a thin aluminium
film with a baseline thickness of 0.1 μm, 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.
Research by Geoffrey Landis in 1998–1999, 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.
In 2000, Energy Science Laboratories developed a new carbon fiber material that might be useful for solar sails. 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, 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, and Energy Science Laboratories' new carbon fiber material masses 3 g/m2.
The least dense metal is lithium,
about 5 times less dense than aluminium. Fresh, unoxidized surfaces
are reflective. At a thickness of 20 nm, lithium has an area density of
0.011 g/m2. A high-performance sail could be made of
lithium alone at 20 nm (no emission layer). It would have to be
fabricated in space and not used to approach the Sun. In the limit, a
sail craft might be constructed with a total areal density of around
0.02 g/m2, giving it a lightness number of 67 and ac of about 400 mm/s2. Magnesium and beryllium are also potential materials for high-performance sails. These 3 metals can be alloyed with each other and with aluminium.
Reflection and emissivity layers
Aluminium
is the common choice for the reflection layer. It typically has a
thickness of at least 20 nm, with a reflectivity of 0.88 to 0.90.
Chromium is a good choice for the emission layer on the face away from
the Sun. It can readily provide emissivity values of 0.63 to 0.73 for
thicknesses from 5 to 20 nm on plastic film. Usable emissivity values
are empirical because thin-film effects dominate; bulk emissivity values
do not hold up in these cases because material thickness is much
thinner than the emitted wavelengths.
Fabrication
Sails
are fabricated on Earth on long tables where ribbons are unrolled and
joined to create the sails. Sail material needed to have as little
weight as possible because it would require the use of the shuttle to
carry the craft into orbit. Thus, these sails are packed, launched, and
unfurled in space.
In the future, fabrication could take place in orbit inside large
frames that support the sail. This would result in lower mass sails
and elimination of the risk of deployment failure.
Operations
Rendering of the deployment of a solar sail, the solar sail of the Advanced Composite Solar Sail System (ACS3)A solar sail can spiral inward or outward by setting the sail angle
Changing orbits
Sailing
operations are simplest in interplanetary orbits, where altitude
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. It is worth
noting that only the Sun's gravity pulls the craft toward the Sun—there
is no analog to a sailboat's tacking to windward. 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.
Trajectory optimizations can often require intervals of reduced
or zero thrust. This can be achieved by rolling the craft around the
Sun line with the sail set at an appropriate angle to reduce or remove
the thrust.
Swing-by maneuvers
A
close solar passage can be used to increase a craft's energy. The
increased radiation pressure combines with the efficacy of being deep in
the Sun's gravity well to substantially increase the energy for runs to
the outer Solar System. The optimal approach to the Sun is done by
increasing the orbital eccentricity while keeping the energy level as
high as practical. The minimum approach distance is a function of sail
angle, thermal properties of the sail and other structure, load effects
on structure, and sail optical characteristics (reflectivity and
emissivity). A close passage can result in substantial optical
degradation. Required turn rates can increase substantially for a close
passage. A sail craft arriving at a star can use a close passage to
reduce energy, which also applies to a sail craft on a return trip from
the outer Solar System.
A lunar swing-by can have important benefits for trajectories
leaving from or arriving at Earth. This can reduce trip times,
especially in cases where the sail is heavily loaded. A swing-by can
also be used to obtain favorable departure or arrival directions
relative to Earth.
A planetary swing-by could also be employed similar to what is
done with coasting spacecraft, but good alignments might not exist due
to the requirements for overall optimization of the trajectory.
Laser powered
Artist rendering of a light sail propelled by an Earth based laser
The following table lists some example concepts using beamed laser propulsion as proposed by the physicist Robert L. Forward:
Mission
Laser power
Vehicle mass
Acceleration
Sail diameter
Maximum velocity (% of the speed of light)
1. Flyby – Alpha Centauri, 40 years
outbound stage
65 GW
1 t
0.036 g
3.6 km
11% @ 0.17 ly
2. Rendezvous – Alpha Centauri, 41 years
outbound stage
7,200 GW
785 t
0.005 g
100 km
21% @ 4.29 ly
deceleration stage
26,000 GW
71 t
0.2 g
30 km
21% @ 4.29 ly
3. Crewed – Epsilon Eridani, 51 years (including 5 years exploring star system)
outbound stage
75,000,000 GW
78,500 t
0.3 g
1000 km
50% @ 0.4 ly
deceleration stage
21,500,000 GW
7,850 t
0.3 g
320 km
50% @ 10.4 ly
return stage
710,000 GW
785 t
0.3 g
100 km
50% @ 10.4 ly
deceleration stage
60,000 GW
785 t
0.3 g
100 km
50% @ 0.4 ly
Interstellar travel catalog to use photogravitational assists for a full stop
Successive assists at α Cen A and B could allow travel times to 75 yr to both stars.
Lightsail has a nominal mass-to-surface ratio (σnom) of 8.6×10−4 gram m−2 for a nominal graphene-class sail.
Area of the Lightsail, about 105 m2 = (316 m)2
Velocity up to 37,300 km s−1 (12.5% c). Ref:
Projects operating or completed
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 on its solar paddles as a method of attitude control to compensate for broken reaction wheels and chemical thruster.
MTSAT-1R (Multi-Functional Transport Satellite)'s
solar sail counteracts the torque produced by sunlight pressure on the
solar array. The trim tab on the solar array makes small adjustments to
the torque balance.
Ground deployment tests
NASA has successfully tested deployment technologies on small scale sails in vacuum chambers.
In 1999, a full-scale deployment of a solar sail was tested on the ground at DLR/ESA in Cologne.
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.
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.
Znamya 2
Znamya-2 (Знамя-2) after its deployment
On February 4, 1993, the Znamya 2, a 20-meter wide aluminized-mylar reflector, was successfully deployed from the Russian Mir
space station. It was the first thin film reflector of such type
successfully deployed in space using the mechanism based on centrifugal
force. Although the deployment succeeded, propulsion was not demonstrated. A second test in 1999, Znamya 2.5, failed to deploy properly.
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. Using a new solar-photon propulsion method, it was the first true solar sail spacecraft fully propelled by sunlight, and was the first spacecraft to succeed in solar sail flight.
JAXA successfully tested IKAROS in 2010. The goal was to deploy
and control the sail and, for the first time, to determine 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.
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 spacecraft, which deployed
a 200 m2 polyimide experimental solar sail on June 10. 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. 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 14×14 m (196 m2) made of a 7.5-micrometre (0.0075 mm) thick sheet of polyimide. The polyimide sheet had a mass of about 10 grams per square metre. 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. IKAROS spent six months traveling to Venus, and then began a three-year journey to the far side of the Sun.
A photo of the experimental solar sail, 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. The second backup version, NanoSail-D2, also sometimes called simply NanoSail-D, 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. 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.
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.
On June 21, 2005, a joint private project between Planetary Society, Cosmos Studios and Russian Academy of Science launched a prototype sail Cosmos 1 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. The launch attempt sparked
public interest according to Louis Friedman. Despite the failed launch attempt of Cosmos 1, The Planetary Society received applause for their efforts from the space community and sparked a rekindled interest in solar sail technology.
On Carl Sagan's 75th birthday (November 9, 2009) the Planetary Society announced plans to make three further attempts, dubbed LightSail-1, -2, and -3. The new design will use a 32 m2 Mylar sail, deployed in four triangular segments like NanoSail-D. The launch configuration is a 3U CubeSat format, and as of 2015, it was scheduled as a secondary payload for a 2016 launch on the first SpaceXFalcon Heavy launch.
"LightSail-1" was launched on 20 May 2015. The purpose of the test was to allow a full checkout of the satellite's
systems in advance of LightSail-2. Its deployment orbit was not high
enough to escape Earth's atmospheric drag and demonstrate true solar
sailing.
Deployed LightSail-2
"LightSail-2" was launched on 25 June 2019, and deployed into a much higher low Earth orbit. Its solar sails were deployed on 23 July 2019. It reentered the atmosphere on 17 November 2022. LightSail-2 successfully demonstrated propulsion by solar sail.
The Near-Earth Asteroid Scout (NEA Scout) was a mission jointly developed by NASA's Marshall Space Flight Center (MSFC) and the Jet Propulsion Laboratory (JPL), consisting of a controllable low-cost CubeSat solar sail spacecraft capable of encountering near-Earth asteroids (NEA). Four 7 m (23 ft) booms were to deploy, unfurling the 83 m2 (890 sq ft) aluminized polyimide solar sail. In 2015, NASA announced it had selected NEA Scout to launch as one of several secondary payloads aboard Artemis 1, the first flight of the agency's heavy-lift SLS launch vehicle. However, the craft was considered lost with the failure to establish communications shortly after launch in 2022.
Advanced Composite Solar Sail System (ACS3)
Advanced Composite Solar Sail System testing
The NASA Advanced Composite Solar Sail System (ACS3) is a technology demonstration of solar sail technology for future small spacecraft. It was selected in 2019 by NASA's CubeSat Launch Initiative (CSLI) to be launched as part of the ELaNa program.
ACS3 consists of a 12U (unit) CubeSat
small satellite (23 cm x 23 cm x 34 cm; 16 kg) that unfolds a quadratic
80 square metres (860 sq ft) solar sail consisting of a polyethylene naphthalate film coated on one side with aluminum for reflectivity and on the other side with chromium to increase thermal emissivity. The sail is held by a novel unfolding system of four 7 metres (23 ft) long carbon fiber reinforced polymerbooms that roll-up for storage.
ACS3 was launched on 23 April 2024 on the Electron "Beginning Of The Swarm" mission. The ACS3 successfully made contact with ground stations following deployment in early May. The solar sail was confirmed as successfully operational by mission operators on 29 August 2024.
On 25 October 2024 it was reported "... a bent support arm has made it (ACS3) lose direction and spin out of control in space."
Projects proposed or cancelled or not selected
Despite the losses of Cosmos 1
and NanoSail-D (about 23cm x 23cm x 34cm) 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. Development of
solar sails for crewed space flight is still in its infancy.
A technology demonstration sail craft, dubbed Sunjammer, was in development with the intent to prove the viability and value of sailing technology. Sunjammer
had a square sail, 38 metres (125 ft) wide on each side, giving it an
effective area of 1,200 square metres (13,000 sq ft). It would have
traveled from the Sun-Earth L1Lagrangian point 1.5 million kilometres (930,000 miles) from Earth to a distance of 3 million kilometres (1.9 million miles). The demonstration was expected to launch on a Falcon 9 in January 2015. It would have been a secondary payload, released after the placement of the DSCOVR climate satellite at the L1 point. Citing a lack of confidence in the ability of its contractor L'Garde to deliver, the mission was cancelled by NASA in October 2014.
OKEANOS (Outsized Kite-craft for Exploration and Astronautics in the
Outer Solar System) was a proposed mission concept by Japan's JAXA to Jupiter's Trojan asteroids using a hybrid solar sail for propulsion; the sail would have been covered with thin solar panels to power an ion engine. In-situ
analysis of the collected samples would have been performed by either
direct contact or using a lander carrying a high-resolution mass
spectrometer. A lander and a sample-return to Earth were options under
study. The OKEANOS Jupiter Trojan Asteroid Explorer was a finalist for Japan's ISAS' 2nd Large-class mission to be launched in the late 2020s. However, it was not selected.
In August 2019, NASA awarded the Solar Cruiser team $400,000 for nine-month mission concept studies. The spacecraft would have a 1,672 m2 (18,000 sq ft) solar sail and would orbit the Sun in a polar orbit, while the coronagraph instrument would enable simultaneous measurements of the Sun's magnetic field structure and velocity of coronal mass ejections. If selected for further development, it would have launched in 2025. However, Solar Cruiser was not approved to advance to phase C of its development cycle and was subsequently discontinued.
Projects still in development or unknown status
Gossamer deorbit sail
As of December 2013, the European Space Agency (ESA) has a proposed deorbit sail, named "Gossamer",
that would be intended to be used to accelerate the deorbiting of small
(less than 700 kilograms (1,500 lb)) artificial satellites from low Earth orbits.
The launch mass is 2 kilograms (4.4 lb) with a launch volume of only
15×15×25 centimetres (0.49×0.49×0.82 ft). Once deployed, the sail would
expand to 5 by 5 metres (16 ft × 16 ft) and would use a combination of
solar pressure on the sail and increased atmospheric drag to accelerate
satellite reentry.
The well-funded Breakthrough Starshot project announced on April 12,
2016, aims to develop a fleet of 1000 light sail nanocraft carrying
miniature cameras, propelled by ground-based lasers and send them to Alpha Centauri at 20% the speed of light. The trip would take 20 years.
In popular culture
Artist rendering of an interstellar light sail space craft
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.
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.).
In the 2009 film Avatar, the spacecraft which transports the protagonist Jake Sully to the Alpha Centauri system, the ISV Venture Star, uses solar sails as a means of propulsion to accelerate the vehicle away from the Earth towards Alpha Centauri.
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.
In the 2022 show Pantheon, a solar sail is used to send the SafeSurf program to Alpha Centauri.
In the final episode of the first season of 2024 Netflix TV show, 3 Body Problem, one of the protagonists, Will Downing, has his cryogenically frozen brain launched into space toward the oncoming Trisolarian spaceship, using solar sails and nuclear pulse propulsion to accelerate it to a fraction of the speed of light.
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