Radiation pressure
Encyclopedia
Radiation pressure is the pressure
exerted upon any surface exposed to electromagnetic radiation
. If absorbed, the pressure is the power flux
density divided by the speed of light. If the radiation is totally reflected, the radiation pressure is doubled.
For example, the radiation of the Sun at the Earth has a power flux
density of 1,370 W/m2, so the radiation pressure is 4.6 µPa
(absorbed).
exerts a pressure upon any surface exposed to it was deduced theoretically by James Clerk Maxwell
in 1871 and Adolfo Bartoli
in 1876, and proven experimentally by Russian physicist Peter Lebedev
in 1900 and by Ernest Fox Nichols
and Gordon Ferrie Hull
in 1901. The pressure is very feeble, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal in a Nichols radiometer
(this should not be confused with the Crookes radiometer
, whose characteristic motion is not caused by radiation pressure but by impacting gas molecules).
, or by thermodynamics
, making no assumptions as to the nature of the radiation, that the pressure against a surface exposed in a space traversed by radiation uniformly in all directions is equal to one third of the total radiant energy per unit volume within that space.
Now consider a beam of light perpendicularly incident on a surface, and let us assume the beam of light is totally absorbed. If we imagine the beam is made of photons, then every second numerous photons strike the surface and are absorbed. The momentum the photons carry is a conserved quantity - it cannot be destroyed - so it must be transferred to the surface, the result is that absorbing the light beam causes the surface to gain momentum.
Newton's Second Law tells us that force equals rate of change of momentum, so during each second the surface experiences a force (or pressure, as pressure is force per unit area) due to the momentum the photons transfer to it. We have:
Pressure = momentum transferred per second per unit area = Energy deposited per second per unit area / c = I/c.
Where I is the intensity of the beam of light (measured in e.g. W⋅m-2).
In the above argument we assumed that the surface totally absorbed the beam, in general light can be transmitted, reflected and/or absorbed. If the light were totally reflected then the radiation pressure is doubled compared to total absorption, this is because the photons arrive with momentum E/c and depart with momentum -E/c (the -ve sign indicates traveling in the opposite direction), so the change of momentum is 2E/c.
, Solar radiation pressure is the force exerted by solar radiation on objects within its reach. Solar radiation pressure is of interest in astrodynamics
, as it is one source of the orbital perturbations.
The disturbance force can be expressed simply as
where:
- Force contributed by the solar radiation pressure
- Force per unit area exerted by the solar radiation
- Coefficient of reflectivity of the object
- Area of the object exposed to the solar radiation
- radial unit vector between object and the Sun
Radiation pressure is about 10−5 Pa
at Earth's distance from the Sun
and decreases by the square of the distance from the Sun.
For example, at the boil
ing point of water
(T = 373 K), a blackbody is emitting about 1,080 watts of energy per square meter of surface. This is somewhat below the Sun's 1373 W/m², but still instructive. If the blackbody absorbs 1,080 watts on its sun-facing surface, it must also emit all 1,080 watts omnidirectionally. The omnidirectional emission is self-cancelling, so that it neither adds nor detracts from the net solar flux force.
By the radiation pressure equation σT4/c; the sun-facing photon pressure is 3.61 µPa (3.6 N/km², 2.08 lbf/mi²). If the sun-facing surface is an almost perfect reflector, the force would approach double that (7.22 µPa) depending on how close to an ideal reflector the surface is polished.
While rather small in comparison to chemical thrusters, the radiation pressure force is inexorable and requires no fuel mass. Thus over months-to-years, the net (integrated) amount of force is substantial, and is thought to be sufficient to speed interplanetary probes to velocities that could traverse the Earth-Pluto distance in 1/2 to 1/4 the time of a chemically accelerated vessel.
Such feeble pressures are able to produce marked effects upon minute particles like gas
ion
s and electron
s, and are important in the theory of electron emission from the Sun, of comet
ary material, and so on (see also: Yarkovsky effect
, YORP effect, Poynting–Robertson effect).
The table shows that the accelerative forces very close to the Sun are very high, and almost of no comparative importance (for macroscopic particles) by the orbital distance of Jupiter. It is for this reason that most interplanetary radiation-pressure probe missions are sun grazers, whose orbital trajectory passes very close to the Sun so that at midpoint, the probe's reflectors can be turned toward the Sun, adding considerable velocity to the craft.
Because the ratio of surface area to volume (and thus mass) increases with decreasing particle size, dusty (micrometre
-size) particles are susceptible to radiation pressure even in the outer solar system. For example, the evolution of the outer rings of Saturn is significantly influenced by radiation pressure.
divided by the speed of light in free space is the radiation pressure exerted by an electromagnetic wave on the surface of a target:
.
interiors the temperatures are very high. Stellar models predict a temperature of 15 MK in the center of the Sun
and at the cores of supergiant
stars the temperature may exceed 1 GK. As the radiation pressure scales as the fourth power of the temperature, it becomes important at these high temperatures. In the Sun, radiation pressure is still quite small when compared to the gas pressure. In the heaviest stars, radiation pressure is the dominant pressure component.
s, a proposed method of spacecraft propulsion
, would use radiation pressure from the Sun as a motive force. Private spacecraft Cosmos 1
was to have used this form of propulsion. The idea was proposed as early as 1924 by Soviet scientist Friedrich Zander
.
The Japan Aerospace Exploration Agency (JAXA) has successfully unfurled a solar sail in space which has already succeeded in propelling its payload with the IKAROS
project.
, radiation pressure is the unidirectional pressure force exerted at an interface between two media due to the passage of a sound wave.
If sound is absorbed in the volume during propagation, a body radiation force builds up. In a fluid, this force generates acoustic streaming
.
is applied to cooling materials very close to absolute zero. Atoms traveling towards a laser light source perceive a doppler effect
tuned to the absorption frequency of the target element. The radiation pressure on the atom slows movement in a particular direction until the Doppler effect moves out of the frequency range of the element, causing an overall cooling effect.
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
exerted upon any surface exposed to electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
. If absorbed, the pressure is the power flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
density divided by the speed of light. If the radiation is totally reflected, the radiation pressure is doubled.
For example, the radiation of the Sun at the Earth has a power flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
density of 1,370 W/m2, so the radiation pressure is 4.6 µPa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
(absorbed).
Discovery
The fact that electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
exerts a pressure upon any surface exposed to it was deduced theoretically by James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
in 1871 and Adolfo Bartoli
Adolfo Bartoli
Adolfo Bartoli was an Italian physicist, who is best known for introducing the concept of radiation pressure from thermodynamical considerations....
in 1876, and proven experimentally by Russian physicist Peter Lebedev
Pyotr Nikolaevich Lebedev
Pyotr Nikolaevich Lebedev was a Russian physicist.He made his doctoral degree in Strasbourg under the supervision of August Kundt in 1887–1891. In 1891 he started working in Moscow State University in the group of Alexander Stoletov. There he made his famous experimental studies of...
in 1900 and by Ernest Fox Nichols
Ernest Fox Nichols
Ernest Fox Nichols was a U.S. educator and physicist. He was born in Leavenworth County, Kansas, and received his undergraduate degree from Kansas State University in 1888. After working for a year in the Chemistry Department at Kansas State, he matriculated to graduate school at Cornell...
and Gordon Ferrie Hull
Gordon Ferrie Hull
Gordon Ferrie Hull was a Canadian / American teacher, mathematician and physicist, especially known for the experimental detection of the radiation pressure exerted by light which he achieved in 1903....
in 1901. The pressure is very feeble, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal in a Nichols radiometer
Nichols radiometer
A Nichols radiometer was the apparatus used by Ernest Fox Nichols and Gordon Ferrie Hull in 1901 for the measurement of radiation pressure. It consisted of a pair of small silvered glass mirrors suspended in the manner of a torsion balance by a fine quartz fibre within an enclosure in which the air...
(this should not be confused with the Crookes radiometer
Crookes radiometer
The Crookes radiometer, also known as the light mill, consists of an airtight glass bulb, containing a partial vacuum. Inside are a set of vanes which are mounted on a spindle. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement...
, whose characteristic motion is not caused by radiation pressure but by impacting gas molecules).
Theory
It may be shown by electromagnetic theory, by quantum theoryQuantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, or by thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, making no assumptions as to the nature of the radiation, that the pressure against a surface exposed in a space traversed by radiation uniformly in all directions is equal to one third of the total radiant energy per unit volume within that space.
Quantum Theory Argument
From the perspective of quantum theory, light is made of photons: particles with zero mass but which carry energy and - importantly in this argument - momentum . According to special relativity, because photons are mass-less their energy (E) and momentum (p) are related by E=pc .Now consider a beam of light perpendicularly incident on a surface, and let us assume the beam of light is totally absorbed. If we imagine the beam is made of photons, then every second numerous photons strike the surface and are absorbed. The momentum the photons carry is a conserved quantity - it cannot be destroyed - so it must be transferred to the surface, the result is that absorbing the light beam causes the surface to gain momentum.
Newton's Second Law tells us that force equals rate of change of momentum, so during each second the surface experiences a force (or pressure, as pressure is force per unit area) due to the momentum the photons transfer to it. We have:
Pressure = momentum transferred per second per unit area = Energy deposited per second per unit area / c = I/c.
Where I is the intensity of the beam of light (measured in e.g. W⋅m-2).
In the above argument we assumed that the surface totally absorbed the beam, in general light can be transmitted, reflected and/or absorbed. If the light were totally reflected then the radiation pressure is doubled compared to total absorption, this is because the photons arrive with momentum E/c and depart with momentum -E/c (the -ve sign indicates traveling in the opposite direction), so the change of momentum is 2E/c.
In interplanetary space
In astronomyAstronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, Solar radiation pressure is the force exerted by solar radiation on objects within its reach. Solar radiation pressure is of interest in astrodynamics
Astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It...
, as it is one source of the orbital perturbations.
The disturbance force can be expressed simply as
where:
- Force contributed by the solar radiation pressure - Force per unit area exerted by the solar radiation - Coefficient of reflectivity of the object - Area of the object exposed to the solar radiation - radial unit vector between object and the SunRadiation pressure is about 10−5 Pa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
at Earth's distance from the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
and decreases by the square of the distance from the Sun.
For example, at the boil
Boil
A boil, also called a furuncle, is a deep folliculitis, infection of the hair follicle. It is always caused by infection by the bacterium Staphylococcus aureus, resulting in a painful swollen area on the skin caused by an accumulation of pus and dead tissue...
ing point of water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
(T = 373 K), a blackbody is emitting about 1,080 watts of energy per square meter of surface. This is somewhat below the Sun's 1373 W/m², but still instructive. If the blackbody absorbs 1,080 watts on its sun-facing surface, it must also emit all 1,080 watts omnidirectionally. The omnidirectional emission is self-cancelling, so that it neither adds nor detracts from the net solar flux force.
By the radiation pressure equation σT4/c; the sun-facing photon pressure is 3.61 µPa (3.6 N/km², 2.08 lbf/mi²). If the sun-facing surface is an almost perfect reflector, the force would approach double that (7.22 µPa) depending on how close to an ideal reflector the surface is polished.
While rather small in comparison to chemical thrusters, the radiation pressure force is inexorable and requires no fuel mass. Thus over months-to-years, the net (integrated) amount of force is substantial, and is thought to be sufficient to speed interplanetary probes to velocities that could traverse the Earth-Pluto distance in 1/2 to 1/4 the time of a chemically accelerated vessel.
Such feeble pressures are able to produce marked effects upon minute particles like gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s and electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s, and are important in the theory of electron emission from the Sun, of comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
ary material, and so on (see also: Yarkovsky effect
Yarkovsky effect
The Yarkovsky effect is a force acting on a rotating body in space caused by the anisotropic emission of thermal photons, which carry momentum...
, YORP effect, Poynting–Robertson effect).
| AU distance | µPa (µN/m²) | N/km² | lbf/mi² |
|---|---|---|---|
| 0.10 AU = Close | 915 | 915 | 526 |
| 0.46 AU = Mercury | 43.3 | 43.3 | 24.9 |
| 0.72 AU = Venus | 17.7 | 17.7 | 10.2 |
| 1.00 AU = Earth | 9.15 | 9.15 | 5.26 |
| 1.52 AU = Mars | 3.96 | 3.96 | 2.28 |
| 5.22 AU = Jupiter | 0.34 | 0.34 | 0.19 |
The table shows that the accelerative forces very close to the Sun are very high, and almost of no comparative importance (for macroscopic particles) by the orbital distance of Jupiter. It is for this reason that most interplanetary radiation-pressure probe missions are sun grazers, whose orbital trajectory passes very close to the Sun so that at midpoint, the probe's reflectors can be turned toward the Sun, adding considerable velocity to the craft.
Because the ratio of surface area to volume (and thus mass) increases with decreasing particle size, dusty (micrometre
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
-size) particles are susceptible to radiation pressure even in the outer solar system. For example, the evolution of the outer rings of Saturn is significantly influenced by radiation pressure.
Poynting vector and radiation pressure
S divided by the square of the speed of light in free space is the density of the linear momentum of the electromagnetic field. The time-averaged intensity divided by the speed of light in free space is the radiation pressure exerted by an electromagnetic wave on the surface of a target:.In stellar interiors
In stellarStar
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
interiors the temperatures are very high. Stellar models predict a temperature of 15 MK in the center of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
and at the cores of supergiant
Supergiant
Supergiants are among the most massive stars. They occupy the top region of the Hertzsprung-Russell diagram. In the Yerkes spectral classification, supergiants are class Ia or Ib . They typically have bolometric absolute magnitudes between -5 and -12...
stars the temperature may exceed 1 GK. As the radiation pressure scales as the fourth power of the temperature, it becomes important at these high temperatures. In the Sun, radiation pressure is still quite small when compared to the gas pressure. In the heaviest stars, radiation pressure is the dominant pressure component.
Solar sails
Solar sailSolar sail
Solar sails are a form of spacecraft propulsion using the radiation pressure of light from a star or laser to push enormous ultra-thin mirrors to high speeds....
s, a proposed method of spacecraft propulsion
Spacecraft propulsion
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. There are many different methods. Each method has drawbacks and advantages, and spacecraft propulsion is an active area of research. However, most spacecraft today are propelled by forcing a gas from the...
, would use radiation pressure from the Sun as a motive force. Private spacecraft Cosmos 1
Cosmos 1
Cosmos 1 was a project by Cosmos Studios and The Planetary Society to test a solar sail in space. As part of the project, an unmanned solar sail spacecraft christened Cosmos 1 was launched into space at 15:46:09 EDT on June 21, 2005 from the submarine Borisoglebsk in the Barents Sea...
was to have used this form of propulsion. The idea was proposed as early as 1924 by Soviet scientist Friedrich Zander
Friedrich Zander
Friedrich Zander , often transliterated Fridrikh Arturovich Tsander, was a pioneer of rocketry and spaceflight in the Russian Empire and the Soviet Union...
.
The Japan Aerospace Exploration Agency (JAXA) has successfully unfurled a solar sail in space which has already succeeded in propelling its payload with the IKAROS
IKAROS
IKAROS is a Japan Aerospace Exploration Agency experimental spacecraft. The spacecraft was launched on 21 May, 2010, aboard an H-IIA rocket, together with the Akatsuki probe and four other small spacecraft...
project.
Radiation pressure in acoustics
In acousticsAcoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
, radiation pressure is the unidirectional pressure force exerted at an interface between two media due to the passage of a sound wave.
If sound is absorbed in the volume during propagation, a body radiation force builds up. In a fluid, this force generates acoustic streaming
Acoustic streaming
Acoustic streaming is a steady current in a fluid driven by the absorption of high amplitude acoustic oscillations. This phenomenon can be observed near sound emitters, or in the standing waves within a Kundt's tube....
.
Laser cooling
Laser coolingLaser cooling
Laser cooling refers to the number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields...
is applied to cooling materials very close to absolute zero. Atoms traveling towards a laser light source perceive a doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
tuned to the absorption frequency of the target element. The radiation pressure on the atom slows movement in a particular direction until the Doppler effect moves out of the frequency range of the element, causing an overall cooling effect.
Further reading
- Dion, J. L.; Malutta, A.; Cielo, P., "Ultrasonic inspection of fiber suspensions", The Journal of the Acoustical Society of America, Volume 72, Issue 5, November 1982, pp.1524-1526
- F.G. Mitri, "Theoretical calculation of the acoustic radiation force acting on elastic and viscoelastic cylinders placed in a plane standing or quasistanding wave field", The European Physical Journal B - Condensed Matter and Complex Systems, Volume 44, Issue 1, March 2005, Pages 71-78. http://dx.doi.org/10.1140/epjb/e2005-00101-0
- F.G. Mitri, "Theoretical and experimental determination of the acoustic radiation force acting on an elastic cylinder in a plane progressive wave—far-field derivation approach", New Journal of Physics, Volume 8, August 2006, art. no. 138. http://dx.doi.org/10.1088/1367-2630/8/8/138
- F.G. Mitri, "Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves", Ultrasonics, Volume 44, Issue 3, July 2006, Pages 244-258. http://dx.doi.org/10.1016/j.ultras.2006.02.002
- F.G. Mitri, "Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers", Annals of Physics, Volume 323, Issue 7, July 2008, Pages 1604-1620. http://dx.doi.org/10.1016/j.aop.2008.01.011