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# 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) (see also Climate model).

## Discovery

The fact that electromagnetic radiation 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 Lebedev in 1900[1] and by Ernest Fox Nichols and Gordon Ferrie Hull in 1901.[2] 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).

## Theory

It may be shown by electromagnetic theory, by quantum theory, 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.

For black body radiation, in equilibrium with the exposed surface, the energy density is, in accordance with the Stefan-Boltzmann law, equal to 4σT4/c; in which σ is the Stefan-Boltzmann constant, c is the speed of light, and T is the absolute temperature of the space.

### In interplanetary space

Radiation pressure is about 10-5 Pa at Earth's distance from the Sun[3] and decreases by the square of the distance from the Sun.

For example, at the boiling point of water (T = 373.15 K), the pressure only amounts to 3 micropascals (about 2 pounds force per square mile). If the radiation is directional (in interplanetary space, the overwhelming proportion of the energy flux comes from the Sun alone), the radiation pressure is tripled, to σT4/c; if the body is a perfect reflector, the pressure can be doubled again, to 2σT4/c. A solar sail at the distance where the equivalent radiation temperature is the boiling point of water could thus achieve about 22 µPa, or nearly 13 lbf/sq mi. Such feeble pressures are, nevertheless, able to produce marked effects upon minute particles like gas ions and electrons, and are important in the theory of electron emission from the Sun, of cometary material, and so on (see also: Yarkovsky effect, YORP effect).

### In stellar interiors

In stellar 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.[4]

## Solar sails

Solar sails, 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.

In 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.

## Laser cooling

Laser cooling 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.

• 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. [1]
• 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. [2]
• 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. [3]
• 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. [4]

## References

1. ^ P. Lebedev, 1901, "Untersuchungen über die Druckkräfte des Lichtes", Annalen der Physik, 1901
2. ^ Nichols, E.F & Hull, G.F. (1903) The Pressure due to Radiation, The Astrophysical Journal,Vol.17 No.5, p.315-351
3. ^ Solar Sail
4. ^ Dale A. Ostlie and Bradley W. Carroll, An Introduction to Modern Astrophysics (2nd edition), page 341, Pearson, San Francisco, CA 2007

# Simple English

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the energy flux density divided by the speed of light. If the radiation is totally reflected, the radiation pressure is doubled. This happens because the waves that make up electromagnetic radiation carry momentum with them and pass that momentum on when they reach a surface.

For example, the radiation of the Sun at the Earth has an energy flux density of 1370 W/m2, so the radiation pressure is 4.6 µPa (absorbed).