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/m
2, 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 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).
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 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 2
σT4/
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.
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.
Radiation pressure in acoustics
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.
See also
