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. 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) (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 proven experimentally by Lebedev in 1900 and by Nichols and 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 (Nichols radiometer).

## 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 1/3 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 σT4/3c; in which σ is the Stefan-Boltzmann constant, c is the speed of light, and T is the absolute temperature of the space. One third of this energy is equal to 6.305×10−17T4 J/m3K4, which is therefore equal to the pressure in pascals.

### In interplanetary space

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.

## Solar sails

Solar sails, a proposed method of spacecraft propulsion, would utilize radiation pressure from the Sun as a motive force. Private spacecraft Cosmos 1 was to have used this form of propulsion.