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Astronomy: A surprising result in Astrophysics that shows how light exerts a small drag force on small dust particles. For large or reflective bodies, radiation pushes on objects very slightly. However, for very small particles (in size, not mass) in orbit around a star, radiation slows the particles, causing them to gradually spiral inwards. This effect was first discovered by J. H. Poynting in 1903 and later derived rigorously by H. P. Robertson in 1937.

Consider an orbiting particle in the inertial frame. This particle is constantly absorbing and re-emitting radiation. If the particle is sufficiently small, it will emit absorbed photons equally in all directions.

The photons emitted in the direction of the particle's motion will have a higher frequency than those emitted in the direction opposite the particle's motion, due to Doppler shift. The higher frequency photons have a higher energy also, as dictated by Planck's equation, and thus, more energy is being emitted in the forward direction than in the backward direction. As a result, the particle slows down, and gradually spirals inwards into the star.

This drag only affects very small particles, and even then, only slightly. Both the "push" and the "drag" are very small effects, negligible when compared the gravitational effects of planetary bodies. But in the absence of other planets, all dust in the asteroid belt, for example, would drift into the sun in about 200,000 years (not much time on the astronomical scale).

Robertson's equation for the drag force is:

F = F0 ( i - vr i / c - v / c )

where

  • F0 is the total energy absorbed by the particle per unit time divided by the speed of light,
  • i is the unit vector corresponding to the radius,
  • vr is the velocity in the direction of the radius,
  • v is the total velocity, and
  • c is the speed of light.
The equation models the star as a point source of radiation.

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