## Question

Howdy!

Ever since I first heard about solar sails I have been curious about how they work. It is my understanding that light is massless whether considered a particle or wave. How does a massless particle impart a force on another object?

Regards,

## Answer

We put this to Dr Natasha Hurley-Walker, from the Curtin University in Perth, Western Australia...

Natasha - To answer your question, in 1871 James Clerk Maxwell predicted that electromagnetic waves would exert a tiny but measurable force on a surface, and this was experimentally verified in 1899 by Pyotr Lebedev. One can integrate the electromagnetic wave equation and show that for an incoming wave, the exerted pressure is equal to half of the energy density of the wave. Or, as shown by Einstein in his Theory of Special Relativity, one can think of light as particles, i.e. photons, which have a momentum. This is equal to the energy of the photon divided by the speed of light. Therefore, when a photon is reflected or observed by a surface, it imparts some momentum to that surface. This is called radiation pressure. Solar sails utilise radiation pressure by combining the imparted pressure over a very large surface area. At Earth's distance from the Sun, this adds up to about 1 micro-Pascal of pressure. Solar sails typically have 20 to 30 square meters of collecting area, but some proposals have been made for designs with half a square kilometre of collecting area. The pressure is small but with a low mass sail, applied for large time, solar sails can build up to large speeds while using no fuel.

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