This is not an easy thing to wrap one’s head around, and part of the reason it’s tricky is because light is a little special. Light manages to behave both like a particle and like a wave. In either case, you’re absolutely right that the particle of light has no mass.
To start to get a handle on how this works, let’s think about light as a wave, and ignore the photon-particle behavior. The way we break up the whole electromagnetic spectrum is by the amount of energy carried by that wave. The more energetic the wave is, the higher its frequency, and so dividing by frequency is just another way of slicing by energy levels. When these waves are absorbed by a surface, they will deposit the energy they carry in that surface. This is why we burn in sunlight; the ultraviolet, which we can’t see, carries a lot of energy with it, and that energy is deposited in our skin. Our skin doesn’t handle this energy dose very well, and so we wind up with a burn, as though we’d touched something hot. (Technically, we did! The sun.)
But what about if the surface doesn’t absorb the light, but reflects it, as a mirror does for visible light? In a perfect world, the wave is totally reflected off of the surface, and none of this transfer of energy to the surface happens. In practice, however, most materials are not perfectly reflective, and so the reflected wave has lost some of its energy to the mirror. In most cases, this energy loss is pretty small (otherwise it’s a terrible mirror), but if you’re in the business of trying to make a solar sail, this energy donation pushes the sail along a little bit.
If we go back to thinking about light as a particle, the light-particle must still carry energy. The light particle is a little weird, because it does manage to carry momentum, even without a rest mass. But there is an energy-momentum translation, even without mass, which is in play for photons. Now, if you think about a string of particles bouncing off of a surface, bouncy-ball style, those collisions also transfer a bit of energy into the surface. This energy transfer is giving a little bit of momentum to the surface, so if that surface is floating freely, as a solar sail does, you’ll slowly add speed to the sail.
It’s important to note that both the wave method and the particle method of thinking about light are totally equivalent, but in some cases it is simpler mentally or mathematically to think about light more as a particle or more as a wave. In this case, either method is a decent description of how light can propel a solar sail along.
The technical term for this gradual, tiny momentum-energy transfer is called radiation pressure, and this gradual pressure across the solar sail is what can propel it through the solar system. In any patch of space where there is strong radiation — a.k.a. a huge source of light, of any frequency — you can wind up with radiation pressure shaping the behavior of things around it.
Our sun isn’t even that extreme of an environment for radiation pressure! If it were more extreme, our solar sails might not need to be quite so large, as the pressure would be stronger and we wouldn’t need such a large surface area. The current solar sails have to be tens of meters on a side to be practical – the Japanese IKAROS light sail is a little over 150 feet along one edge, with an even larger one planned now that we know that this sort of technology is feasible!
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