Weekend posting here is usually pretty light, but it’s only the second day here so I think a little extra is a nice way to kick things off. How about a little bit of solar sailing, since it fits pretty well with what I’m teaching in my intro class?
We all know light carries energy. Go outside on a sunny day and you can feel the energy being absorbed by your skin. You feel it as heat, but visible light energy allows you to see and ultraviolet light will induce chemical changes which will finally result in your body making itself a bit more tan. What’s less apparent is that light also carries momentum. Take two electrons, separate them by some large distance, and wiggle around the first electron. The wiggling electron is an accelerating charge, and so it induces electromagnetic waves which propagate outward and eventually hit the second electron which makes it wiggle as well.
That electron wasn’t moving before the wave got there, and it is moving after. So it didn’t have momentum before, but it does after. Therefore the incoming electromagnetic wave has to carry momentum.
It’s a pretty snazzy revelation, one which took some of my students by suprise. “Isn’t momentum given by mass times velocity, and doesn’t light not have a mass?” Yes and yes, but it turns out that the old p = mv formula only works for things with mass. We skipped the technical details since it’s just an intro class, and fortunately the resulting formula for the momentum of light is very easy to work with.
Find the power per area of a beam of light. (For sunlight at the surface of the earth, it’s about 1000 watts per square meter.) Call that quantity S. The time rate of change in the momentum p of something with that light shining on it is
Where A is the area which the light is shining on. You can more conveniently write this as a pressure (call it P)
Not bad. So why is it that we don’t feel the pressure from the sun when we stand outside? It’s because the speed of light c is such a huge number. If you plug in the numbers, you’ll find that the radiation pressure from the sun is something like 4.8 x 10-10 pounds per square inch. Way, way too tiny to measure.
But if you have a big sail in the vacuum of space where there’s no friction…
Let’s see, a square mile of reflective sail would have about 4 pounds of force. That’s not very much, but it requires no fuel at all and will keep going as long as the sun shines. To an aerospace engineer that sounds like something of beauty.