Today I was pointed via New Scientist via YAWL via Stet to this abstract of an article by Dr Thomas Gold of Cornell University, suggesting that solar sails may in fact be unworkable due to thermodynamic considerations. I would be greatly displeased if this were the case, because (a) solar sails are a neat idea, and (b) I hate thermodynamics. There are at least two points that trouble me about this abstract.
In fact, three. The first two are not terribly insightful.
First, and this may be just a misinterpretation due to the phrasing, he seems to suggest that the usual law of momentum conservation may not apply in interactions between radiation and matter. This would seem to represent a substantial hole in classical electrodynamics. But maybe it's true; I don't know. I want to find out more.
Second, and this I think I can comment on, in the final paragraph he claims that the momentum transferred by radiation is a scalar, rather than a vector. Unless I'm horribly misremembering, the momentum stored in an electromagnetic field is indeed a vector; the momentum density is proportional to the Poynting vector S, which in turn is proportional to the cross product of the electric E and magnetic B field vectors at each point:
pdensity=m0e0S=e0ExB
Relativistically, too, a photon's momentum comes as three of the four components of a 4-vector. I don't understand how this can be called a scalar. The magnitude of the momentum carried by a photon is indeed E/c as he says (where E is now energy), but that doesn't rob the momentum of its vectorial character.
On the other hand (and here we're at #3, if you're keeping count), energy absorption does seem as if it would bring a solar sail into thermal equilibrium with the radiation after a time. But I don't think this means momentum transfer will cease. This is completely a conceptual argument, nothing remotely precise, but...Suppose a sail is at the same average temperature as the radiation; it is still absorbing radiation (photons, and hence energy, and momentum), but it will re-radiate an equal amount of energy, for no net gain. Energy's scalar, so that's all well and good; it makes no difference how the energy is re-radiated. However, it does matter for the momentum. Solar radiation is not hitting it symmetrically: essentially, it is all coming in more or less perpendicularly to the surface of the sail, from one side only. The momentum boost from this is all in one direction. (Ideally.) When the sail re-radiates away excess energy, however, won't it do so more or less symmetrically? Pretend it's a two-dimensional sheet; if the whole sail is at the same temperature now, both sides should be radiating away equally. The incident energy is all lost, but there should be no net momentum loss from this, since radiation is being emitted equally both ahead and behind. The momentum from the incident radiation still has to go somewhere; the only place left is into the sail, and so it should continue to accelerate even in thermal equilibrium.
It's been a long time since I did thermodynamics or electrodynamics, and they were only at an undergraduate level; I make no guarantees as to my accuracy here. You are welcome to expose any and all holes in my woolly thinking you may find. But this seems plausible. The radiation emitted by the sail can't exert a net force on the sail itself; that would be silly. So no matter how much energy it absorbs and re-radiates, this cannot act as a sink for the incident momentum.
As I said, please savage me if you can. It's okay to sound like a braying ass-clown talking about politics, but this is physics. Which is not as sacred as mathematics, but still.
FURTHERMORE (24/08/03): I know the rough model I described above violates conservation of energy. If the sail is accelerating, it is certainly gaining kinetic energy, which has to come from somewhere. But equally, the momentum has to go somewhere, too. The conclusion seems to me to be that the sail just isn't going to behave like a blackbody in equilibrium.
Posted by aloysius at August 23, 2003 02:52 PM | TrackBack |