Thursday, June 23, 2005

Sailing on Radiation

Due to summer temperatures, I am not quite able to do proper work, so I waste my time in the blogsphere. Alasdair Allen is an astronomer that I know from diving in the English Channel. In his blog, he reports on the recent fuzz about Cosmos-1 not reaching its orbit.

Cosmos-1 was a satellite that was supposed to use huge mirror sails to catch the solar radiation for propulsion. Al also mentions a paper together with a rebuttal that claims that this whole principle cannot work.

In physics 101, we've all seen the light mill that demonstrates that the photons that bounce off the reflecting sides of the panels transfere their momentum to the wheel. So this shows that you can use radiation to move things.

Well, does it?

Gold argues, that the second law of thermodynamics is in the way of using this effectively. So what's going on? His point is that once the radiation field and the mirrors are in thermal equilibrium, the mirror would emit photos to both sides and there is no net flux of momentum. On general grounds, you should not be able to extract mechanical energy from heat in a world where everything has the same temperature.

The reason that the light mill works is really that the mill is much colder than the radiation. So, it seems to me that the real question (if Gold is right, which I tend to think, but as I said above, it's hot and I cannot really convice myself, that at equilibrium the emission and absorption of photons to both sides balances) is how long it takes for the sails to heat up. If you want to archive a significant amount of acceleration they should be very light which on the other hand means the absolute heat capacity is small.

At least, the rebuttle is so vague, it's written by an engineer of the project, that I don't think he really understood Gold's argument. But it seems, that some physics in the earlier stages of the flight was ill understood, as cosmos-1 did not make it to orbit...


Arun said...

But its not at equilibrium. The sun is busy pumping photons that hit one side only of the mirror.

Quantoken said...

Is that a serious article by a physics professor at Cornell, or is that an April Fools joke? I think even an elementary school students can repute his argument.

The important things is Dr. Gold confused two different logical concept which unfortunately uses the same English word "equilibrium". Thermal equilibrium is the state when everything is at the same temperature and there is no heat exchange between any part of the system. Thermal "equilibrium", mean while, is just thermal balance: The net heat exchange is balanced. But the balance is absorbing more heat from one source and then emitting more heat to another heat sink. It's similar to China having a balanced import/export. But the reality is China has a trade deficit to Japan and a trade surplus to USA, and the two cancel out. That is not equilibrium.


Anonymous said...

In physics 101, we've all seen the light mill that demonstrates that the photons that bounce off the reflecting sides of the panels transfere their momentum to the wheel. So this shows that you can use radiation to move things.

I think you are implying that the light mill (a kind of radiometer) operates on the basis of photon momentum transfer. Although this example isn't central to your topic, it seems worth clarifying that the light mill doesn't work on that principle, although many educated people seem to think it does. The fact that the radiometer won't work in a vacuum is the first clue... There is a discussion of this on John Baez' web site:

Best regards,

Robert said...

I trust John Baez, however writing this post I did some googling and came across>

there is the statement:

If there is a near-perfect vacuum, the vanes do not spin unless they are held in a frictionless way. If the vanes have a frictionless support and the vacuum is complete, then photons bouncing off the silver side of the vanes push the vanes, causing them to rotate. However, this force is exceedingly small.

So what is "exceedingly small"?

Anonymous said...

Each reflected photon contributes twice its momentum E/c bouncing off silver foil, and its momentum if absorbed. The solar constant is about 1.4 kilowatts/squared meter. Thus per squared meter, a solar sail will have about 9.3 * 10^-6 Newtons pushing it. The radiation from the foil due to its non-zero temperature will be equal in both forward and backward directions and is irrelevant except insofar as it is necessary to keep the foil from raising its temperature till it melts.

Robert said...

At start, this is not at equilibrium, you're right. But eventually the sail will heat up until it reaches (asymptotically of course) the temperature of the sun's black body radiation.

Anonymous said...

Consider the following two scenarios:

1) Consider some photon gas confined in a tube by a mirror/piston which is "imperfect", meaning it absorbs some fraction of the photons that hit it. Assume the other end of the tube (which is fixed) and the walls of the tube are perfect mirrors at absolute zero.

| (photon gas) |->movable piston

All the photons that bounce off the piston will transfer momentum to it, but the ones that get absorbed will also heat up the piston, and the latter will start to radiate in both directions. This process will asymptotically "leak" all the photons to the outside.

2) Now assume that the wall on the left hand side is a blackbody at a nonzero constant temperature. Since we do not start with a fixed finite amount of photon energy inside the tube, the "leak" due to the heat-up of the piston will not make the acceleration of the piston asymptote to zero, even if the temperature of the piston becomes equal to the temperature of the radiation by the wall.

In fact, I think the piston will accelerate forever even if it is a blackbody rather than a mirror--every photon absorbed transfers momentum, but the ones that are radiated in both directions do not take away any, on average.

(I am ignoring a different sort of effect here: the piston will start to see a lower and lower temperature for the photons that come from the wall as its speed gets closer to the speed of light, but this is an entirely different effect from the one considered in the post by Robert.)

I believe the second scenario is a simple version of the solar sail.

(I guess this could be considered to be just an elaboration of Arun's comment.)

arkadas ozakin

Anonymous said...

The sail will no more asymptotically reach the temperature of the sun than the earth has in 4+ billion years.