Solar Sailing and Physics

Roland Piquepaille writes "In this article, the New Scientist writes that the next generation of spacecraft might be propelled with the help of the sun. "Both NASA and the European Space Agency are developing solar sails and, although never tested, the concept is quite simple. A solar sail is essentially a giant mirror that reflects photons of sunlight back in the direction they came from." But Thomas Gold from Cornell University in New York says the proponents of solar sailing have forgotten about thermodynamics, the branch of physics governing heat transfer." And this is where it's becoming interesting. Gold's paper, "The solar sail and the mirror," states that "either Carnot's accepted rule is in error, or the solar sail proposal will not work at all." So, as this illustration from New Scientist shows, the real question is: "Can it really sail away?" We'll know it in September when the first tests are done. In the mean time, read this summary for more details and read the original stories for far more information."

Comments

I don't think so

[PhysicsGenius]

Gold's claim isn't merely that solar sails won't work, but that radiation pressure in general is non-existent. This is patently false, since my undergrad physics book has an actual picture of a small sphere being levitated by a powerful laser. So where has he gone wrong?

Here's the crux of his argument: But what will be the performance of the mirror as a heat engine? If the mirror receives heat energy from the Sun and converts some of this into free energy, namely the kinetic energy of its motion, it falls into the strict definition of a heat engine, and Carnot's rule defining the maximum efficiency for this energy conversion must apply. We can determine the incoming temperature of the radiation by measuring the temperature an absorbing (black) body would reach when exposed to the radiation being sent to the mirror, and the temperature a black body would reach exposed to the outgoing radiation from the mirror, both measurements carried out in common motion with the mirror. Carnot's rule would then give the maximum efficiency as that fraction of the heat flow trough the mirror, given by the difference of the two temperatures, divided by the input temperature. It would be that fraction of the heat flow that could maximally appear as kinetic energy gained by the mass of the mirror. If this was a perfect mirror, the two temperatures will be the same, and it follows that the mirror cannot act as a heat engine at all: no free energy can be obtained from the light. The proposed solar sail cannot be accelerated by sunlight.

Carnot only applies to closed systems. In textbook examples of heat engines, the engine, the heat source and the heat sink are all included in the analysis. Gold has included the engine (the sail) and heat source (the sun), but he's neglected the heat sink (the almost-perfect blackbody of intergalactic space). It isn't the temperature difference between absorption and emittance that matters, it's the temperature difference between source and sink, and that difference is huge here.

Oh, it's worse than that...

[gilroy]

The crucial bit is, Carnot's argument holds for a heat engine, a device that executes a cycle and returns to its original state. The solar sail is not returning to its original state.

Actually, the number of misconceptions and errors in this "article" boggle the mind... For example,

From a formal point of view, it is clear that one could not equate radiative momentum content with Newtonian momentum. Newtonian momentum is Mv, clearly a vector, while the momentum attributed to radiation is E/c, a scalar, since E is a scalar and c is a universal constant of nature.

Except, of course, that that expression is for the magnitude of the momentum. Duh. The momentum carried by the photons emitted by the Sun lies in the direction those photons take; for any given photon, the momentum is radially away from the Sun. For all of them together, the momentum is zero because they all cancel -- but that happens only when you integrate over the entire sphere. For the tiny portion hitting a sail, there would be net momentum.

Tacking sail boats

[LemonYellow]

The trouble with that analogy is that you can only tack a sail boat because it has a centreboard to stop it from going sideways, which is difficult to arrange for in space. Try it without sometime.

The other comments about gravity doing the moving-towards-the-sun bit sound right, though.

Absolute rubbish

[Captain Igloo]

The article is cluttered with flaws and unfortunate misinterpretations of laws of physics. These flaws do not turn better if they are part of a complex theoretical explanation.
1.) Electromagnetic radiation has momentum, otherwise, there would be no electromagnetic forces. Period.
2.) Light is not heat - it is a directed stream of photons and a solar sail is by no means a heat engine being limited by the Carnot principle.
3.) Energy conversion holds due to doppler effect - reflected photons get their frequency shifted to red.
4.) Sailing boats have been working perfectly for thousands of years, using a similar principle with air carrying the momentum. And the air was not absorbed by the sails!

Solar Intensity

[Unknown Kadath]

The sun provides negligable energy out past the orbit of Mars.

Not negligible, but solar intensity does fall off as 1/r^3. In Mars orbit, the solar radiation on a surface normal to the incipient light is about 60% of that in Earth orbit. This represents the fact that the photon are spreading out in a sphere from their source--though there are just as many as there were on the surface of the Sun, there's now a whole lot more space in between them.

I'm most familiar with this in the context of solar powered spacecraft. To operate a solar S/C near Mars, you need massive unwieldy solar arrays that are expensive to launch. The only other viable power source for space, currently, is thermoelectric conversion from the heat generated by nuclear decay (not a live reaction), and is only 6-7% efficient.

We still need someting like Prometheus in order get around and about in places where the sun doesn't shine brightly.

Agreed. The Nuclear Space Initiative is the only way we will ever get something sizeable to the outer planets--and back. Spaceflight requires too much power to be generated any other way, at least with the science we can do now.

-Carolyn

No, it IS a heat engine. But he's still wrong.

[Ungrounded Lightning]

The solar sail is a heat engine. But he's still wrong.

The basic claim is that the photon doesn't lose energy to a perfect mirror. But that's wrong. It neglects both the ACCELLERATION of the mirror due to the impact of the photon, and the red/blue shift of the photon when reflected from a mirror in motion relative to the observer.

It's easy to understand the lightsail/sun/photons system as a heat engine: The lightsail is the piston and the photons are the working fluid.

Just as with a piston, if the lightsail were held still (and the mirror were perfect or imperfect but at solar temperature) the photons would rebound without loss of energy. But the high photon-gas "pressure" on one side of the "piston" versus the near-vacuum (dark sky) on the other side means there is a force on the mirror. If not held it will accellerate.

Just as with a piston, no work is done on it until it starts to move - and the faster it moves the more work is done on it. But the faster it moves the more the light is red-shifted, i.e. the "gas is cooled", so the more rapidly work is done. Exactly what you expect in a piston engine.

You could also push the light sail toward the sun (as when decellerating at the far end of the trip). In this case the photons would be blue-shifted and the work from pushing the sail against light pressure would thus go into "heating" the photons - and the sun, if the sail was pointed properly so the "photon gas" hit the far end of the "cylinder" rather than escaping.

His analysis assumed the sail was unmoving and unaccellerating, which is just plain confused.

Re:Laws? Who needs them?

[sigwinch]

I'll repeat it again because too many seem to believe that crap: That sail is not a heat engine.

And the reason why is that the so-called "temperature" of sunlight is not a thermodynamic temperature. Thermodymanics assumes not merely that there is a dynamic equilibrium involving two entities, but that the entities come into mutual equilibrium by affecting each other. In the solar sail case, the incoming sunlight is completely unaffected by the behavior of the solar sail. The solar sail could be glowing x-ray hot, or it could be a perfect blackbody attached to a perfect heat sink, and the spectrum and energy density of the incoming sunlight would not be affected one whit. Thus there is no mutual equilibrium, and thermodynamics does not apply.

On a more technical level, the incoming photons do not obey Maxwell-Boltzmann statistics (not even vaguely approximately), so it is not semantically valid to make thermodynamic statements about them.

As to energy conservation, photon reflection is physically an absorption followed by a reemission. Since the mirror is accelerated by the process, an observer in the rest frame sees a doppler redshift of the reflected photons, and thus energy balance is maintained.

Finally, even if you wanted to sprinkle goat blood on the photon spectrum and call it a thermodynamic quantity, the redshifting preserves the blackbody spectrum (one of physic's remarkable results) while making it "colder", and thus the "temperature" decreases appropriately.

Show me the Planckian radiators, Gold! And then we can talk thermodynamics.