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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."
This works well for exploring the inner planets, or if you just want to do a flyby of the outer ones. The sun provides negligable energy out past the orbit of Mars. We still need someting like Prometheus in order get around and about in places where the sun doesn't shine brightly.
My rights don't need management.
The article is wrong in the sense that it treats the photons from Sun to be in the form of heat - they are not, because their velocities are not randomised - there is a net momentum radially away from the sun. Carnot's cycle assumed the thermal energy to be in the thermodynamic form, i.e. say internal KE of gas, etc... You could simply adapt this guy's argument to a bullet hitting a plank of wood and show that wood gaining motion would break carnot's law - this is not the case.
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.
The Solar Sail and the Mirror says:
"If this was a perfect mirror, the two temperatures will be the same"
This ignores the frequency shift due to the moving mirror. Proof falls down. Thermodynamics and conservation of momentum both still hold.
Physics correct! News at 10!
Yawn.
NO ID: BEING FREE MEANS NOT HAVING TO PROVE IT
Gold's theory ignores one important aspect- the doppler effect.
Let's do a gedankenexperiment (thought experiment).
Hypothesize that you have such a solar sail and it's already in orbit and starting to pull away from earth (say, because an ullage rocket has initiated a short accelleration)
The incoming solar photons - IN THE FRAME OF REFERENCE OF THE SAIL - enter and leave at constant wavelength. But the sail is moving with respect to the rest of the solar system (the ullage rocket kick-started this motion)... so the wavelength measured in the frame of reference of the sail mirror is not correct.
In the external (non-accellerated) frame of reference of the solar system, the photons hit the mirror at some particular wavelength, but exit at a longer wavelengh (because the mirror is moving).
The count of photons is the same- but their energy is lower.
So, where did the energy go? Draw the Feynmann diagram: there's only one place it could have gone- and that's into the sail itself. Therefore the sail accellerates further.
A similar gedankenexperiment will show that a sail moving _toward_ the sun pumps energy into the photons, and so decellerates.
I suspect Feynmann proposed this as an exercise, since the flaw is obvious to anyone with a degree in theoretical physics.
Flaw: Light is red-shifted climbing out of the gravity well. So when it reaches d2 there is not so much energy as when it left D1, so a smaller amount of mass will be produced. When it falls back down, the mass difference is equivalent to the kinetic energy gaind from falling by the equivalence relation E=mc^2.
NO ID: BEING FREE MEANS NOT HAVING TO PROVE IT
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.
You are correct that the Carnot efficiency cannot be calculated for this case, as it is not returning to it's original position. However, in the postulated case of a perfect mirror, there is no heat sink, as the photons will be reflected back towards the sun, and not radiated from the back of the sail. If the photons are absorbed by the sail, then some are radiated to the heat sink, and the expansion is no longer adiabatic (which is consistent with the lower momentum transfer). Note that if the mirror ~was~ returned to its original position, and the sun was insulated against losses in directions other than towards the sail, you would have an adiabatic expansion and then compression of the photons, leaving you with no net change in energy.
Gold complains in his paper of physicists not treating photons thermodynamically. That's funny - I seem to remember working out a problem using an adiabatic expansion of a photon "gas" in my undergraduate days. I don't remember the equation of state off the top of my head, but I guarantee you can find it in Callen or any other thourough thermo book.
Yes, IAAP. I also think that slashdotters should note that this was published in the Arxiv, which is NOT a peer reviewed publication (although I must say that the Arxiv rocks!). The Arxiv is sort of like an open source scientific journal, or a BBS for scientific papers. I highly recommend wandering around in it for a few hours, but remember to take everything in there with a grain of salt.
Darn. I was going to try NOT posting to slashdot today. Oh, well. Feed the addiction (sticks needle labeled "/." in arm).
Um, sorry, no. Photons have no mass. You need the full form of the equation: E^2=(pc)^2+(mc^2)^2 which for a massless photon (m=0) would become E=pc. p in this case is momentum, which photons do have.
When the photon strikes the sail it imparts momentum to it. LOTS of photons=lots of momentum and near the Sun there are a LOT of photons. Bear in mind the sail will need to be HUGE. Also momentum has direction (vector not scalar).
Oh, and the effect of the odd hydrogen atom should be very small in comparison to the LOTS of photons constantly (alright, discretely if you're delving into duality) striking the surface of the sail. It will be slowed down slightly by atoms floating through space but if the sail is large enough and light enough then theory says it should be able to break free of the Sun's gravity (of course that's what the original argument is about). Do you really think one or two little hydrogen atoms will be much of a problem?
No numbers were harmed during the course of this diatribe, but a few ego's were bruised...
If you can't think of something nice to say then don't say anything at all. No, REALLY.
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!
Gold says that as the sail is a perfect mirror the light is reflected at the same temperature and so Carnot's law applies. But of course, if the light were reflected at the same temperature it wouldn't be losing any energy so a working solar sail would violate conservation of energy and the laws of thermodynamics would be the least of our problems.
Gold's problem is that he forgets both conservation of momentum and conservation of energy. What happens is that as the sail is kicked forward (gaining both energy and momentum) the photon is reflected with slightly less energy than it arrived with (ie is cooler) and conservation of momentum, conservation of energy and the laws of thermodynamics still apply.
My back of an envelope calculations tell the fractional energy loss is E/(M*c*c) where E is the photon energy and M the sail mass.
You will notice that Gold's article doesn't appear in a refereed journal: this is because most referees have heard of conservation of energy.
Dr John Rowe
School of Physics
Exeter
UK
It is obvious that if he is at the Cornell Center for Radiophysics and Space Research, then he is not an actual physicist there. I actually suspect some ulterior motive behind this.
There is no thermodynamic problem with radiation pressure and solar sails, Carnot, Maxwell and Einstein are correct, and Thomas Gold is wrong.
The photons that leave from the Sun are at a Maxwellian distribution at the temperature of the Solar photosphere, many thousands of degrees.
The photons which are re-emitted by the heat of the sail are at the temperature of the sail, which is obviously less than the temperature of the Sun.
There is a temperature gradient, hence work is done.
Gold is also obviously uneducated in physics because of his assertions about how momentum is 'E/c' and how 'E' is a scalar but momentum is a vector, blah blah blah.
The correct way to do an electromagnetic problem like this in purely classical E&M (which is all that is necessary to solve this problem) is to use the stress energy tensor, which is certainly non-zero for propagating electromagnetic waves.
You then use this to find the forces on material bodies, e.g. dielectrics or conductors. You have to think about the stress-energy tensor on both sides of the material body and add up forces.
(interesting note, you can also get angular momentum out of this too, appropriately polarized electromagnetic waves can exert a torque).
I learned this in my sophomore year physics class.
Actually, this sounds like a good problem set problem. "Hmmm....now that you ask about it--------yes, it WILL be on the final exam! muahahha."
Given a plane wave source of incoming radiation with flux F_0, with a certain amount of it R1 reflected and the remainder absorbed, what would be the net acceleration in the direction of the radiation of the solar sail with emissivity E once it has reached thermal equilibrium, accounting for all radiation forces. Assume space is at 0 degrees.
What you would do is to put in on the incoming side, the stress energy tensor for the incoming radiation, the outgoing radiation, plus, on both sides, radiation emitted from a black body.
You first get the energy balance right, and then solve for the acceleration.
If you want to be tricky, you would go into the accelerating frame of the sail, and then appropriately red-shift down the incoming frequency of the radiation.
Here is my suspected ulterior motive. This thermodynamic fallacy is exactly the same one that creationists use to deny the obvious explanation for why plants live and complex life evolved.
Namely that the Sun has been providing input energy at 10,000 degrees and the Earth has been re-emitting energy at 300 degrees K and the temperature difference over 4 billion years can do a fair amount of work.