# Solar Sail Questions

I'm just looking for a good (better) analogy.

How do massless photons put pressure on a surface especially when it's a mirror? Using the analogy of the wind (atmosphere) on a sail breaks down when I think that an air sail catches the wind and that the wind has mass and is an object in motion but how can a mirror catch a proton and how would it matter if it does if it's massless? Where does the force come from? The one article that mentions red shift was a math equation so it did not help me get my brain around it.

Does it have more to do with the momentum energy of the proton and can that be explained in simple terms?

As a child I imagined a solar wind sail but a light sail is a different concept.

I hope it's not too dumb of a question and that this type of question is appropriate here.

This is newton second law: $$\mathbf F = \frac{\Delta\mathbf p}{\Delta t}$$

As you can see, its variation of momentum that brings force. So, its the transfer of momentum. Granted, photons are massless, but they do have momentum.

There are two ways of a photon transfer momentum to a solar sail: The photon is absorbed (also heats up the sail), or, the photon is reflected.

• Thanks, I imagined that some photons were absorbed (by chance?) and that that would be converted to heat but how is that energy potential then converted into the work of moving the sail? Is it by being re-emited? – John H Jun 21 '16 at 3:20
• @JohnH There is a rate of absorption/reflection depending on the EM properties of the sail. Its easily calculable using EM Theory. And about the second question, its a fully inelastic collision. The sail will gain the momentum of incoming photon, and have a definite speed. The the sail will move because of it. Conservation of energy tells: Energy of photon = Kinetic energy of sail (from the speed derived earlier) + heating of sail. If you want I can insert all those relations in my answer =). – Physicist137 Jun 21 '16 at 17:54
• Isn't there also a lot force on the sail by all the electrons and protons of the solar wind plasma? – John H Jun 21 '16 at 23:59
• @ Physicist137, Is this article on Resolution of the Abraham-Minkowski Controversy old news? arxiv.org/ftp/arxiv/papers/1208/1208.0872.pdf – John H Jun 22 '16 at 18:28
• @JohnH Well..I haven't read the article. But, whatever is the model you use: light passing through the medium, light reflecting, light magically vanishing and transforming in heat (absorption), It does not matter: The momentum will be conserved, and so as energy. So you can disregard how exactly the process happens, and come up with a crude model, of light as a ball hitting sail, and getting reflected (elastic collision) or absorbed (innelastic collision), and then apply conservation of momentum and energy to figure out what will happen to the sail (speed and heating). And that's what I did. – Physicist137 Jun 25 '16 at 17:48

Most people believe that you need mass to transmit a force, or even to be able make one, but the more fundamental concept happens not the force but the momentum. The momentum is the capacity to interact with another entity and transfer it some change in speed. In the case of the photon, it is massless but however has momentum and energy. The energy and momentum of a photon depend only on its frequency ($\nu$) or inversely, its wavelength ($\lambda$):

$E=\hbar\omega=h\nu=\frac{hc}{\lambda}$

$\boldsymbol{p}=\hbar\boldsymbol{k}$

• Yes, I imagine most people don't even understand what mass is which is why we explain everything by analogy (except for mathematicians) ;) – John H Jun 21 '16 at 3:29
• Newton couldn't have known better... cut him some slack. :-) – CuriousOne Jun 21 '16 at 4:42