How do solar sails work if photons don’t have mass?
In: Physics
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Because newtonian physics is wrong, momentum is usually described as p=mv, which is usually very close but wrong in this case. The better equation is p=E/c where E is energy, photons have energy so they have momentum and can push a solar sail.
They have energy! And Einstein has shown by his famous equation E=mc^2 that they are one and the same thing.
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They don’t have mass, but they do have momentum and energy.
The sail bounces the photon off and conservation of moments takes over.
E^2 = (mc^(2))^2 + (pc)^2
You may be familiar with the case where momentum is 0 (p=0)
E=mc^2
Well, if we take the case where mass is 0 (m=0)
E=pc
The energy of a photon is E=hf (f being frequency and h being planck’s constant)
hf=pc
p=hf/c
c=fλ (λ being wavelength)
So p=h/λ
I got automoderated for providing a one-liner which included the correct equation, so I will elaborate.
– Force is the rate of change of momentum.
– Photons carry momentum despite being massless.
– The value of said momentum is p in the equation E=pc
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Whelp, guess I need to downgrade myself to ELI3?
I actually looked this up the other day and summarized what I read to my friend:
Despite that they have no mass, the equation of their energy instead uses λ which is the wavelength, and shorter wavelengths carry more momentum.
In everyday applications this energy is negligible to a person overall, like even high frequency photons like X-Rays are not going to truly affect a macro object like a person.
But if you take the λ value to it’s logical extreme and assume “minimal wavelength” as the shortest wavelength possible, or the theoretical minimum, the Planck length, a single photon would have I N S A N E energy. A human being struck by a photon with a λ equal to the Planck length would result in immediate vaporization. The energy involved is many orders of magnitude higher than what is needed to instantly vaporize any material, including human tissue.
So, in the original Legend of Zelda, you know how when Link is at full hearts, he can shoot out the light beam sword? The energy sword weighs zero and is always moving. Not that you can, but if you caught it in your hand it wouldn’t weight anything. But even though it weighs 0, it still does damage and shoves enemies around when you hit them with it, just like things that actually do have mass in game, like his real metal sword, boomerang, arrows and bombs.
Light photons are kind of the same way!
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