if photons are massless, how can it push something like a light sail, and how can sunlight adds weight to earth?
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Photons are weird, since they move at the speed of light, we’re into relativity which allows odd things like being sort of a wave and sort of a particle and having momentum but not mass, like a photon.
I won’t try to properly explain it, I can’t, I just want to get across the idea that as you approach the speed of light the Newtonian physics we all cover in high school fall apart. Einsteinian relatively and subsequent work building on it lets us theorize and make more accurate observations near or at the speed of light and it’s a different rule set.
Indeed, photons have no mass but they have energy and it this energy (and momentum) that push the solar sail forward.
As for adding weight to earth, that happens when light is converted to chemical energy via the way of photosynthesis from plants, which “traps” the energy in chemical form, which has mass.
Photons don’t have mass, but they have momentum because they carry electromagnetic energy. The change of direction of this energy is what creates the force that pushes a solar sail.
It doesn’t accumulate though, so the Earth is being constantly pushed away from the sun by a tiny force but it’s not getting bigger because of it.
The idea that *momentum = mass × velocity* (or *p = mv*) is from Newtonian physics—which means that it’s a good approximation for slow-moving objects with mass, but it’s an oversimplification that fails to accurately describe physics at velocities near the speed of light or for particles without mass. Under relativity, pioneered by Einstein, photons have momentum despite having zero mass, and that momentum is calculated as *Planck’s constant ÷ the photon’s wavelength,* or *p = h / λ*.
Photons have no “rest” mass. So in the frame they aren’t moving they have no mass.
But photons do move at the speed of light, hence have energy, and a relativistic mass. But the term relativistic mass isn’t really used much, and people use total energy instead.
If c=1 (pretty much always the case because it makes math EZ) we have m^2 = E^2 − p^2 .
m = mass
E = energy
p = momentum
If m = 0 (as is the case of a photon) then it follows trivially that E = |p|. Or in other words a photon has momentum equal to its energy. The Planck Relation will give you the energy: 𝐸=ℎ𝜈 where ℎ is Planck’s constant, and 𝜈 is the frequency of the light.
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