surjective wrote:1) How does Newton's theory predict the bending of light in the first place? Light doesn't have mass, so it can't be gravity. Is it other effects like diffraction?
In newtonian theory, the acceleration of a test body in a gravitational field is independent of it's mass (same with G.R. - this is the equivalence principal) :
f = m*a = G*m*M/r^2, where M is the source mass (ie: the body the photon passes by) and m is the body mass (in the photon case, zero).
Cancelling out the m's, you get a = G*M/r^2
So you see the photon accelerates in the presence of a gravitational field, even in newtonian theory.
2) I can think of numerical methods to calculate the deflection of a particle in a gravitational field. But how would one analytically solve the problem? I'm imagining a small particle (maybe a satellite) traveling at a certain velocity that passes near a large massive object, (like a planet). I'm thinking in terms of momentum conservation, angular momentum, energy conservation, and I can't see a way to setup the problem...
In G.R., you can just solve the geodesic equation in the appropriate metric (which is likely the schwarschild metric if the planet in question is spherically symmetric, uncharged, and has small angular momentum).
In newtonian theory, it's simpler; you just integrate along the particle path.
3) so then how about light (as above?) ?
Same as for massive body (the mass doesn't matter).
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