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).

There is an initial mathematical step you forgot in 1): due to the photon being massless, when one divides the Newtonian force by the mass, one has to use L'Hopitale's (bleeping spelling, not to mention that I can't see a single letter I'm typing

) rule resulting in (if use Newton's 2nd law) acceleration+((d/dm)acceleration)m->acceleration. While it makes little to no difference in your end result it is still required to avoid mathematicians calling you up at 3 or 4 in the morning and ranting at you (

). And, inconsequentially, I would like to point out that while Newtonian can do this, GR makes more physical sense when setting up this problem as there you can just think of it as moving coordinates (the photon I mean) as opposed to the Newtonian requirement that it be "something" (mass/particle/matter/antimatter(with assumptions)/what-not).