
By how much is a ray of light bent and slowed down when it passes by the earth at certian angles and distances?
  Answer 1:
When a ray of light passes by the earth, it doesn't get slowed at all. It does get bent a little, but it's a very small amount, and also depends on how far away the light is from the earth. A basic calculation gives approximations GM/(4R), where the G is Newtons constant, M is the mass of the earth, and R is the radius it passes by the earth. This gives the angular deviation.
  Answer 2:
It doesn't slow down. As for the bending, that's general relativity, and I don't know how to calculate it. One quick backoftheenvelope type of calculation would be to imagine a particle traveling past the Earth at a speed of c(light), and determine using Newtonian physics how much it would change course. Even that requires calculus, and general relativity requires much more, and you would only get an approximation from the Newtonian physics.
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