light bent in gravitational field..

tomz

i am new to GTR. Mytext book use an example to show ligt bendinf.
when a light release from the back of the rocket which goes around the earth, since the rocket is in free fall, light would not bent relative to the rocket, but bent relative to earth.

my problem is, is that means the amount of bending depend on the speed of the rocket?
if the rocket is very fast, than light would travel greater distance relative the earth, so there more bending?

If there is no rocket, but just a light source above the earth, would it bent at all?

Thank you...

bcrowell

The notion of whether a world-line is or is not curved (is or is not a geodesic) is defined independently of other world-lines. I think what's probably confusing you here is that you're imagining two trajectories in space, the rocket's and the light beams. These two trajectories are initially tangent, but later diverge. But the relevant notion is not a trajectory in space, it's a world-line in spacetime. The world-lines of the rocket and the light beam are *not* initially tangent.

It would indeed be a problem if two geodesics, initially tangent at a given point in spacetime, later diverged. But that isn't the case here.

Nothing here depends on the source. Given the initial position and direction of motion of a ray of light, you can find its later motion.