- #1
clandarkfire
- 31
- 0
Homework Statement
The gravitational redshift tends to decrease the frequency of light as it travels upwards a distance h,\frac{\Delta{f}}{f_{0}}=\frac{-gh}{c^2}
integrate both sides of this equation (from the surface of the gravitation body out to infinity) to derive the expression for the change in frequency near a high gravitational field:\frac{f}{f_{0}}\cong{1-\frac{GM}{Rc^2}}
Homework Equations
Given above. A photon is emitted at the surface of the gravitational body (M) with radius R. It's frequency is measured distance h above the gravitational body to be f, while its frequency at the gravitational body is f0. g is the gravitational attraction of the body on the photon.
The Attempt at a Solution
Well, I've gotten far enough to see that \frac{f}{f_{0}}-1=\frac{-gh}{c^2}, which makes sense because gh is the increase in gravitational potential energy.
However, I don't know how to express g. I would use F_{g}=G\frac{Mm}{r^2}, but because a photon's mass is zero, I don't know what to do.
I guess I also need to integrate with respect to h.
Help!?
