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## Main Question or Discussion Point

I am trying to derive the gravitational red shift effect but I think I am going about it all wrong. Specifically, I want to derive the change in frequency/ wavelength when a photon moves away from the surface of a star mass M and radius R.

So I tried to use relativistic mass of the photon and I got something along the lines of:

[itex]\Delta E= h\Delta f = GMm_{rel}\left(\frac{1}{R}-\frac{1}{r}\right)[/itex]

And then substituting in [itex]m_{rel}=\frac{hf}{c^2}[/itex]

Would give [itex]\Delta f =\frac{GMf}{c^2}\left(\frac{1}{R}-\frac{1}{r}\right)[/itex]

But then I realised that f would be changing as the photon leaves the surface, so I thought that maybe I have to integrate?

Considering the photon rising a small distance [itex]\delta r [/itex] and rearranging would give

[itex]\int\frac{1}{f} df =\frac{GM}{c^2}\int\frac{dr}{r(r+dr)}[/itex]

So it is a big mess right now! Would appreciate if someone could tell me where I am going wrong...

So I tried to use relativistic mass of the photon and I got something along the lines of:

[itex]\Delta E= h\Delta f = GMm_{rel}\left(\frac{1}{R}-\frac{1}{r}\right)[/itex]

And then substituting in [itex]m_{rel}=\frac{hf}{c^2}[/itex]

Would give [itex]\Delta f =\frac{GMf}{c^2}\left(\frac{1}{R}-\frac{1}{r}\right)[/itex]

But then I realised that f would be changing as the photon leaves the surface, so I thought that maybe I have to integrate?

Considering the photon rising a small distance [itex]\delta r [/itex] and rearranging would give

[itex]\int\frac{1}{f} df =\frac{GM}{c^2}\int\frac{dr}{r(r+dr)}[/itex]

So it is a big mess right now! Would appreciate if someone could tell me where I am going wrong...