adsar2
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On 8/10/2017 at 9:44 AM, Ethan O'Farrell said:
I am curious about the formula for gravitational time dilation. I have scoured the internet and can't seem to find any explanation for the variables in the formula. I am aware of velocity time dilation and that formula, but gravitational time dilation stumps me. It should be noted I am only a sophomore in high school so i might not fully grasp all of the mathematics yet however, any help is much appreciated.
The variables stem from using the [url=https://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric]Schwarzschild solution[/url] to the Einstein Field Equations.
1
Gravitational Time Dilation Formula?
in Relativity
Posted
This may be an easy or a very difficult question, depending how you looked at it:
1. The easy way - ignore the gravitational mass of the Moon. Apply the Schwarzschild solution
[math](d\tau/dt)^2=(1-r_s/r) -(v/c)^2[/math]
Where r is the distance between the Earth and Moon centers, r_s=9mm is the Earth Schwarschild radius, v is the tangential speed of the Moon wrt the Earth
2. The very difficult way, use the "two body solution" for the EFE's. This solution has become available only recently. The same steps apply as above.