- #1

Buzz Bloom

Gold Member

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## Summary:

- I need help to figure out how the formula for the velocity of a circular orbit can be derived from the Schwartzschild metric .

## Main Question or Discussion Point

Below are equations/formulas/text from

I apologize for not remembering the source for the "v=" equation, or for my inability to find it again.

For a circular orbit, the distance r and proper distance s are both constant. Therefore

##{r^2 {dθ}^2} = {c^2} /sqrt {1-r_s/r}} {dt}^2 ##

## r = 1##

I apologize for not remembering the source for the "v=" equation, or for my inability to find it again.

For a circular orbit, the distance r and proper distance s are both constant. Therefore

ds = dr = 0.

Assume the coordinates are such that the orbit has:sin ϑ = 1, and dϑ = 0.

Therefore the metric an be written##{r^2 {dθ}^2} = {c^2} /sqrt {1-r_s/r}} {dt}^2 ##

## r = 1##