If an object is orbiting on a circular time-like geodesic path around a mass then the Wikipedia claims that the first component of its four-velocity is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dt}{d\tau} = \frac{1}{\sqrt{1-\frac{3}{2}\cdot \frac{r_0}{r}}}[/tex]

where [itex]r_0[/itex] is the Schwarzchild radius.

Is this right and how would one show it using the Schwarzchild metric and the geodesic equation for a circular orbit?

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# Proper time in circular orbit

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