- #1
johne1618
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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
[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 Schwarzschild radius.
Is this right and how would one show it using the Schwarzschild metric and the geodesic equation for a circular orbit?
[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 Schwarzschild radius.
Is this right and how would one show it using the Schwarzschild metric and the geodesic equation for a circular orbit?