Reference: Moore, Thomas A., *A General Relativity Workbook*, University Science Books (2013) – Chapter 10; Box 10.3; Problems 10.10, 10.11.

For a circular orbit, the Schwarzschild angular speed is obtained from the angular momentum:

We can write this as

Comparing this with the angular speed measured at infinity we have

Thus .

The relation between and for a circular orbit is

In the Newtonian case, we can use Kepler’s law at all distances, so we have

Note that we can get the same result by defining the Newtonian energy

and then solving

In the Newtonian case, the potential energy has only one minimum.

For large , we can expand 5 to get (using the minus sign)

Thus the Schwarzschild case reduces to the Newtonian case for large .

### Like this:

Like Loading...

*Related*