denotes derivation with respect to proper time .

For a massive particle, the components of the four-velocity satisfy the following equation:
:

We use the geodesic equation:
:The only nontrivial equation is the one for . It gives:
:From this, we get:
:Substituting this into the equation for a massive particle gives:
:Hence:
:

Assume we have an observer at radius , who is not moving with respect to the central body, that is, their four-velocity

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