The Schwarzschild metric can also be derived using the known physics for a circular orbit and a temporarily stationary point mass [REF].
-c^2 = \left ( {ds \over d\tau} \right )^2 = A(r)\left ( {dr \over d\tau} \right )^2 + r^2\left ( {d\phi \over d\tau} \right )^2 + B(r)\left( {dt \over d\tau} \right)^2.