Celestial bodies possess a fraction of their own mass which results from their internal gravitational binding, and celestial bodies have finite size (rather than being point- bodies). Such bodies undergo their most revealing motions when located in the strong gravitational fields close to black holes or other highly compact bodies. The equations of motion of such bodies when located in the strong gravity environment will be calculated from first principles, both in general relativity theory and in alternative theories. Perturbation theory will be applied to the exact, strong field Schwarzschild environment, rather than working with the perturbations to the empty space Minkowski environment of the classic studies of this problem of motion. Direct application of the results of these calculations can be made to interpreting the results of present-day radio telescope observations of pulsars, and to near-future efforts to detect and understand gravity wave signals from the cosmos.
