Planetary perihelion precession is theoretically examined within the framework of special relativity. The Eötvos experiment is used to motivate an assumption that the inertial and gravitational masses have the same velocity dependence. The resultant orbit equation is then approximated by one that is soluble in terms of trigonometric functions, and the accuracy of the approximation is examined. The perihelion advance predicted by the approximate equation is twice that predicted by special relativity without a velocity-dependent gravitational mass. Finally, the behavior of a photon in a gravitational field is investigated in a way consistent with the assumptions of this paper, and the usual values for the gravitational red-shift and light deflection as calculated with special relativity and the postulate of equivalence result.