General relativistic mechanics in gravitational fields exterior to homogeneous spheroidal masses is developed using a new approach. Einstein's field equations in the gravitational field exterior/interior to a static homogenous prolate spheroid are derived and a solution for the first field equations constructed. The field equations exterior and interior to the mass distribution have only one unknown function determined by the mass or pressure distribution. The obtained solutions yield the unknown function as generalizations of Newton's gravitational scalar potential. Remarkably, this solution puts Einstein's geometrical theory of gravity on same footing with Newton's dynamical theory; with the dependence of the field on one unknown function comparable to Newton's gravitational scalar potential.The consequences of the homogeneous spheroidal gravitational field on the motion of test particles has been theoretically investigated. The effects of the oblate nature of the Sun and planets on some gravitational phenomena has been examined. These are gravitational time dilation, gravitational length contraction and gravitational spectral shift.