In this article, we extend the metric tensor exterior to astrophysically real or imaginary spherical distributions of mass whose tensor field varies with polar angle only; to derive equations of motion for test particles in this field. The time, radial, polar and azimuthal equations of motion for particles of non-zero rest masses moving in this gravitational field have been derived. The expression for the variation of the time on a clock moving in this gravitational field has been obtained for pure radial motion, the particles move with a constant velocity.