Motion of particles of non-zero rest masses exterior to astrophysically real or hypothetical spherical distributions of mass whose tensor field varies with polar angle only

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. Keywords: Tensor field, spherical distribution, mass, motion, polar angl