Lumbi, W.L.Uchenna, E.T.Ewa, I.I.Loko, A.Z.Ndikilar, Chifu E.2023-12-142023-12-142018-12-10Howusu , S.X.K. (2003). Discourse on General Relativity, Jos University Press,Ltd; 2003, 98 -105 Howusu , S.X.K. (2007). The 210 Astrophysical Solutions Plus the 210 Cosmological Solutions of Einstein’s Geometrical Gravitational Field Equations. Jos University Press, Jos, 2007. Howusu , S.X.K. (2010). Exact Analytical Solutions of Einstein’s Geometrical Gravitational Field Equations. Jos University Press, Jos, 2010. Izam, M. M. & Jwanbot, D. I. (2013).Complete Solution for Particles of nonzero Rest Mass in Gravitational Fields. Advances in Physics Theories and Applications 17:224 - 227 Lumbi, L. W., Ewa, I. I. & Tsaku, N. (2014). Einstein’s Equations of Motion for Test Particle Exterior to Spherical Distributions of Mass whose Tensor Field varies with Time, Radial Distance and Polar angle. Archives of Applied Science Research Library. Ndikilar C. E, Howusu,S.X.K, & Usman,A.,(2008). Motion of Photons in Time Dependent Spherical Gravitational Fields. Journals of Physics Students. 2:10 -14. Ndikilar C. E & Howusu, S. X. K. (2009). Solution of Einstein’s Geometrical Gravitational Field Equations Exterior to Astrophysically Real or Hypothetical Time varying Distributions of Mass within Regions of Spherical Geometry. Progress in Physics 3: 45-48 Ndikilar C. E.,Howusu S.X.K. & Lumbi L.W. (2009). “Relativistic Mechanics in Gravitational Fields Exterior to Rotating Homogeneous Mass Distribution within Regions of Spherical Geometry.” Progress in Physics, 3:31-67. Ndikilar C. E (2014). Orbits in Homogeneous Time Varying Spherical Space-time. Progress in Physics.10:52-55. Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. 231-315.https://keffi.nsuk.edu.ng/handle/20.500.14448/6009In this article, the generalized Schwarzschild metric for time varying spherical fields is used to derive equations of motion for test particles in the vicinity of a time varying spherical mass. A generalized gravitational scalar potential is expanded and used to construct equations of motion for test particles exterior to a time varying spherical distribution of mass. The world line element at the equatorial plane of a spherical massive body was constructed. This was used to study the motion of photons. The equations of motion obtained have additional terms not found in equivalent equations in the Schwarzschild’s field. These are uncovered for theoretical and astrophysical development and applications. Remarkably, when the time varying scalar gravitational potential reduces to that of a static field, results obtained in Schwarzschild's field are obtained. Thus, our generalization is mathematically satisfactory and has astrophysical implications for the study of time varying spherical gravitational fields.enMotion, Test Particles, Photons, Planets, Mass, Non StaticArticle