Orbits of Particles Around Compact Objects: From Newtonian Theory to General Relativity

This thesis gives a general overview of orbital trajectories of particles around compact objects in Newtonian theory and in general relativity. Only two particle systems are considered, with only gravitational attraction taken into account. Orbits are calculated from a set of initial conditions, using different methods such as finding roots of an effective potential, by parameterizing, and solving linear and non-linear differential equations