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We investigate perturbations in the Kepler problem. We offer an overview ofthe dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics tobuild a foundation for analyzing perturbations. We consider the effects of adeterministic perturbation in the form of a first order relativistic correctionwhich change bounded orbits from standard to precessing ellipses. We alsoconsider the effects of stochastic perturbations with certain potentials andevaluate the analytical results of mean exit times using Monte Carlosimulations.

Deterministic and Random Perturbations of the Kepler Problem