We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a deterministic perturbation in the form of a first order relativistic correction which change bounded orbits from standard to precessing ellipses. We also consider the effects of stochastic perturbations with certain potentials and evaluate the analytical results of mean exit times using Monte Carlo simulations.

翻译：我们调查开普勒问题的扰动情况,我们利用牛顿、拉格朗江和汉密尔顿机械学来概述动态系统,以建立分析扰动的基础。我们考虑以第一顺序相对性修正的形式确定性扰动的影响,将连接轨道从标准轨道改变为预断省略。我们还考虑具有某些潜力的随机扰动的影响,并利用蒙特卡洛模拟评估平均退出时间的分析结果。