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This paper poses the following question: How precisely must an Earth orbiter's dynamics be mapped to accurately capture the statistical evolution of its uncertainty? This question is addressed by using a simplified dynamical system that replaces the short-period variations with constants. The systems are defined and applied to the propagation of uncertainty for a non-Keplerian orbit. The simplified dynamical system is defined with two different types of approximate solutions: one is based on the Brouwer-Lyddane theory, and another is based on Lagrange planetary equations. The simplified dynamical system allows exploration of the relationship between dynamical model precision and uncertainty propagation accuracy, as well gained insight into effects due to individual variations: that is, secular, short, and long periods. Accuracy of propagation of uncertainty with the simplified dynamical system is verified with statistical methods for dynamical models including perturbations of J 2 and third-body gravity. In conclusion, the simplified dynamical system is capable of propagating uncertainty accurately and efficiently, as well as discovering that the secular variations are dominant in uncertainty mapping.

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