Effect of Dynamical Accuracy for Uncertainty Propagation of Perturbed Keplerian Motion

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 J2 and third-body gravity. I...

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