Analytical Nonlinear Propagation of Uncertainty in the Two-Body Problem

One topic of recent interest in the field of space situational awareness is the accurate and consistent representation of an observed object’s uncertainty under nonlinear dynamics. This paper presents amethod of analytical nonlinear propagation of uncertainty under two-bodydynamics. In particular, the probability density function over state space and itsmean and covariancematrix are expressed analytically for all time via a special solution of the Fokker-Planck equations for deterministic Hamiltonian systems. The state transition tensor concept is used to express the solution flow of the dynamics. Some numerical examples, where a second-order state transition tensor is found to sufficiently capture the nonlinear effects, are also discussed.