Classifying State Uncertainty for Earth-Moon Trajectories

While the evolution of state uncertainties from Gaussian to non-Gaussian is well understood in geocentric orbits, the only data product made publicly available by the United States Space Force, the Two-Line Element, does not include state uncertainties at all. With a new international focus on cislunar space situational awareness, it is useful to determine how this complex dynamical environment influences trajectory uncertainties and the resultant implications for data association, orbit determination, and force model algorithms. This paper utilizes a new tensor eigenpair measure of nonlinearity (TEMoN) to quantify the nonlinearity of gravitational forces in the cislunar regime. This measure is then compared with various characterizations of Gaussian distributions to determine the value of TEMoN at which trajectory uncertainties become non-Gaussian. This novel advancement combines the cumulative effect of time and physical location of the trajectory into one value. The result is a predictive method that obviates highly parameterized Monte Carlo runs, and allows an objective assessment of how sensor tasking cadence, measurement uncertainty, and force model selection can be balanced to enable nascent cislunar space situational awareness capabilities with legacy space surveillance network assets.