On a set of J$$_2$$ equinoctial orbital elements and their use for uncertainty propagation

Abstract

This paper defines a set of six non-singular orbital elements designed specifically for the characterization of uncertainty in the state of a resident space object in circular or elliptic orbit and demonstrates their use for uncertainty propagation in the context of the perturbed two-body problem of orbital mechanics. As evidenced by the time evolution of the Cramer–von\xa0Mises test statistic, representation of the orbital state probability density function in J\n $$_2$$\n EqOE yields less nonlinear uncertainty propagation and provides covariance and uncertainty realism for much longer periods of time than what is possible using Cartesian coordinates or even equinoctial orbital elements, without an appreciable increase in computational cost.