NON-GAUSSIAN ERROR PROPAGATION IN ORBITAL MECHANICS

The problem of propagating orbit initial condition uncertainty is exam ined. The dominant Earth oblateness (J(2)) and atmospheric drag pertur bations are included in the equations of motion. The covariance due to uncertainty in position and velocity is propagated forward in time in the conventional rectangular coordinates, polar coordinates and the o rbit element space. The orbit elements are considered as a candidate s et because all but one of them are ''slow-varying'' varying functions of time. The orbit averaged effects of the perturbations are derived t o establish variational expressions valid over long time periods. Cert ain measures of ''nonlinearity'' are developed to evaluate the validit y of the linearization approximations. After linearization in polar co ordinates, the nonlinear transformation from polar to rectangular coor dinates analytically maps Gaussian statistics in polar coordinates int o highly non-Gaussian statistics in rectangular coordinates. These res ults are in close qualitative agreement with Monte-Carlo simulations. Results due to linearization in orbit elements appear most promising f or long-term uncertainty propagation.