Analytical expressions for orbit covariance due to gravity errors
Abstract
Analytical expressions for the LEO covariance due to geopotential errors are presented in equinoctial orbit elements. The analytical method is a sufficient approximation to an existing numerical method, but its evaluation is an order of magnitude faster. The 6 x 6 matrix covariance is singular (or near singular), it is approximately transitive, and it identifies the geopotential driven error in orbital mean longitude as a stochastic Wiener-Levy process (random walk) when the prediction time is significant.