Impact of the integration stop-condition on the accuracy of regularized orbit formulations

Abstract

The tight relationship between the stop-condition of a numerical integrator and the resulting accuracy of regularized orbit propagators is addressed. It is noted that the use of events as a means to halt the numerical orbit propagation introduces timing or phasing errors in formulations involving a Sundman transformation. The fundamentals of this timing error are described, along with the mechanisms that produce this apparent loss in the achievable accuracy. This behavior is linked to the dynamical instabilities of the orbital motion. Examples are provided to support that the purely geometrical description provided by regularized methods is typically orders of magnitude more accurate than when the timing error is taken into account.