Time elements in Keplerian orbital elements

Abstract

Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with the intermediate anomaly. Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone.