Two locations, two times, and the element set

Abstract

A robust analytical formulation is developed to apply classical initial orbital determination to artificial satellites whose locations are uncertain to about 1 cu km and separated in time by no more than 30 min. An analytical simplification reduces Gauss's method, iteration on the semilatus rectum, iteration on the true anomaly, and the Lambert-Euler technique, to the solution of a single equation in one unknown, instead of the usual coupled triplet of three equations in three unknowns. The method is demonstrated for all common artificial satellite orbits over a variety of time intervals between the two location vectors, and for a varied set of position and distance errors.