A Simple Lambert Algorithm

A classic result for the two-point boundary value problem in the framework of Keplerian motion allows the derivation of a novel parametrization of orbits passing through two arbitrary points in space. In particular, it is shown that these orbits can be unambiguously identified in terms of their eccentricity vector component in the direction perpendicular to the chord connecting the two points. The parametrization, in terms of transverse eccentricity component, lends itself to an efficient and intuitive solution algorithm for the classical Lambert problem, that is, the determination of the orbit that connects two points in space in a prescribed time. Although, from the computational point of view, the resulting numerical procedure does not provide advantages over the elegant Battin’s method, its derivation is considerably less demanding from the mathematical standpoint and physically more intuitive.