Solution for the Lambert's Problem

摘要

An this work, we have formulated and solved the well known Lambert problem, one of the most important topics in celestial mechanics. As Lambert stated, the transfer time depends only on the unknown parameter a (semi major axis), the two radii and the chord length are already known from the definition of the problem. It should be possible to write the transfer time as a function of the semi major axis only (t_2 — t_1= Δt = f(a)). Also the transfer time can be written as a function of some other parameter such as ΔE, this allows for a well-behaved iteration, and is the chosen method for the universal variable formulation. We solve Lambert problem by using this method, for two cases, elliptic orbits and hyperbolic orbits. Parabolic orbits are of no practical importance. We consider the Earth - Mars trajectory case, as a numerical example.