An elementary solution to Lambert's problem

Abstract

A fundamental problem in spacecraft mission design is to find a free flight path from one place to another with a given transfer time. This problem for paths in a central force field is known as Lambert's problem. Although this is an old problem, we take a new approach. Given two points in the plane, we produce the conic parameters for all conic paths between these points. For a given central force gravitational parameter, the travel time between the launch and destination points is computed along with the initial and final velocities for each transfer conic. For a given travel time, we calculate the parameters for a transfer conic having that travel time.