Gravitational Orbits and the Lambert Problem

TL;DR

This paper reviews gravitational orbits and presents a direct solution to the Lambert problem, which determines the orbit between two points with a specified time of flight, including a search procedure for the solution.

Contribution

It introduces a direct method for solving the Lambert problem using the path equation and details a search procedure for the specified time interval.

Findings

Effective solution method demonstrated with example

Direct use of path equation simplifies the Lambert problem

Provides a practical approach for orbital transfer calculations

Abstract

The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of the Lambert problem is presented using the path equation directly. However, because the time interval is specified, the solution requires a search procedure. An example is given to illustrate the method.