An elementary solution to Lambert's problem

TL;DR

This paper presents a new, elementary method for solving Lambert's problem by deriving conic parameters for all possible transfer paths between two points in a plane, facilitating mission design in spaceflight.

Contribution

It introduces a novel approach to Lambert's problem by explicitly calculating conic parameters for all transfer paths and corresponding velocities for any given travel time.

Findings

Provides explicit conic parameters for all transfer paths

Calculates initial and final velocities for each transfer

Determines transfer conic parameters for specified travel times

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.