Connect the dots ... finding all possible orbits between two points

TL;DR

This paper explores the problem of determining all possible orbital paths connecting two points under gravitational influence, using conic sections and angular momentum, with applications in orbit determination and space mission planning.

Contribution

It introduces a method to find all possible orbits connecting two points using conic sections parameterized by angular momentum, applicable to various space navigation problems.

Findings

Derived a family of solutions for connecting two points with conic orbits.

Applied the method to solve the Lambert problem for transfer orbit calculation.

Provided accessible techniques suitable for advanced undergraduates in physics and aerospace engineering.

Abstract

You have a satellite spacecraft or asteroid that moves under the gravitational influence of a massive central body and follows a Keplerian orbit around it ellipse parabola or hyperbola Given measurements of two positions in its orbit what is the family of possible orbital paths that connects them I use the conic section orbits semilatus rectum directly related to orbital angular momentum to parameterise these orbits The solutions have applications to orbit determination ballistic missiles interplanetary interception and targeted reentry I also show how they can be applied to solve the Lambert problem of finding the unique transfer orbit that connects two points in a specified time interval These results are accessible to advanced undergraduate students in physics or aerospace engineering. Supplementary materials are provided online