Connect the dots ... finding all possible orbits between two points
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
Keywords
Cite
@article{arxiv.2508.02695,
title = {Connect the dots ... finding all possible orbits between two points},
author = {Philip R. Blanco},
journal= {arXiv preprint arXiv:2508.02695},
year = {2025}
}
Comments
14 pages, 4 figures. Supplementary data (supplement PDF, Excel spreadsheet, and animation) at https://iopscience.iop.org/article/10.1088/1361-6404/ade37d/data