How many Keplerian arcs are there between two points of spacetime?
Mathematical Physics
2023-04-12 v1 math.MP
Abstract
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition case" where infinitely many planes of motion are possible, there are at most two such arcs of each "type". There is a bilinear quantity that we call b which is in all the cases a good parameter for the Keplerian arcs joining two distinct positions. The flight time satisfies a "variational" differential equation in b, and is a convex function of b.
Keywords
Cite
@article{arxiv.2302.06013,
title = {How many Keplerian arcs are there between two points of spacetime?},
author = {Alain Albouy and Antonio J. Ureña},
journal= {arXiv preprint arXiv:2302.06013},
year = {2023}
}
Comments
16 pages, 3 figures