Hill's level surfaces in the circular restricted three-body problem solved
Instrumentation and Methods for Astrophysics
2026-05-18 v2
Abstract
We report the closed-form expression for Hill's surfaces in the circular restricted three-body problem. The solution , derived in the primary-centric spherical coordinate system, is deduced from a cubic equation delivering at most two roots on each side of a separatrix. The famous patterns (tadpole, horseshoe and peanut shapes, Roche lobes and Hill's quasi-spheres) are exactly produced.
Cite
@article{arxiv.2604.21426,
title = {Hill's level surfaces in the circular restricted three-body problem solved},
author = {Jean-Marc Huré},
journal= {arXiv preprint arXiv:2604.21426},
year = {2026}
}
Comments
Accepted for publication in Phys. Rev. D Letters