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arXiv · 2604.21426

Hill's level surfaces in the circular restricted three-body problem solved

Jean-Marc Huré
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Abstract

We report the closed-form expression for Hill's surfaces in the circular restricted three-body problem. The solution $ϕ(r,θ)$, 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.

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Jean-Marc Huré. 2026-04-29. Hill's level surfaces in the circular restricted three-body problem solved. https://doi.org/10.1103/t63t-j15q

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