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

Abstract

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

Accepted for publication in Phys. Rev. D Letters

References in corpus (7)

• Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity
• The role of mass transfer and common envelope evolution in the formation of merging binary black holes
• On rapid binary mass transfer -- I. Physical model
• Radiation pressure and pulsation effects on the Roche lobe
• A theory of mass transfer in binary stars
• ELISa: A new tool for fast modelling of eclipsing binaries
• Binary mass transfer in 3D: Mass Transfer Rate and Morphology