Hill stability and distance curves for the general three-body problem

DOI10.1007/BF01230725zbMath0519.70010OpenAlexW2059050851MaRDI QIDQ3668907

Christian Marchal, George Bozis

Publication date: 1982

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01230725

zbMATH Keywords

critical valuesintegrals of motionHill curveslimit casesextend Hill stability from circular restricted problem to general problemgeneralized semi-latus rectumgeneralized semi-major axislunar casemean harmonic distancemean quadratic distancenegative and positive energyone mass zeroplanetary casetwo masses small

Mathematics Subject Classification ID

Three-body problems (70F07) Orbital mechanics (70M20) (n)-body problems (70F10)

Related Items (17)

Triple close approach in the three-body problem: A limit for the bounded orbits ⋮ A study of the plane unrestricted three-body problem ⋮ Stability of planetary systems with respect to masses ⋮ The 1/1 resonance in extrasolar systems. Migration from planetary to satellite orbits ⋮ On the co-orbital motion of two planets in quasi-circular orbits ⋮ About the Hill stability of extrasolar planets in stellar binary systems ⋮ Bounded motion for a modified three-body problem ⋮ Evolution of the moment of inertia in the many-body problem in the field of general attraction ⋮ Stability criteria for hierarchical triple systems ⋮ Hill stability of the planar three-body problem: General and restricted cases ⋮ On the stability of hierarchical four-body systems ⋮ The Hill stability of low mass binaries in hierarchical triple systems ⋮ Shannon entropy diffusion estimates: sensitivity on the parameters of the method ⋮ A test of escape valid even for very small mutual distances I. The acceleration and the escape velocities of the third body ⋮ Three-body problem ⋮ Limits on the orbits of possible eccentric and inclined moons of extrasolar planets orbiting single stars ⋮ The Shannon entropy: an efficient indicator of dynamical stability

Cites Work

• Unnamed Item
• Zero velocity surfaces for the general planar three-body problem
• Topology and mechanics. II: The planar \(n\)-body problem
• Stability of planetary orbits in binary systems
• Hill regions for the general three-body problem
• The effects of integrals on the totality of solutions of dynamical systems
• Bifurcation points in the planar problem of three bodies
• Stability of artificial and natural satellites

This page was built for publication: Hill stability and distance curves for the general three-body problem