Adiabatic invariants and phase equilibria for firstorder orbital resonances.
Abstract
In the planar circular restricted threebody problem, the evolution of nearcommensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through nearzero eccentricity; as in the ordinary case (no transition), pre and postevolutionary states are linked by solution of a twopoint boundaryvalue problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre and postevolutionary states are linked by solution of a threepoint boundaryvalue problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.
 Publication:

The Astronomical Journal
 Pub Date:
 June 1975
 DOI:
 10.1086/111767
 Bibcode:
 1975AJ.....80..465H
 Keywords:

 Asteroids;
 Lagrangian Equilibrium Points;
 Mass Ratios;
 Orbit Perturbation;
 Orbital Resonances (Celestial Mechanics);
 Solar Orbits;
 Three Body Problem;
 Adiabatic Equations;
 Boundary Value Problems;
 Circular Orbits;
 Libration;
 Numerical Integration;
 Orbit Calculation;
 PhaseSpace Integral;
 Solar System;
 Stellar Mass Ejection;
 Variational Principles;
 Astronomy