A mathematical treatise on the restricted threebody problem of celestial mechanics
Abstract
Development of a new approach to the solution of the coplanar problem of a satellite orbiting two primaries. First, the stability of the libration points is discussed, by examining weak variations of a topological surface. Collinear points are shown to reside on local maxima, while triangular points reside on local minima of this surface. Second, a conjecture is made concerning the correctness of the gravity potential, and canonical classification is discussed from the viewpoint of simplifying the governing partial differential equations. A transformation is constructed which reduces these equations to an inhomogeneous Laplace equation describing the satellite's motion. An inverse procedure, coupled with this approach, generates an unknown gravity potential for a known satellite trajectory. This potential must solve an inhomogeneous wave equation.
 Publication:

AIAA, 13th Aerospace Sciences Meeting
 Pub Date:
 January 1975
 Bibcode:
 1975aiaa.meetQ....M
 Keywords:

 Celestial Mechanics;
 EarthMoon System;
 Gravitational Fields;
 Lagrangian Equilibrium Points;
 Orbit Calculation;
 Three Body Problem;
 Boundary Value Problems;
 Canonical Forms;
 Equations Of Motion;
 Fredholm Equations;
 Green'S Functions;
 Iteration;
 Laplace Equation;
 Librational Motion;
 Numerical Analysis;
 Satellite Orbits;
 Wave Equations;
 Astrodynamics