Symmetric doubly asymptotic orbits at collinear equilibrium points in the general three-body problem

Department of Engineering Sciences, University of Patras, 26500 Patras, Greece e-mail: e.perdios@des.upatras.gr; v.kalantonis@des.upatras.gr

Corresponding author: E. A. Perdios, e.perdios@des.upatras.gr

Received: 22 March 2002
Accepted: 23 July 2002

Abstract

This paper concerns the numerical determination of doubly asymptotic orbits at the collinear equilibrium points of the general three-body problem. To compute a doubly asymptotic orbit we use a linear analysis to determine the relevant outgoing eigenvector and a combined iterative method based on the characteristic bisection and Newton's method to solve the resulting system of equations for the mass parameters of the problem. Many such orbits are presented.