Three-Body Problem Some Applications of the Tests of Escape

Abstract

Some recent tests have given excellent results in the analysis of three-body systems with three equal masses. These analyses are here extended to systems of unequal masses and lead to the following.

• A) For all mass ratios the smallest mass is the most unstable and the most subject to be ejected. The largest mass is generally very stable.

• B) The bounded orbits are very rare, their region in phase space is very small, much smaller than was generally expected.

• C) The usual Lagrange and Euler three-body solutions are not only some simple solutions of the three-body problem, they have also, under many respects, a role of limit and bifurcation with respect to the other solutions.

• D) The latest tests of escape approach very near to the true limit of bounded orbits.