An examination of the mass limit for stability at the triangular lagrange points for a three-body system and a special case of the four-body problem.

摘要

While the three-body problem has been without an exact analytical solution for some 400 odd years, we have learned a great deal about the dynamics of three-body systems in that time. There are five points relative to two massive bodies where a third body will remain in a stable orbit. These are called the Lagrange points. Two of these points, located at the vertices of equilateral triangles, are stable equilibria. We find clear evidence for these stable points within our own solar system, most notably Jupiter's Trojan satellites.;It may be possible to place a massive body at one of these triangular Lagrange points for the Earth-Moon system. This third massive body might be used to occult bright objects for deep space astronomy or to mine for platinum and other useful materials. The question then arises: how massive an object can one place at one of these triangular Lagrange points? Here we present answers to this question.;There is the possibility of placing an object at both of the triangular Lagrange points simultaneously. We present an analysis of the relative motion of the Earth-Moon system when two massive bodies are added to the configuration. The system will remain stable if any two near Earth asteroids are placed at these Lagrange points.