Restricted Five-Body Problem: An Analysis with Computer Algebra

摘要

Three bodies of equal mass m revolve in a plane around their gravitational center in circular orbits under the influence of their mutual gravitational attraction; at the center a mass of beta.m is present where beta = or > 0. A fifth body of negligible mass compared to m, moves in the plane under the gravitational attraction of the other bodies. All bodies are considered to be point masses. The problem is then the description of the motion of the small body: it is called here a restricted five-body problem (beta not = 0). The existence and location of Lagrangian equilibrium points is discussed and the motion is characterized in the vicinity of these points - all of this is done analytically using tools from computer algebra.