An analysis of the three body problem

by (Mark Edward), 1974- Hannah

In this paper we will be presenting my approach to generating two possible solutions to the three-body problem. We will first discuss the theory of reducing the dimension of the dynamical system through the use of symmetry and constants of motion. However, we can reduce no farther than to 5 degrees of freedom, which is still too high to solve and therefore we must change our attack from trying to find a general solution, to simply finding a specific solution. We will then make use of the program Maple, which will allow me to create a simulation of this system. Through the simulations we will try and find the stable figure eight solution as well as a solution having a light satellite coming in from infinity and being captured in a stable orbit around a tight binary. We can adjust the initial conditions of the three bodies until we have generated a simulation that has the potential to be a stable periodic orbit. Unfortunately Maple will not prove that any solution found is stable, and we are therefore left with only a conjecture as to the stability of the system. Index words: Celestial Mechanics, n-Body Problem, Three-Body Problem, 3-Body Problem An Analysis of the Three Body Problem by Mark E. Hannah B.S., Oglethorpe University 1996 A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Master of Arts Athens, Georgia 2002 c? 2002 Mark E. Hannah All Rights Reserved An Analysis of the Three Body Problem by Mark E. Hannah Approved: Major Professor: Dr. Malcolm Adams Committee: Dr. Thomas Gard Dr. Robert Varley Electronic Version Approved: Gordhan L. Patel Dean of the Graduate School The University of Georgia