Three-Body Problem and Multiple Stellar Systems

Dynamical Systems, the Three-Body Problem and Space Mission Design

This paper concerns heteroclinic connections and resonance transitions in the planar circular restricted 3-body problem, with applications to the dynamics of comets and asteroids and the design of space missions such as the Genesis Discovery Mission and low energy Earth to Moon transfers. The existence of a heteroclinic connection between pairs of equal energy periodic orbits around two of the ...

Three - Body Problem

A Trilinear Three-Body Problem

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...

Chaos in the N-body Problem of Stellar Dynamics

Stellar dynamics shares these equations with celestial mechanics (a term which is used here to denote the study of the orbital dynamics of bodies in the solar system), but there are important differences of emphasis. In stellar dynamics all masses are comparable, whereas in celestial mechanics one mass tends to dominate (either the sun or a primary). This has an effect on the methods used and t...

Multiple Gravity Assists, Capture, and Escape in the Restricted Three-Body Problem

For low energy spacecraft trajectories such as multimoon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we investigate a special class of multiple gravity assists which can occur outside of the perturbing body’s sphere of influence (the Hill sphere) and which is dynamically...