Hill's lunar equations and the three-body problem

Quasi-periodic Solutions of the Spatial Lunar Three-body Problem

In this paper, we consider the spatial lunar three-body problem in which one body is far-away from the other two. By applying a well-adapted version of KAM theorem to Lidov-Ziglin’s global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar three-body problem.

Three - Body Problem

05035 and Meteorite Hills 01210 : Two Basaltic Lunar Meteorites

Introduction: The lunar meteorites Miller Range 05035 (MIL) and Meteorite Hills 01210 (MET) were collected during the 2005 and 2001 ANSMET (Antarctic Meteorite Search) field seasons [1,2]. MET is a 22.8 g regolith breccia composed primarily of basaltic material [3-6]. MIL is a 142.2 g coarse-grained basalt [2]. The bulk composition, mineral assemblage, and texture of MIL is similar to lunar met...

Integral equations for the four-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...