The collinear central configuration of n equal masses

Abstract

Moulton's Theorem says that given an ordering of masses m1, ..., mnthere exists a unique collinear central configuration. The theorem allows us to ask the questions: What is the distribution of n equal masses in the collinear central configuration? What is the behavior of the distribution as n → ∞? These questions are due to R. Moekel (personal conversation). Central configurations are found to be attracting fixed points of a flow — a flow we might call an auxiliary flow (in the text it is denoted F(X)), since it has little to do with the equations of motion. This flow is studied in an effort to characterize the mass distribution. Specifically, for a collinear central configuration of n equal masses, a bound is found for the position of the masses furthest from the center of mass. Also some facts concerning the distribution of the inner masses are discovered.