Traveling Wave Solutions For Newton's Equations of Celestial Mechanics: Kepler's Problem

TL;DR

This paper derives explicit traveling wave solutions related to Newton's celestial mechanics equations, revealing wave front behaviors and singularities in 2-body problems.

Contribution

It introduces closed-form traveling wave solutions for Newton's equations, specifically applied to 2-body and relative 2-body problems, linking wave phenomena to celestial mechanics.

Findings

Wave solutions are expressed in elementary functions.

Wave fronts and singularities are characterized.

Applications to 2-body celestial problems.

Abstract

This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary functions. They are specialized to the 2-body and the relative 2-body problem. The traveling wave solutions disclose the shape and position of wave fronts emanating from collisions by determining the location of the singularities of the traveling wave solutions.