## by Carl D. Murray and Stanley F. Dermott

# Chapter 2

# The Two-Body Problem

Before using the software supplied at this web site, please read this
disclaimer.
- Structure of the Solar System
**THE TWO-BODY PROBLEM**
**Introduction**
**Equations of motion**
**Orbital position and velocity**
**The mean and eccentric anomalies**
**Elliptic expansions**
**The guiding centre approximation**
**Barycentric orbits**
**The orbit in space**
**Perturbed orbits**
**Hamiltonian formulation**
**Exercises**

- The Restricted Three-Body Problem
- Tides, Rotation and Shape
- Spin-Orbit Coupling
- The Disturbing Function
- Secular Perturbations
- Resonant Perturbations
- Chaos and Long-term Evolution
- Planetary Rings

- Appendix - Solar System Data
- Appendix - Expansion of the Disturbing Function
- References (PDF)

All links presented on this page are to HTML files except those marked as
an animation (*QuickTime®* format), a notebook
(*Mathematica®* notebook format), or PDF (portable document
format).
The latest list of known errors and a
compilation of symbols used in the book are
available as PDF files. Highlighted text within PDF files are links to
external online documents.

See the software page for
more information regarding these alternative formats.

Table of Contents

Copyright © 1999-2006 by Carl D. Murray

Last modified on 8 September 2006

Maintained by Carl D. Murray

Designed by Lynne Marie Stockman