# Orbital Resonance

**DOI:**https://doi.org/10.1007/978-3-642-27833-4_1121-3

## Definition

An orbital resonance is either a stabilizing or a disrupting phenomenon produced by the cumulative effect of gravity between at least two bodies in periodic orbits, generally around a third, more massive body.

## Overview

The motion of a body in a fixed gravitational field is described by an ordinary differential equation. The solution of this problem is entirely determined provided we know its initial conditions.

In several physical cases, this solution has some periodic characteristics. The period of such a periodic motion depends essentially on a mean distance between bodies in gravitational interaction. For the two-body Keplerian problem, this is Kepler’s third law: The square of the orbital period is directly proportional to the cube of the semi-major axis of its elliptical orbit (see Gravitation).

If several bodies are in orbit in a fixed gravitational potential and the ratio of the periods of two of these particular motions is rational (ratio of two integers), a special...

## Keywords

Gravitation Instability Period Orbits## References and Further Reading

- Carl DM, Stanley FD (1999) Solar system dynamics. Cambridge University Press, CambridgeGoogle Scholar