Orbital resonance

In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly this relationship is found for a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other body doing the 'pushing' will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e., their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large Solar System bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet. A binary resonance ratio in this article should be interpreted as the ratio of number of orbits completed in the same time interval, rather than as the ratio of orbital periods, which would be the inverse ratio. Thus the 2:3 ratio above means Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships among three or more bodies, either type of ratio may be used (in such cases the smallest whole-integer ratio sequences are not necessarily reversals of each other) and the type of ratio will be specified. Since the discovery of Newton's law of universal gravitation in the 17th century, the stability of the Solar System has preoccupied many mathematicians, starting with Pierre-Simon Laplace. The stable orbits that arise in a two-body approximation ignore the influence of other bodies. The effect of these added interactions on the stability of the Solar System is very small, but at first it was not known whether they might add up over longer periods to significantly change the orbital parameters and lead to a completely different configuration, or whether some other stabilising effects might maintain the configuration of the orbits of the planets. It was Laplace who found the first answers explaining the linked orbits of the Galilean moons (see below). Before Newton, there was also consideration of ratios and proportions in orbital motions, in what was called 'the music of the spheres', or Musica universalis.