Editing Orbital resonance (section)

== History ==
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 [[N-body problem|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 moon]]s (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]]''.

The article on [[resonant interaction]]s describes resonance in the general modern setting. A primary result from the study of [[dynamical system]]s is the discovery and description of a highly simplified model of mode-locking; this is an oscillator that receives periodic kicks via a weak coupling to some driving motor. The analog here would be that a more massive body provides a periodic gravitational kick to a smaller body, as it passes by. The mode-locking regions are named [[Arnold tongue]]s.