Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i. e. their ability to alter or constrain each others orbits. In most cases, this results in an interaction, in which the bodies exchange momentum. Under some circumstances, a resonant system can be stable and self-correcting, examples are the 1,2,4 resonance of Jupiters moons Ganymede, Europa and Io, and the 2,3 resonance between Pluto and Neptune. Unstable resonances with Saturns inner moons give rise to gaps in the rings of Saturn, 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 between three or more bodies, either type of ratio may be used and the type of ratio will be specified. Since the discovery of Newtons law of gravitation in the 17th century. The stable orbits that arise in a two-body approximation ignore the influence of other bodies and it was Laplace who found the first answers explaining the remarkable dance of the Galilean moons. It is fair to say that this field of study has remained very active since then. Before Newton, there was consideration of ratios and proportions in orbital motions, in what was called the music of the spheres. In general, a resonance may involve one or any combination of the orbit parameters. Act on any scale from short term, commensurable with the orbit periods, to secular. Lead to either long-term stabilization of the orbits or be the cause of their destabilization, a mean-motion orbital resonance occurs when two bodies have periods of revolution that are a simple integer ratio of each other. Depending on the details, this can either stabilize or destabilize the orbit, stabilization may occur when the two bodies move in such a synchronised fashion that they never closely approach. For instance, The orbits of Pluto and the plutinos are stable, despite crossing that of the much larger Neptune, the resonance ensures that, when they approach perihelion and Neptunes orbit, Neptune is consistently distant. Other Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune. There are also smaller but significant groups of resonant trans-Neptunian objects occupying the 1,1,3,5,4,7,1,2 and 2,5 resonances, among others, with respect to Neptune. In the asteroid belt beyond 3.5 AU from the Sun, orbital resonances can also destabilize one of the orbits. For small bodies, destabilization is actually far more likely, for instance, In the asteroid belt within 3.5 AU from the Sun, the major mean-motion resonances with Jupiter are locations of gaps in the asteroid distribution, the Kirkwood gaps
Image: PIA17173 Titan resonances in Saturn's C ring
Illustration of Io–Europa–Ganymede resonance. From the centre outwards: Io (yellow), Europa (gray) and Ganymede (dark)
Depiction of the Earth:Venus 8:13 near resonance. With Earth held stationary at the center of a nonrotating frame, the successive inferior conjunctions of Venus over eight Earth years trace a pentagrammic pattern (reflecting the difference between the numbers in the ratio).