In a system of bodies orbiting a central primary (planets around a star, satellites around a planet), possible resonances exist between these moving bodies.
They occur when there is a commensurable ratio between orbital parameters.
The most "simple" resonances concern revolution periods. They are called "mean motion resonances". The "mean motion" is the angular speed , with the revolution period.
There is a resonance if the mean motion of the planet , , is commensurable with that of the planet , . For instance, there is a 1/2 resonance if the planet is twice as fast as planet , which can be written , or . There is a resonance of order n/m, where n and m are two integers, if a planet makes n revolutions when the other one makes m revolutions.
In Neptune's rings, the edge of the Adams ring is in a resonance 42:43 with the satellite Galatea.
Resonances between the rotation motion of a body and its revolution motion are also possible.
When the orbits are eccentric and/or inclined, other "velocities" can appear. The mutual perturbations between planets make their orbits : this is precession.The precession velocities can also be in resonance between themselves and/or with the mean motions.
Gravitation is a very simple law that leads to complex phenomena.
Resonances are everywhere in the Solar System :