Observatoire de Paris
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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 n=2*pi/P, with P the revolution period.


There is a resonance if the mean motion of the planet 1 , n_1, is commensurable with that of the planet 2, n_2 . For instance, there is a 1/2 resonance if the planet 1 is twice as fast as planet 2, which can be written n_1=2*n_2, or 2*P_1=P_2. 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 :

  • The rotation motion of the moon on itself is in a 1:1 resonance with its revolution motion. The same time is necessary to rotate or to make a revolution around the Earth. That is the reason why, from Earth, we always see the same side of the moon.
  • The rotation motion of Mercury on itself is in a 3:2 resonance with its revolution motion around the Sun. The planet rotates three times when it makes two revolutions around the Sun.
  • Neptune and Pluto are in a 3:2 resonance. Neptune makes three revolutions around the Sun when Pluto makes two. The angular velocity of Neptune, n_N, is greater than that of Pluto, n_P. It can be written 2*n_N = 3*n_P
  • In Saturn's rings, there are numerous resonances between satellites, or between satellites and rings.