Resonance is a very general physical mechanism, that takes place when two phenomena have particular frequencies (or periods) that amplify the phenomena. Talking about dynamics, resonance is one of the main mechanisms that make the minor planets' orbits umpredictable over long periods of time.
consider the orbit of a light body (for example an asteroid) around the Sun.. If the orbit of the asteroid brings it sufficiently close to Jupiter, the asteroid will be influenced by the attraction of the planet which is maximum at the moment of closest approach (in other words, when Jupiter and the asteroid come to their closest approach, the asteroid receives its maximum pull from the planet, which contributes to move it from its original orbit).

If the periods of Jupiter and the asteroid are not proportional, the two bodies come close to each other randomly, and the overall effect of the attraction between them is null. On the other hand, the interaction between Jupiter and the asteroid is not negligible when the orbits of the two bodies have resonant periods, meaning that the period of the asteroid is a fraction of the period of Jupiter.
For example, knowing that Jupiter revolves around the Sun with a period of 12 years, let's consider an asteroid with a period of about 4 years: it will complete 3 revolutions for every one of Jupiter, and in this case, the two bodies will come near each other, three times every 12 years (resonance 3:1). In this and in other similar resonant cases the perturbation is maximum, and the asteroid's orbit becomes unstable.
The main consequence of this resonant mechanism is the fact that the characteristics of the orbits change in time in a perodical way: it's the phenomenon of libration. This kind of resonance, has a time-scale that can range from "short" periods of thousands years, to much longer periods.

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