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The circumstance in which the ratio of the orbital periods of two bodies, such as satellites or planets, is an exact fraction such as one-half or two-thirds. In the Solar System there are many near-commensurabilities in orbital periods. For example, the orbital periods of Jupiter and Saturn have a ratio of nearly two-fifths, while the Saturnian satellite pairs Dione and Enceladus, and Mimas and Tethys, have ratios of almost one-half. Such situations give rise to resonances. In some cases the commensurabilities provide stability, while in others they lead to instability, as with the Kirkwood gaps in the asteroid belt where asteroids tend to avoid orbits in which they would have periods commensurable with that of Jupiter.

Subjects: Astronomy and Astrophysics.

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