Commensurability is the property of two

orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such a ...

ing objects, such as

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...

satellites A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotop ...

, or

asteroid An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic o ...

s, whose

orbital period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...

s are in a

rational Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abil ...

proportion. Examples include the 2:3 commensurability between the orbital periods of

Neptune Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 time ...

and

Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Sun. It is the largest k ...

, the 3:4 commensurability between the orbital periods of the

Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; ...

ian satellites

Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...

and

Hyperion Hyperion may refer to: Greek mythology * Hyperion (Titan), one of the twelve Titans * ''Hyperion'', a byname of the Sun, Helios * Hyperion of Troy or Yperion, son of King Priam Science * Hyperion (moon), a moon of the planet Saturn * ''Hyp ...

, the orbital periods associated with the Kirkwood gaps in the

asteroid belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...

relative to that of

Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandt ...

, and the 2:1 commensurability between Gliese 876 b and Gliese 876 c. Commensurabilities are normally the result of an

orbital resonance In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relations ...

, rather than being due to coincidence.

References

{{DEFAULTSORT:Commensurability (Astronomy) Asteroids Celestial mechanics Orbits Planetary satellite systems zh:通約性

See also

References