Commensurability is the property of two
orbit
In celestial mechanics, an orbit (also known as orbital revolution) 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 ...
ing objects, such as
planet
A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
s,
satellites
A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scientif ...
, or
asteroid
An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...
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 reason. 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 ...
proportion.
Examples include the 2:3 commensurability between the orbital periods of
Neptune
Neptune is the eighth and farthest known planet from the Sun. It is the List of Solar System objects by size, fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 t ...
and
Pluto
Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of Trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Su ...
,
[ 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 9 times that of Earth. It has an eighth the average density of Earth, but is over 95 tim ...
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,[ the orbital periods associated with the ]Kirkwood gap
A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. The gaps were first n ...
s in the asteroid belt
The asteroid belt is a torus-shaped region in the Solar System, centered on the Sun and roughly spanning the space between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies called asteroids ...
relative to that of Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...
,[ 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 relation ...
, rather than being due to coincidence.
See also
*Harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
*Ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
References
Asteroids
Celestial mechanics
Orbits
Planetary satellite systems
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