Commensurability is the property of two orbit

Orbit

In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

ing objects, such as planet

Planet

A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s, satellites

Natural satellite

A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....

, or asteroid

Asteroid

Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

s, whose orbital period

Orbital period

The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

s are in a rational

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

 proportion

Proportionality (mathematics)

In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

.

Examples include the 2:3 commensurability between the orbital periods of Neptune

Neptune

Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...

 and Pluto

Pluto

Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...

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

Saturn

Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

ian satellites Titan

Titan (moon)

Titan , or Saturn VI, is the largest moon of Saturn, the only natural satellite known to have a dense atmosphere, and the only object other than Earth for which clear evidence of stable bodies of surface liquid has been found....

 and Hyperion

Hyperion (moon)

Hyperion , also known as Saturn VII, is a moon of Saturn discovered by William Cranch Bond, George Phillips Bond and William Lassell in 1848. It is distinguished by its irregular shape, its chaotic rotation, and its unexplained sponge-like appearance...

, the Kirkwood Gaps in the asteroid belt

Asteroid belt

The asteroid belt is the region of the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets...

, and the 2:1 commensurability between the extrasolar planet

Extrasolar planet

An extrasolar planet, or exoplanet, is a planet outside the Solar System. A total of such planets have been identified as of . It is now known that a substantial fraction of stars have planets, including perhaps half of all Sun-like stars...

s Gliese 876

Gliese 876

Gliese 876 is a red dwarf star approximately 15 light-years away from Earth in the constellation of Aquarius. As of 2011, it has been confirmed that four extrasolar planets orbit the star...

b and Gliese 876

Gliese 876

Gliese 876 is a red dwarf star approximately 15 light-years away from Earth in the constellation of Aquarius. As of 2011, it has been confirmed that four extrasolar planets orbit the star...

c.

Commensurabilities are believed to result from orbital resonance

Orbital resonance

In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...

 effects.

See also

• Harmonic
  Harmonic
  A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
  
  
• Ratio
  Ratio
  In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...