Commensurability (astronomy)

Commensurability is the property of two orbiting objects, such as planets, satellites, or asteroids, whose orbital periods are in a rational proportion.

Examples include the 2:3 commensurability between the orbital periods of Neptune and Pluto,[1] the 3:4 commensurability between the orbital periods of the Saturnian satellites Titan and Hyperion,[2] the orbital periods associated with the Kirkwood gaps in the asteroid belt relative to that of Jupiter,[3] and the 2:1 commensurability between Gliese 876 b and Gliese 876 c.

Commensurabilities are normally the result of an orbital resonance, rather than being due to coincidence.

See also

• Harmonic
• Ratio

References

1. Williams, J. G.; Benson, G. S. (March 1971), "Resonances in the Neptune-Pluto System", Astronomical Journal, 76: 167, Bibcode:1971AJ.....76..167W, doi:10.1086/111100, S2CID 120122522.
2. Bevilacqua, R.; et al. (April 1980), "Resonances and close approaches. I - The Titan-Hyperion case", Laboratorio di Astrofisica Spaziale di Frascati, European Workshop on Planetary Sciences, Rome, Italy, Apr. 23-27, 1979, vol. 22, p. 141, Bibcode:1980M&P....22..141B, doi:10.1007/BF00898423, S2CID 119442634.
3. Moons, Michèle (March 1996), "Review of the dynamics in the Kirkwood gaps", Celestial Mechanics and Dynamical Astronomy, 65 (1−2): 175−204, Bibcode:1996CeMDA..65..175M, doi:10.1007/BF00048446, S2CID 121242252.