# Rotation period

Short description: Time that it takes to complete one revolution relative to the background stars
Animated rotation of asteroid 433 Eros

The rotation period of a celestial object (e.g., star, gas giant, planet, moon, asteroid) may refer to its sidereal rotation period, i.e. the time that the object takes to complete a single revolution around its axis of rotation relative to the background stars, measured in sidereal time. The other type of commonly used rotation period is the object's synodic rotation period (or solar day), measured in solar time, which may differ by a fraction of a rotation or more than one rotation to accommodate the portion of the object's orbital period during one day.

## Measuring rotation

For solid objects, such as rocky planets and asteroids, the rotation period is a single value. For gaseous or fluid bodies, such as stars and gas giants, the period of rotation varies from the object's equator to its pole due to a phenomenon called differential rotation. Typically, the stated rotation period for a gas giant (such as Jupiter, Saturn, Uranus, Neptune) is its internal rotation period, as determined from the rotation of the planet's magnetic field. For objects that are not spherically symmetrical, the rotation period is, in general, not fixed, even in the absence of gravitational or tidal forces. This is because, although the rotation axis is fixed in space (by the conservation of angular momentum), it is not necessarily fixed in the body of the object itself. As a result of this, the moment of inertia of the object around the rotation axis can vary, and hence the rate of rotation can vary (because the product of the moment of inertia and the rate of rotation is equal to the angular momentum, which is fixed). For example, Hyperion, a moon of Saturn, exhibits this behaviour, and its rotation period is described as chaotic.

## Earth

Earth's rotation period relative to the Sun (its mean solar day) consists of 86,400 seconds of mean solar time, by definition. Each of these seconds is slightly longer than an SI second because Earth's solar day is now slightly longer than it was during the 19th century, due to tidal deceleration. The mean solar second between 1750 and 1892 was chosen in 1895 by Simon Newcomb as the independent unit of time in his Tables of the Sun. These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second. The SI second was made equal to the ephemeris second in 1967.[1]

Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s).[2][3] Earth's rotation period relative to the precessing or moving mean vernal equinox, its sidereal day, is 86164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s).[2] Thus the sidereal day is shorter than the stellar day by about 8.4 ms.[4] The length of the mean solar day in SI seconds is available from the IERS for the periods 1623–2005[5] and 1962–2005.[6] Recently (1999–2005) the average annual length of the mean solar day in excess of 86400 SI seconds has varied between 0.3 ms and 1 ms, which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds.

## Rotation period of selected objects

Celestial objects Rotation period with respect to distant stars, the sidereal rotation period (compared to Earth's mean Solar days) Synodic rotation period (mean Solar day) Apparent rotational period
viewed from Earth
Sun* 25.379995 days (Carrington rotation)
35 days (high latitude)
25d 9h 7m 11.6s
35d
~28 days (equatorial)[7]
Venus −243.0226 days[8][9] −243d 0h 33m −116.75 days[10]
Earth 0.99726968 days[11][12] 0d 23h 56m 4.0910s 1.00 days (24h 00m 00s)
Mars 1.02595675 days[11] 1d 0h 37m 22.663s 1.02749125[13] days
Ceres 0.37809 days[14] 0d 9h 4m 27.0s 0.37818 days
Jupiter 0.41354 days(average)
0.4135344 days (deep interior[15])
0.41007 days (equatorial)
0.4136994 days (high latitude)
0d 9h 55m 30s[11]
0d 9h 55m 29.37s[11]
0d 9h 50m 30s[11]
0d 9h 55m 43.63s[11]
0.41358 d (9 h 55 m 33 s)[16] (average)
Saturn 0.44002+0.00130
−0.00091
days (average, deep interior[17])
0.44401 days (deep interior[15])
0.4264 days (equatorial)
0.44335 days (high latitude)
10h 33m 38s + 1m 52s− 1m 19s[18][19]
0d 10h 39m 22.4s[20]
0d 10h 14m 00s[21]
0d 10h 38m 25.4s[21]
0.43930 d (10 h 32 m 36 s)[16]
Uranus −0.71833 days[11][8] −0d 17h 14m 24s −0.71832 d (−17 h 14 m 23 s)[16]
Neptune 0.67125 days[11] 0d 16h 6m 36s 0.67125 d (16 h 6 m 36 s)[16]
Pluto −6.38718 days[11][8] (synchronous with Charon) –6d 9h 17m 32s −6.38680 d (–6d 9h 17m 0s)[16]
Haumea 0.1631458 ±0.0000042 days[22] 0d 3h 56m 43.80 ±0.36s 0.1631461 ±0.0000042 days
Makemake 0.9511083 ±0.0000042 days[23] 22h 49m 35.76 ±0.36s 0.9511164 ±0.0000042 days
Eris ~1.08 days[24] 25h ~54m ~1.08 days

* See Solar rotation for more detail.

## References

1. Aoki, the ultimate source of these figures, uses the term "seconds of UT1" instead of "seconds of mean solar time". Aoki, et al., "The new definition of Universal Time", Astronomy & Astrophysics 105 (1982) 359–361.
2. Explanatory Supplement to the Astronomical Almanac, ed. P. Kenneth Seidelmann, Mill Valley, Cal., United States Naval Observatory University Science Books, 1992, p.48, ISBN:0-935702-68-7.
3. Phillips, Kenneth J. H. (1995). Guide to the Sun. Cambridge University Press. pp. 78–79. ISBN 978-0-521-39788-9.
4. This rotation is negative because the pole which points north of the invariable plane rotates in the opposite direction to most other planets.
5. Margot, Jean-Luc; Campbell, Donald B.; Giorgini, Jon D. et al. (29 April 2021). "Spin state and moment of inertia of Venus". Nature Astronomy 5 (7): 676–683. doi:10.1038/s41550-021-01339-7. Bibcode2021NatAs.tmp...74M.
6. Cite error: Invalid <ref> tag; no text was provided for refs named Allen296
7. Reference adds about 1 ms to Earth's stellar day given in mean solar time to account for the length of Earth's mean solar day in excess of 86400 SI seconds.
8. Allison, Michael; Schmunk, Robert. "Mars24 Sunclock — Time on Mars".
9. Chamberlain, Matthew A.; Sykes, Mark V.; Esquerdo, Gilbert A. (2007). "Ceres lightcurve analysis – Period determination". Icarus 188 (2): 451–456. doi:10.1016/j.icarus.2006.11.025. Bibcode2007Icar..188..451C.
10. Rotation period of the deep interior is that of the planet's magnetic field.
11. Seligman, Courtney. "Rotation Period and Day Length".
12. Found through examination of Saturn's C Ring
13. McCartney, Gretchen; Wendel, JoAnna (18 January 2019). "Scientists Finally Know What Time It Is on Saturn". NASA.
14. Mankovich, Christopher (17 January 2019). "Cassini Ring Seismology as a Probe of Saturn's Interior. I. Rigid Rotation". The Astrophysical Journal 871 (1): 1. doi:10.3847/1538-4357/aaf798. Bibcode2019ApJ...871....1M.
15. Lacerda, Pedro; Jewitt, David; Peixinho, Nuno (2008-04-02). "High-Precision Photometry of Extreme KBO 2003 EL61". The Astronomical Journal 135 (5): ((1,749–1,756)). doi:10.1088/0004-6256/135/5/1749. Bibcode2008AJ....135.1749L. Retrieved 2008-09-22.
16. T. A. Hromakina; I. N. Belskaya; Yu. N. Krugly; V. G. Shevchenko; J. L. Ortiz; P. Santos-Sanz; R. Duffard; N. Morales et al. (2019-04-09). "Long-term photometric monitoring of the dwarf planet (136472) Makemake". Astronomy & Astrophysics 625: A46. doi:10.1051/0004-6361/201935274. Bibcode2019A&A...625A..46H.