Rotation period

Animated rotation of asteroid 433 Eros

In astronomy, the rotation period of a celestial object is the time that it takes to complete one revolution around its axis of rotation relative to the background stars. It differs from the planet's solar day, which includes an extra fractional rotation needed to accommodate the portion of the planet'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/fluid bodies, such as stars and gas giants, the period of rotation varies from the equator to the poles due to a phenomenon called differential rotation. Typically, the stated rotation period for a gas giant (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). Hyperion, a satellite 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) (23^h 56^m 4.098 903 691^s).^[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) (23^h 56^m 4.090 530 832 88^s).^[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
Sun	25.379995 days (equatorial)[7][8] 35 days (high latitude)	25ᵈ 9ʰ 7ᵐ 11.6ˢ 35ᵈ
Mercury	58.6462 days[9]	58ᵈ 15ʰ 30ᵐ 30ˢ
Venus	–243.0187 days[9][10]	−243ᵈ 0ʰ 26ᵐ
Earth	0.99726968 days[9][11]	0ᵈ 23ʰ 56ᵐ 4.0910ˢ
Moon	27.321661 days[12] (synchronous toward Earth)	27ᵈ 7ʰ 43ᵐ 11.5ˢ
Mars	1.02595675 days[9]	1ᵈ 0ʰ 37ᵐ 22.663ˢ
Ceres	0.37809 days[13]	0ᵈ 9ʰ 4ᵐ 27.0ˢ
Jupiter	0.4135344 days (deep interior)[14] 0.41007 days (equatorial) 0.41369942 days (high latitude)	0ᵈ 9ʰ 55ᵐ 29.37^s[9] 0ᵈ 9ʰ 50ᵐ 30ˢ[9] 0ᵈ 9ʰ 55ᵐ 43.63ˢ[9]
Saturn	0.44403 days (deep interior)[14] 0.426 days (equatorial) 0.443 days (high latitude)	0ᵈ 10ʰ 39ᵐ 24ˢ[9] 0ᵈ 10ʰ 14ᵐ[9] 0ᵈ 10ʰ 38ᵐ[9]
Uranus	−0.71833 days[9][10][14]	−0ᵈ 17ʰ 14ᵐ 24ˢ
Neptune	0.67125 days[9][14]	0ᵈ 16ʰ 6ᵐ 36ˢ
Pluto	−6.38718 days[9][10] (synchronous with Charon)	–6ᵈ 9ʰ 17ᵐ 32ˢ
Haumea	0.163145 days[15]	0ᵈ 3ʰ 54ᵐ 56ˢ

See also

• Apparent retrograde motion
• Orbital period
• Poles of astronomical bodies
• Retrograde motion
• Rotational speed
• Synodic day

References

1. Leap seconds by USNO
2. IERS EOP Useful constants
3. 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 and Astrophysics 105 (1982) 359–361.
4. Explanatory Supplement to the Astronomical Almanac, ed. P. Kenneth Seidelmann, Mill Valley, Cal., University Science Books, 1992, p.48, ISBN 0-935702-68-7.
5. IERS Excess of the duration of the day to 86400s … since 1623 Graph at end.
6. IERS Variations in the duration of the day 1962–2005
7. Rotation and pole position for the Sun and planets Rotation period in days is 360° divided by the coefficient of d.
8. "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000" (PDF). (215KB) pp7–8
9. Clabon Walter Allen & Arthur N. Cox (2000). Allen's Astrophysical Quantities. Springer. p. 296. ISBN 0-387-98746-0.
10. This rotation is negative because the pole which points north of the ecliptic rotates in the opposite direction to most other planets.
11. 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.
12. Clabon Walter Allen & Arthur N. Cox (2000). Allen's Astrophysical Quantities. Springer. p. 308. ISBN 0-387-98746-0.
13. Chamberlain, Matthew A.; Sykes, Mark V.; Esquerdo, Gilbert A. (2007). "Ceres lightcurve analysis – Period determination". Icarus. 188 (2): 451–456. Bibcode:2007Icar..188..451C. doi:10.1016/j.icarus.2006.11.025.
14. Rotation period of the deep interior is that of the planet's magnetic field.
15. Pedro Lacerda; David Jewitt & Nuno Peixinho (2008-04-02). "High-Precision Photometry of Extreme KBO 2003 EL61". The Astronomical Journal. 135 (5): 1749–1756. arXiv:0801.4124. Bibcode:2008AJ....135.1749L. doi:10.1088/0004-6256/135/5/1749. Retrieved 2008-09-22.

External links

• Murray, Carl D. & Stanley F. Dermott (1999). Solar System Dynamics. Cambridge UP. p. 531. ISBN 0-521-57295-9. Rotation periods of Mercury and Earth are wrong.