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Encyclopedia > Sidereal day
On a prograde planet like the Earth, the sidereal day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again but the Sun is not (1→2 = one sidereal day). It is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day).

To be more precise, we must recognize that the Earth's rotation rate is not quite constant. There are many causes of small perturbations to the rotation rate, but over long periods the most important change is the precession of the equinoxes, in which the Earth's axis of rotation itself rotates about a second axis, taking about 25,800 years to perform a complete rotation. Because of this precession, the stars appear to move around the earth in a manner more complicated than a simple constant rotation. The precession of Earths axis of rotation with respect to inertial space is also called the precession of the equinoxes. ...

For this reason, to simplify the description of earth orientation in astronomy and geodesy, it is conventional to describe earth rotation relative to a frame which is itself precessing slowly. In this reference frame, earth rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this reference frame that the tropical year, the year related to the earth's seasons, represents one orbit of the earth around the sun. The precise definition of a sidereal day is the time taken for one rotation of the earth in this precessing reference frame. Given a tropical year of 365.242190402 days from Simon et al.[1] this gives a sidereal day of 86400×365.242190402/366.242190402, or 86164.09053 seconds. A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ...

According to Aoki et al.,[2] an accurate value for the sidereal day is 86164.090530833 seconds. This web based sidereal time calculator assumes a slightly larger value of 86164.090530901 seconds.

Because this is the period of rotation in a precessing reference frame, it is not directly related to the mean rotation rate of the earth in an inertial frame, which is given by ω=2π/T where T is the slightly longer stellar day given by Aoki et al.[3] as 86164.09890369732 seconds. This can be calculated by noting that ω is the magnitude of the vector sum of the rotations leading to the sidereal day and the precession of that rotation vector. In fact, the period of the earth's rotation varies on hourly to interannual timescales by around a millisecond [4], together with a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the earth's rotation by tidal friction. [5]

The Earths rotation is the rotation of the solid earth around its own axis, which is called Earths axis or rotation axis. ... In Egyptian mythology, Month is an alternate spelling for Menthu. ... Sidereal time is time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical with, the motion of stars. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ...

## References

1. ^ Simon, J. L., P. Bretagnon, J. Chapront, M. Chapronttouze, G Francou and J. Laskar: Numerical expressions for precession formulas and mean elements for the moon and the planets. Astronomy and Astrophysics 282(2), 663-683, 1994.
2. ^ Aoki, S., B. Guinot, G. H. Kaplan, H. Kinoshita, D. D. McCarthy and P. K. Seidelmann: The new definition of Universal Time. Astronomy and Astrophysics 105(2), 359-361, 1982.
3. ^ Aoki, S., B. Guinot, G. H. Kaplan, H. Kinoshita, D. D. McCarthy and P. K. Seidelmann: The new definition of Universal Time. Astronomy and Astrophysics 105(2), 359-361, 1982.
4. ^ Hide, R., and J. O. Dickey: Earth's variable rotation. Science 253, 629-637, 1991.
5. ^ Stephenson, F.R.: Historical eclipses and earth's rotation. Cambridge University Press, 1997, 557pp.

Results from FactBites:

 Day - Wikipedia, the free encyclopedia (1282 words) A civil clock day is typically 86400 SI seconds long, but will be 86401 s long in the event of a leap second (or possibly 86399 s in the event of a reverse leap second, but a reverse leap-second has never happened yet). In astronomy, the sidereal day is also used; it is about 3 minutes 56 seconds shorter than the solar day, and close to the actual rotation period of the Earth, as opposed to the Sun's apparent motion. Days such as Christmas Eve, Hallowe'en, and the Eve of Saint Agnes are the remnants of the older pattern when holidays began the evening before.
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