SIDEREAL DAY

Traditionally, the sidereal day is described as the time it takes for the Earth to complete one rotation relative to the stars. Because, relative to the stars, the Sun appears to move around the Earth once per year, there is one more mean solar day per year than there are sidereal days. This makes a sidereal day a factor of approximately 365.25/366.25 shorter than the 24 hour solar day, giving approximately 23 hours, 56 minutes, 4.1 seconds (86,164.1 seconds).
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.
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.
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.^[2] 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]

Contents

See also

References

External link

See also

★ Earth rotation

★ sidereal month

★ sidereal time

★ time

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.

External link

★ Web based Sidereal time calculator