Sidereal Time - Definition

Definition

Sidereal time, at any moment (and at a given locality defined by its geographical longitude), more precisely Local Apparent Sidereal Time (LAST), is defined as the hour angle of the vernal equinox at that locality: it has the same value as the right ascension of any celestial body that is crossing the local meridian at that same moment.

At the moment when the vernal equinox crosses the local meridian, Local Apparent Sidereal Time is 00:00. Greenwich Apparent Sidereal Time (GAST) is the hour angle of the vernal equinox at the prime meridian at Greenwich, England.

Local Sidereal Time at any locality differs from the Greenwich Sidereal Time value of the same moment, by an amount that is proportional to the longitude of the locality. When one moves eastward 15° in longitude, sidereal time is larger by one sidereal hour (note that it wraps around at 24 hours). Unlike the reckoning of local solar time in "time zones," incrementing by (usually) one hour, differences in local sidereal time are reckoned based on actual measured longitude, to the accuracy of the measurement of the longitude, not just in whole hours.

Apparent Sidereal Time (Local or at Greenwich) differs from Mean Sidereal Time (for the same locality and moment) by the Equation of the Equinoxes: This is a small difference in Right Ascension R.A. (parallel to the equator), not exceeding about +/-1.2 seconds of time, due to nutation, the complex 'nodding' motion of the Earth's polar axis of rotation. It corresponds to the current amount of the nutation in (ecliptic) longitude and to the current obliquity of the ecliptic, so that .

Greenwich Mean Sidereal Time (GMST) and UT1 differ from each other in rate, with the second of sidereal time a little shorter than that of UT1, so that (as at 2000 January 1 noon) 1.002737909350795 second of mean sidereal time was equal to 1 second of Universal Time (UT1). The ratio varies slightly with time, reaching 1.002737909409795 after a century.

To an accuracy within 0.1 second per century, Greenwich (Mean) Sidereal Time (in hours and decimal parts of an hour) can be calculated as

GMST = 18.697374558 + 24.06570982441908 * D ,

where D is the interval, in UT1 days including any fraction of a day, since 2000 January 1, at 12h UT (interval counted positive if forwards to a later time than the 2000 reference instant), and the result is freed from any integer multiples of 24 hours to reduce it to a value in the range 0-24.

In other words, Greenwich Mean Sidereal Time exceeds mean solar time at Greenwich by a difference equal to the longitude of the fictitious mean Sun used for defining mean solar time (with longitude converted to time as usual at the rate of 1 hour for 15 degrees), plus or minus an offset of 12 hours (because mean solar time is reckoned from 0h midnight, instead of the pre-1925 astronomical tradition where 0h meant noon).

Sidereal time is used at astronomical observatories because sidereal time makes it very easy to work out which astronomical objects will be observable at a given time. Objects are located in the night sky using right ascension and declination relative to the celestial equator (analogous to longitude and latitude on Earth), and when sidereal time is equal to an object's right ascension the object will be at its highest point in the sky, or culmination, at which time it is usually best placed for observation, as atmospheric extinction is minimised.

Sidereal time is a measure of the position of the Earth in its rotation around its axis, or time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical to, the motion of stars. They differ by the precession of the vernal equinox in right ascension relative to the stars.
Earth's sidereal day also differs from its rotation period relative to the background stars by the amount of precession in right ascension during one day (8.4 ms). Its J2000 mean value is 23h56m4.090530833s.