Sidereal time
Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars.
More exactly, sidereal time is the angle, measured along the celestial equator, from the observer's meridian to the great circle that passes through the March equinox (the northern hemisphere's vernal equinox) and both celestial poles, and is usually expressed in hours, minutes, and seconds.
(In the context of sidereal time, "March equinox" or "equinox" or "first point of Aries" is currently a direction, from the center of the Earth along the line formed by the intersection of the Earth's equator and the Earth's orbit around the Sun, toward the constellation Pisces; during ancient times it was toward the constellation Aries.)
[2] Common time on a typical clock (using mean Solar time) measures a slightly longer cycle, affected not only by Earth's axial rotation but also by Earth's orbit around the Sun.
The March equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 25,800 years, so the misnamed "sidereal" day ("sidereal" is derived from the Latin sidus meaning "star") is 0.0084 seconds shorter than the stellar day, Earth's actual period of rotation relative to the fixed stars.
Solar time is measured by the apparent diurnal motion of the Sun.
Local noon in apparent solar time is the moment when the Sun is exactly due south or north (depending on the observer's latitude and the season).
Earth makes one rotation around its axis each sidereal day; during that time it moves a short distance (about 1°) along its orbit around the Sun.
So after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time.
The stars are so far away that Earth's movement along its orbit makes nearly no difference to their apparent direction (except for the nearest stars if measured with extreme accuracy; see parallax), and so they return to their highest point at the same time each sidereal day.
Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation.
For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it was conventional to chart the positions of the stars in the sky according to right ascension and declination, which are based on a frame of reference that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well.
(The conventional reference frame, for purposes of star catalogues, was replaced in 1998 with the International Celestial Reference Frame, which is fixed with respect to extra-galactic radio sources.
The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing frame of reference.
During the past, time was measured by observing stars with instruments such as photographic zenith tubes and Danjon astrolabes, and the passage of stars across defined lines would be timed with the observatory clock.
[7] Beginning during the 1970s, the radio astronomy methods very-long-baseline interferometry (VLBI) and pulsar timing overtook optical instruments for the most precise astrometry.
The linear coefficient represents the Earth's rotation speed around its own axis.
ERA replaces Greenwich Apparent Sidereal Time (GAST).
The lack of motion of the origin of ERA is considered a significant advantage.
[11] The ERA may be converted to other units; for example, the Astronomical Almanac for the Year 2017 tabulated it in degrees, minutes, and seconds.
Since it is not feasible to publish tables for every longitude, astronomical tables use Greenwich sidereal time (GST), which is sidereal time on the IERS Reference Meridian, less precisely termed the Greenwich, or Prime meridian.
There are two varieties, mean sidereal time if the mean equator and equinox of date are used, and apparent sidereal time if the apparent equator and equinox of date are used.
The following relationships are true:[14] The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are:
such that t represents the number of Julian centuries elapsed since noon 1 January 2000 Terrestrial Time.
For prograde rotation, the formula relating the lengths of the sidereal and solar days is: or, equivalently: When calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign (put another way, in the original formula the length of the sidereal day must be treated as negative).
