Sidereal time

Author: Leandro Alegsa Creation date: November 13, 2022

en.wikipedia.org · CC BY 3.0

Sidereal time is a time-keeping system. It is used by astronomers to find celestial objects. Using sidereal time it is possible to point a telescope to the proper coordinates in the night sky.

Sidereal time is a "time scale based on Earth's rate of rotation measured relative to the fixed stars".

Because the Earth moves in its orbit about the Sun, a mean solar day is about four minutes longer than a sidereal day. Thus, a star appears to rise four minutes earlier each night, compared to solar time. Different stars are visible at different times of the year.

By contrast, solar time is reckoned by the movement of the Earth from the perspective of the Sun. An average solar day (24 hours) is longer than a sidereal day (23 hours, 56 minutes, 4 seconds) because of the amount the Earth moves each day in its orbit around the Sun.

Definition and properties

The sidereal time is defined as the hour angle of the vernal equinox. If you refer to the mean vernal equinox, you get the mean sidereal time. If you refer to the true vernal equinox, you get the apparent or true sidereal time.

The cause for the continuous increase of the mentioned hour angle is the earth rotation. The sidereal time is subject to all short- and long-term irregularities of the earth's rotation and is therefore not a uniformly proceeding measure of time. However, it is always a faithful reflection of the angle of rotation of the Earth with respect to the vernal equinox.

Since the vernal equinox moves relative to the fixed star background due to precession, a sidereal day (i.e., one full revolution of the Earth relative to the vernal equinox) is slightly shorter than a rotation of the Earth (i.e., one full revolution of the Earth relative to the fixed star background). Since the vernal equinox moves backwards along the ecliptic by about 0.137 arc seconds per day, a mean sidereal day is 0.009 seconds shorter than a rotation of the Earth.

The true vernal equinox differs from the mean vernal equinox by its variable nutation. The apparent sidereal time is therefore subject to an additional non-uniformity compared to the (itself already non-uniform) mean sidereal time, whose main component varies with a period of 18.6 years and an amplitude of ±1.05 seconds.

The hour angle of the vernal equinox is the same for observers located at the same longitude, but different for observers at different longitudes. The sidereal time derived from this is therefore a local time. The sidereal time of the reference location Greenwich is the Greenwich sidereal time. It is particularly often used in calculations. The different types of sidereal time are often designated by their English abbreviations:

LAST: local apparent sidereal time, apparent local sidereal time
LMST: local mean sidereal time, mean local sidereal time
GAST: Greenwich apparent sidereal time, apparent Greenwich sidereal time
GMST: Greenwich mean sidereal time, mean Greenwich sidereal time

The hour angle of the vernal equinox is the angle counted along the celestial equator from the meridian to the vernal equinox. The right ascension of a star, on the other hand, is the angle counted along the celestial equator from the vernal equinox to the star. If the star is on the meridian (that is: culminating), both angles are equal. It follows: At the moment of culmination of a star, the sidereal time is equal to the right ascension of the star.

The sidereal time is the right ascension in the upper culmination.

This can be used to directly determine the right ascension of the star by observing the culmination time. This is the reason why the right ascension is often given in time units instead of angular units: it is then directly the sidereal time read at the time of culmination. Wega, for example, has a right ascension of 18h 36m 56s, so it will always culminate at 18h 36m 56s local sidereal time.

On the other hand, by observing the culmination of a star of known right ascension, the instantaneous sidereal time can be determined: When Vega culminates, the sidereal time is 18h 36m 56s (in practice, corrections for precession, proper motion, parallax, etc. must still be applied).

1. the "sidereal hour hand" rotates on a dial fixed on the horizon: after a 15° turn (scale 0°, 15°, 30°, ...) one sidereal hour (scale 23, 0, 1, ...) has passed. 2. the "sidereal hour hand" rotates on a dial dragged along by the sun around the pole star: after about one month (scale 06, 07, 08, ...) one sidereal hour has passed. 2. the "sidereal hour hand" turns on a dial dragged along by the sun and rotating around Polaris: after about one month (scale 06, 07, 08, ...) it has moved ahead of the sun by 30° (scale 0°, 15°, 30°, ...).

Rotation of the starry sky

Daily rotation

One can imagine the starry sky as a large clock disk, which rotates once around itself in a counterclockwise direction (in the northern hemisphere) on a starry day. In the picture, this disk is marked with a hand between Polaris and the Great Bear. The 24-hour dial (scale 23, 0, 1, ...) is fixed at the horizon. If the hand has turned 15° further (scale 0°, 15°, 30°, ...), one sidereal hour has passed. For a solar time hour it must turn slightly further.

Annual rotation

On a dial dragged along by the sun and rotating around the pole star, one notices a very slow advance of the hand. The hand circles it once a year: 30° (scale 0°, 15°, 30°, ...) in about one month (scale 06, 07, 08, ...).

The picture was taken in early July (numeral 07) around 2:00 am. Two hours later (about 4:00) the Big Dipper has moved on to the number 4. One month later in August (number 08) it is already at the number 4 at 2:00 o'clock.