Sidereal time — astronomical timekeeping and practical uses
Sidereal time is a time scale tied to Earth's rotation relative to the fixed stars. Astronomers use it to locate celestial objects and to schedule observations because it aligns right ascension with the observer's meridian.
Sidereal time is a system of timekeeping that tracks Earth’s rotation relative to the distant stars rather than to the Sun. Unlike civil or solar time, which follows the Sun’s apparent motion, sidereal time advances at the rate that brings the same stars back to the same local positions. Because it is keyed to the fixed celestial sphere, sidereal time is the natural clock for star charts and telescopic pointing.
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Key definitions and characteristics
- Sidereal day: the interval in which Earth completes one rotation relative to the stars. A mean sidereal day is about 23 hours, 56 minutes, 4 seconds, roughly four minutes shorter than the average solar day.
- Local Sidereal Time (LST): the sidereal time at a particular longitude; when the LST equals a star’s right ascension, that star crosses the observer’s meridian and is at its highest point in the sky.
- Greenwich Sidereal Time (GST): a reference sidereal time measured at the prime meridian; local values are obtained by adding the observer’s east longitude (expressed in time units).
- Mean vs. apparent: mean sidereal time averages small periodic variations; apparent sidereal time accounts for the instantaneous effects of nutation and the true equinox.
The relationship between angular and temporal coordinates is convenient: the celestial sphere is divided into 24 hours of right ascension, so 1 hour corresponds to 15 degrees on the sky and 1 degree corresponds to 4 minutes of sidereal time. This mapping makes sidereal time directly useful for converting between a star’s catalog coordinates and a telescope’s pointing.
History and development
The concept of tracking the heavens with a star-based clock dates to pre-telescopic astronomy, but sidereal time became formalized with mechanical clocks and later precision astronomical instruments. Observatories maintain sidereal clocks to schedule transits and calibrate instruments. In modern practice, sidereal time is computed from universal time with corrections for precession, nutation and the observer’s longitude.
Practical uses and examples
- Pointing equatorial-mounted telescopes: the mount’s setting circles use right ascension and declination together with the local sidereal time to aim at objects precisely.
- Scheduling observations: because stars rise about four minutes earlier each night in solar time, astronomers plan targets by sidereal time and calendar date.
- Radio astronomy and pulsar timing: sidereal timing aligns repeating sky patterns with terrestrial receivers.
- Celestial navigation and astrometry: sidereal references underlie catalogs of stellar positions and long-term measurements.
Sidereal time differs fundamentally from solar time, which is based on the apparent motion of the Sun. The discrepancy arises because Earth also moves in its orbit around the Sun, so the planet must rotate slightly more than 360° for the Sun to return to the same apparent meridian, making a solar day about four minutes longer.
Notable points: sidereal time is tied to the celestial coordinate system rather than local daylight; it slowly drifts relative to calendar dates because of precession of the equinoxes; and modern computerized telescope systems compute sidereal time internally so observers can translate catalog coordinates into practical pointing commands.
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).
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.
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AlegsaOnline.com Sidereal time — astronomical timekeeping and practical uses Leandro Alegsa
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