![Sidereal Clock made for Sir George Augustus William Shuckburgh](https://upload.wikimedia.org/wikipedia/commons/1/1b/Sidereal_Clock_made_for_Sir_George_Augustus_William_Shuckburgh.jpg)
Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a
timekeeping
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to co ...
system that
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
s use to locate
celestial objects
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
. Using sidereal time, it is possible to easily point a
telescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
to the proper
coordinates
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
in the
night sky
The night sky is the nighttime appearance of celestial objects like stars, planets, and the Moon, which are visible in a clear sky between sunset and sunrise, when the Sun is below the horizon.
Natural light sources in a night sky include ...
. In short, sidereal time is a "time scale that is based on
Earth's rate of rotation measured relative to the
fixed stars
In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backgro ...
", or more correctly, relative to the
March equinox
The March equinox or northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the verna ...
.
Viewed from the same
location
In geography, location or place are used to denote a region (point, line, or area) on Earth's surface or elsewhere. The term ''location'' generally implies a higher degree of certainty than ''place'', the latter often indicating an entity with an ...
, a star seen at one position in the sky will be seen at the same position on another night at the same sidereal time. This is similar to how the time kept by a
sundial
A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat ...
(
Solar time
Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial ti ...
) can be used to find the location of the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
. Just as the Sun and
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both Solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time following the Sun while, roughly speaking, sidereal time follows the distant fixed stars on the celestial sphere.
More exactly, sidereal time is the angle, measured along the
celestial equator
The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projectio ...
, from the observer's
meridian
Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to
Science
* Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon
* ...
to the
great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...
that passes through the
March equinox
The March equinox or northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the verna ...
and both
celestial pole
The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...
s, and is usually expressed in hours, minutes, and seconds. Common time on a typical clock (
mean Solar time
Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial ti ...
) measures a slightly longer cycle, accounting not only for Earth's axial rotation but also for Earth's orbit around the Sun.
A sidereal day on Earth is approximately 86164.0905
second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
s (23 h 56 min 4.0905 s or 23.9344696 h).
''(
Seconds
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
here follow the
SI definition and are not to be confused with
ephemeris second.)''
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 second shorter than the
stellar day
Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Pola ...
, Earth's period of rotation relative to the fixed stars.
The slightly longer "true" sidereal period is measured as the
Earth Rotation Angle
Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...
(ERA), formerly the stellar angle. An increase of 360° in the ERA is a full rotation of the Earth.
Because Earth orbits the Sun once a year, the sidereal time at any given place and time will gain about four minutes against local
civil time
In modern usage, civil time refers to statutory time as designated by civilian authorities. Modern civil time is generally national standard time in a time zone at a fixed offset from Coordinated Universal Time (UTC), possibly adjusted by daylig ...
, every 24 hours, until, after a year has passed, one additional sidereal "day" has elapsed compared to the number of solar days that have gone by.
Comparison to solar time
Solar time
Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial ti ...
is measured by the apparent
diurnal motion
Diurnal motion (, ) is an astronomical term referring to the apparent motion of celestial objects (e.g. the Sun and stars) around Earth, or more precisely around the two celestial poles, over the course of one day. It is caused by Earth's rotatio ...
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). A mean solar day (what we normally measure as a "day") is the average time between local solar noons ("average" since this varies slightly over the year).
Earth makes one rotation around its axis in a 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. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day.
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 if having high accuracy, see
parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects ...
), and so they return to their highest point in a sidereal day.
Another way to see this difference is to notice that, relative to the stars, as viewed from Earth, the Sun appears to move around Earth once per year. A year has around 365.24 solar days but 366.24 sidereal days. Therefore, there is one fewer
solar day
A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time.
The synodic day is distinguished from the sidereal day, which is ...
per year than there are sidereal days, similar to an observation of the
coin rotation paradox
The coin rotation paradox is the counter-intuitive observation that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes two full rotations after going all the way around the stationary coin.
Descript ...
. This makes a sidereal day approximately times the length of the 24-hour solar day.
Precession effects
Earth's rotation is not a simple rotation around an axis that would always remain parallel to itself. Earth's rotational axis itself rotates about a second axis,
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
to Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is called the
precession of the equinoxes
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particu ...
. 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
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
, it was conventional to chart the positions of the stars in the sky according to
right ascension
Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth.
When paired w ...
and
declination
In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the ...
, which are based on a frame that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well. In this reference frame, Earth's 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
A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time fro ...
, the year related to Earth's seasons, represents one orbit of Earth around the Sun. The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing reference frame.
Modern definitions
In 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. Then, using the
right ascension
Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth.
When paired w ...
of the stars from a star catalog, the time when the star should have passed through the meridian of the observatory was computed, and a correction to the time kept by the observatory clock was computed. Sidereal time was defined such that the March equinox would
transit
Transit may refer to:
Arts and entertainment Film
* ''Transit'' (1979 film), a 1979 Israeli film
* ''Transit'' (2005 film), a film produced by MTV and Staying-Alive about four people in countries in the world
* ''Transit'' (2006 film), a 2006 ...
the meridian of the observatory at 0 hours local sidereal time.
Beginning in the 1970s, the
radio astronomy
Radio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The first detection of radio waves from an astronomical object was in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming f ...
methods
very long baseline interferometry
Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. T ...
(VLBI) and
pulsar timing
Any planet is an extremely faint light source compared to its parent star. For example, a star like the Sun is about a billion times as bright as the reflected light from any of the planets orbiting it. In addition to the intrinsic difficulty of ...
overtook optical instruments for the most precise
astrometry
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way.
His ...
. This led to the determination of
UT1
Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with ...
(mean solar time at 0° longitude) using VLBI, a new measure of the Earth Rotation Angle, and new definitions of sidereal time. These changes were put into practice on 1 January 2003.
Earth rotation angle
The Earth rotation angle (ERA) measures the rotation of the Earth from an origin on the celestial equator, the ''Celestial Intermediate Origin'', also called the ''Celestial Ephemeris Origin'', that has no instantaneous motion along the equator; it was originally referred to as the ''non-rotating origin''. This point is very close to the equinox of J2000.
ERA, measured in
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
s, is related to
UT1
Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with ...
by a simple linear relation:
where ''t
U'' is the
Julian UT1 date (JD) minus 2451545.0, that is, 12:00 (midday)
Terrestrial Time
Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.
For example, the Astronomical Almanac uses T ...
of January 1, 2000. (Note that this differed from 12h
UTC on that day by around a minute.)
The linear coefficient represents the
Earth's rotation speed.
ERA replaces ''Greenwich Apparent Sidereal Time'' (GAST). The origin on the celestial equator for GAST, called the true
equinox
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...
, does move, due to the movement of the equator and the ecliptic. The lack of motion of the origin of ERA is considered a significant advantage.
The ERA may be converted to other units; for example, the ''Astronomical Almanac for the Year 2017'' tabulated it in degrees, minutes, and seconds.
As an example, the ''Astronomical Almanac for the Year 2017'' gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″.
Mean and apparent varieties
![20180505 123207-sidereal-clock](https://upload.wikimedia.org/wikipedia/commons/1/1e/20180505_123207-sidereal-clock.jpg)
Although ERA is intended to replace sidereal time, there is a need to maintain definitions for sidereal time during the transition, and when working with older data and documents.
Similarly to mean solar time, every location on Earth has its own local sidereal time (LST), depending on the longitude of the point. Since it is not feasible to publish tables for every longitude, astronomical tables make use of Greenwich sidereal time (GST), which is sidereal time on the
IERS Reference Meridian
The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east ...
, less precisely called the Greenwich, or
Prime meridian
A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great c ...
. 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 former ignores the effect of
astronomical nutation
Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Al ...
while the latter includes it. When the choice of location is combined with the choice of including astronomical nutation or not, the acronyms GMST, LMST, GAST, and LAST result.
The following relationships hold:
The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are:
where ''θ'' is the Earth Rotation Angle, ''E''
PREC is the accumulated precession, and ''E''
0 is equation of the origins, which represents accumulated precession and nutation. The calculation of precession and nutation was described in Chapter 6 of Urban & Seidelmann.
As an example, the ''Astronomical Almanac for the Year 2017'' gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″. The GAST was 6 h 43 m 20.7109 s. For GMST the hour and minute were the same but the second was 21.1060.
Relationship between solar time and sidereal time intervals
![ConantClock](https://upload.wikimedia.org/wikipedia/commons/a/a5/ConantClock.png)
If a certain interval ''I'' is measured in both mean solar time (UT1) and sidereal time, the numerical value will be greater in sidereal time than in UT1, because sidereal days are shorter than UT1 days. The ratio is:
where ''t'' represents the number of Julian centuries elapsed since noon 1 January 2000
Terrestrial Time
Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.
For example, the Astronomical Almanac uses T ...
.
Sidereal days compared to solar days on other planets
Six of the eight solar
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s have
prograde rotation—that is, they rotate more than once per year in the same direction as they orbit the Sun, so the Sun rises in the east.
Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...
and
Uranus
Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus (mythology), Uranus (Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars (mythology), Mars), grandfather ...
, however, have
retrograde rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is:
or, equivalently:
But do note, when calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign. This is due to the solar day being shorter than the sidereal day, as the rotation of the planet would be against the direction of orbital motion.
If a planet rotates prograde, and the sidereal day exactly equals the orbital period, then the formula above gives an infinitely long solar day (
division by zero
In mathematics, division by zero is division (mathematics), division where the divisor (denominator) is 0, zero. Such a division can be formally expression (mathematics), expressed as \tfrac, where is the dividend (numerator). In ordinary ari ...
). This is the case of a planet in
synchronous rotation
Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked b ...
; one hemisphere experiences eternal day, the other eternal night, with a "twilight belt" separating them.
All the solar planets more distant from the Sun than Earth are similar to Earth in that, since they experience many rotations per revolution around the Sun, there is only a small difference between the length of the sidereal day and that of the solar day – the ratio of the former to the latter never being less than Earth's ratio of 0.997. But the situation is quite different for
Mercury
Mercury commonly refers to:
* Mercury (planet), the nearest planet to the Sun
* Mercury (element), a metallic chemical element with the symbol Hg
* Mercury (mythology), a Roman god
Mercury or The Mercury may also refer to:
Companies
* Merc ...
and Venus. Mercury's sidereal day is about two-thirds of its orbital period, so by the prograde formula its solar day lasts for two revolutions around the Sun – three times as long as its sidereal day. Venus rotates retrograde with a sidereal day lasting about 243.0 Earth days, or about 1.08 times its orbital period of 224.7 Earth days; hence by the retrograde formula its solar day is about 116.8 Earth days, and it has about 1.9 solar days per orbital period.
By convention, rotation periods of planets are given in sidereal terms unless otherwise specified.
See also
*
Anti-sidereal time
*
Earth's rotation
Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in retrograd ...
*
International Celestial Reference Frame
The International Celestial Reference System (ICRS) is the current standard celestial reference system adopted by the International Astronomical Union (IAU). Its origin is at the barycenter of the Solar System, with axes that are intended to "sho ...
*
Nocturnal (instrument)
A nocturnal is an instrument used to determine the local time based on the relative positions of two or more stars in the night sky. Sometimes called a ''horologium nocturnum'' (time instrument for night) or ''nocturlabe'' (in French and occasio ...
*
Sidereal month
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona, Middle Eastern, and Euro ...
*
Sidereal year
*
Synodic day
A synodic day (or synodic rotation period or solar day) is the rotation period, period for a astronomical object, celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time.
The synodic day is disting ...
*
Transit instrument
In astronomy, a transit instrument is a small telescope with extremely precisely graduated mount used for the precise observation of star positions. They were previously widely used in astronomical observatories and naval observatories to measu ...
Notes
Citations
References
*
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External links
Web-based Sidereal time calculator
{{Authority control
Horology
Time in astronomy
Time scales
Units of time