Sidereal time
Encyclopedia
Sidereal time s is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star
in the night sky
. Briefly, a sidereal day is a "time scale that is based on the Earth's rate of rotation measured relative to the fixed stars."
From a given observation point, a star found at one location in the sky will be found at nearly the same location on another night at the same sidereal time. This is similar to how the time kept by a sundial
can be used to find the location of the Sun
. Just as the Sun and Moon
appear to rise in the east and set in the west, so do the stars. Both solar time
and sidereal time make use of the regularity of the Earth's rotation about its polar axis, solar time following the Sun while sidereal time roughly follows the stars. More exactly, sidereal time follows the vernal equinox, which is not quite fixed among the stars; Precession and nutation
shift the equinox slightly from one day to the next, so sidereal time is not an exact measure of the rotation of the Earth relative to inertial space. Common time on a typical clock measures a slightly longer cycle, accounting not only for the Earth's axial rotation but also for the Earth's annual revolution around the Sun of slightly less than 1 degree per day.
A mean sidereal day is about 23 hours, 56 minutes, 4.091 seconds (23.93447 hours or 0.99726957 mean solar days), the time it takes the Earth to make one rotation relative to the vernal equinox. (Due to nutation, an actual sidereal day is not quite so constant.) The vernal equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 26,000 years, so the misnamed sidereal day ("sidereal" is derived from the Latin sidus meaning "star") is some 0.008 seconds shorter than the Earth's period of rotation relative to the fixed stars.
The longer "true" sidereal period is called a stellar day by the International Earth Rotation and Reference Systems Service
(IERS). It is also referred to as the sidereal period of rotation.
Maps of the stars in the night sky use declination
and right ascension
as coordinates. These correspond to latitude
and longitude
respectively. While declination is measured in degrees, right ascension is measured in units of time, because it was most natural to name locations in the sky in connection with the time when they crossed the meridian
.
In the sky, the meridian
is the imaginary north to south line that goes through the point directly overhead (the zenith
). The right ascension of any object crossing the meridian is equal to the current local (apparent) sidereal time, ignoring for present purposes that part of the circumpolar region north of the north celestial pole (for an observer in the northern hemisphere) or south of the south celestial pole (for an observer in the southern hemisphere) that is crossing the meridian the other way.
Because the Earth orbits the Sun once a year, the sidereal time at any one place at midnight will be about four minutes later each night, until, after a year has passed, one additional sidereal day has transpired compared to the number of solar days that have gone by.
Solar time
is measured by the apparent diurnal motion
of the sun, and local noon in solar time is the moment when the sun is at its highest point in the sky (exactly due south or north depending on the observer's latitude and the season). The average time for the sun to return to its highest point is 24 hours.
The Earth makes a 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 the Earth still needs to rotate a bit more before the sun reaches its highest point. A solar day is, therefore, nearly 4 minutes longer than a sidereal day.
The stars are so far away that the Earth's movement along its orbit makes nearly no difference to their apparent direction (see, however, parallax
), 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, the Sun appears to move around the Earth once per year. Therefore, there is one less solar day per year than there are sidereal days. This makes a sidereal day approximately times the length of the 24-hour solar day, giving approximately 23 hours, 56 minutes, 4.1 seconds (86,164.1 seconds).
For this reason, to simplify the description of Earth's orientation in astronomy and geodesy
, it is conventional to chart the positions of the stars in the sky according to right ascension
and declination
, which are based on a frame that follows the 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
, the year related to the Earth's seasons, represents one orbit of the Earth around the sun. The precise definition of a sidereal day is the time taken for one rotation of the Earth in this precessing reference frame.
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
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.
and at the United States Naval Observatory
.
Given a tropical year of 365.242190402 days from Simon et al. this gives a sidereal day of 86,400 ×
, or 86,164.09053 seconds.
Aoki et al., defined UT1 such that the observed sidereal day at the beginning of 2000 would be times a UT1 day of 86,400 seconds, which gives 86,164.090530833 seconds of UT1. For times within a century of 1984, the ratio only alters in its 11th decimal place. This web-based sidereal time calculator uses a truncated ratio of .
Because this is the period of rotation in a precessing reference frame, it is not directly related to the mean rotation rate of the Earth in an inertial frame, which is given by ω=2π/T where T is the slightly longer stellar day given by Aoki et al. as 86,164.09890369732 seconds. This can be calculated by noting that ω is the magnitude of the vector sum of the rotations leading to the sidereal day and the precession of that rotation vector. In fact, the period of the Earth's rotation varies on hourly to interannual timescales by around a millisecond
, together with a secular increase in length of day of about 2.3 milliseconds per century, mostly from tidal friction
slowing the Earth's rotation.
s, all but Venus
and Uranus
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 and Uranus, however, have retrograde
rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is
or equivalently
On the other hand, the formula in the case of retrograde rotation is
or equivalently
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 .997 . But the situation is quite different for Mercury
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.
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
in the night sky
Night sky
The term night sky refers to the sky as seen at night. The term is usually associated with astronomy, with reference to views of celestial bodies such as stars, the Moon, and planets that become visible on a clear night after the Sun has set. Natural light sources in a night sky include moonlight,...
. Briefly, a sidereal day is a "time scale that is based on the Earth's rate of rotation measured relative to the fixed stars."
From a given observation point, a star found at one location in the sky will be found at nearly the same location on another night at the same sidereal time. This is similar to how the time kept by a sundial
Sundial
A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a...
can be used to find the location of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
. Just as the Sun and Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
appear to rise in the east and set in the west, so do the stars. Both solar time
Solar time
Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time and mean solar time .-Introduction:...
and sidereal time make use of the regularity of the Earth's rotation about its polar axis, solar time following the Sun while sidereal time roughly follows the stars. More exactly, sidereal time follows the vernal equinox, which is not quite fixed among the stars; Precession and nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...
shift the equinox slightly from one day to the next, so sidereal time is not an exact measure of the rotation of the Earth relative to inertial space. Common time on a typical clock measures a slightly longer cycle, accounting not only for the Earth's axial rotation but also for the Earth's annual revolution around the Sun of slightly less than 1 degree per day.
A mean sidereal day is about 23 hours, 56 minutes, 4.091 seconds (23.93447 hours or 0.99726957 mean solar days), the time it takes the Earth to make one rotation relative to the vernal equinox. (Due to nutation, an actual sidereal day is not quite so constant.) The vernal equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 26,000 years, so the misnamed sidereal day ("sidereal" is derived from the Latin sidus meaning "star") is some 0.008 seconds shorter than the Earth's period of rotation relative to the fixed stars.
The longer "true" sidereal period is called a stellar day by the International Earth Rotation and Reference Systems Service
International Earth Rotation and Reference Systems Service
The International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
(IERS). It is also referred to as the sidereal period of rotation.
Maps of the stars in the night sky use declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
and right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
as coordinates. These correspond to latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
respectively. While declination is measured in degrees, right ascension is measured in units of time, because it was most natural to name locations in the sky in connection with the time when they crossed the meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
.
In the sky, the meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
is the imaginary north to south line that goes through the point directly overhead (the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
). The right ascension of any object crossing the meridian is equal to the current local (apparent) sidereal time, ignoring for present purposes that part of the circumpolar region north of the north celestial pole (for an observer in the northern hemisphere) or south of the south celestial pole (for an observer in the southern hemisphere) that is crossing the meridian the other way.
Because the Earth orbits the Sun once a year, the sidereal time at any one place at midnight will be about four minutes later each night, until, after a year has passed, one additional sidereal day has transpired compared to the number of solar days that have gone by.
Sidereal time and solar time
Solar time
Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time and mean solar time .-Introduction:...
is measured by the apparent diurnal motion
Diurnal motion
Diurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle, that is called the diurnal circle. The time for...
of the sun, and local noon in solar time is the moment when the sun is at its highest point in the sky (exactly due south or north depending on the observer's latitude and the season). The average time for the sun to return to its highest point is 24 hours.
The Earth makes a 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 the Earth still needs to rotate a bit more before the sun reaches its highest point. A solar day is, therefore, nearly 4 minutes longer than a sidereal day.
The stars are so far away that the Earth's movement along its orbit makes nearly no difference to their apparent direction (see, however, parallax
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. The term is derived from the Greek παράλλαξις , meaning "alteration"...
), 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, the Sun appears to move around the Earth once per year. Therefore, there is one less solar day per year than there are sidereal days. This makes a sidereal day approximately times the length of the 24-hour solar day, giving approximately 23 hours, 56 minutes, 4.1 seconds (86,164.1 seconds).
Precession effects
The Earth's rotation is not a simple rotation around an axis that would always remain parallel to itself. The Earth's rotational axis itself rotates about a second axis, orthogonal to the Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is called the precession of the equinoxes. Because of this precession, the stars appear to move around the 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
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
, it is conventional to chart the positions of the stars in the sky according to right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
and declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
, which are based on a frame that follows the 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
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
, the year related to the Earth's seasons, represents one orbit of the Earth around the sun. The precise definition of a sidereal day is the time taken for one rotation of the Earth in this precessing reference frame.
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 angleHour angle
In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the position of a point on the celestial sphere....
of the vernal equinox at that locality: it has the same value as the right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
of any celestial body that is crossing the local meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
at that same moment.
At the moment when the vernal equinox crosses the local meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
, Local Apparent Sidereal Time is 00:00. Greenwich Apparent Sidereal Time (GAST) is the hour angle of the vernal equinox at the prime meridian
Prime Meridian
The Prime Meridian is the meridian at which the longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian , which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.An international...
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
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
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 nutationNutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...
, the complex 'nodding' motion of the Earth's polar axis of rotation. It corresponds to the current amount of the nutation in (ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
) longitude (
) and to the current obliquity () of the eclipticEcliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
, 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
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
and declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
relative to the celestial equator (analogous to longitude and latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
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
Extinction (astronomy)
Extinction is a term used in astronomy to describe the absorption and scattering of electromagnetic radiation by matter between an emitting astronomical object and the observer. Interstellar extinction—also called Galactic extinction, when it occurs in the Milky Way—was first...
is minimised.
Sidereal time is a measure of the position of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
in its rotation around its axis, or time measured by the apparent diurnal motion
Diurnal motion
Diurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle, that is called the diurnal circle. The time for...
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
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
relative to the stars.
Earth's sidereal day also differs from its rotation period
Rotation period
The rotation period of an astronomical object is the time it takes to complete one revolution around its axis of rotation relative to the background stars...
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.
Exact duration and its variation
A mean sidereal day is about 23 h 56 m 4.1 s in length. However, due to variations in the rotation rate of the Earth, the rate of an ideal sidereal clock deviates from any simple multiple of a civil clock. In practice, the difference is kept track of by the difference UTC–UT1, which is measured by radio telescopes and kept on file and available to the public at the IERSIERS
IERS may refer to:* International Earth Rotation and Reference Systems Service* Independent Electricity Retail Solutions Pty Ltd* Information Exchange Requirements - used within MODAF and DODAF as the OV-3 view - called Information Exchange Matrix....
and at the United States Naval Observatory
United States Naval Observatory
The United States Naval Observatory is one of the oldest scientific agencies in the United States, with a primary mission to produce Positioning, Navigation, and Timing for the U.S. Navy and the U.S. Department of Defense...
.
Given a tropical year of 365.242190402 days from Simon et al. this gives a sidereal day of 86,400 ×
, or 86,164.09053 seconds.Aoki et al., defined UT1 such that the observed sidereal day at the beginning of 2000 would be times a UT1 day of 86,400 seconds, which gives 86,164.090530833 seconds of UT1. For times within a century of 1984, the ratio only alters in its 11th decimal place. This web-based sidereal time calculator uses a truncated ratio of .
Because this is the period of rotation in a precessing reference frame, it is not directly related to the mean rotation rate of the Earth in an inertial frame, which is given by ω=2π/T where T is the slightly longer stellar day given by Aoki et al. as 86,164.09890369732 seconds. This can be calculated by noting that ω is the magnitude of the vector sum of the rotations leading to the sidereal day and the precession of that rotation vector. In fact, the period of the Earth's rotation varies on hourly to interannual timescales by around a millisecond
Millisecond
A millisecond is a thousandth of a second.10 milliseconds are called a centisecond....
, together with a secular increase in length of day of about 2.3 milliseconds per century, mostly from tidal friction
Tidal acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...
slowing the Earth's rotation.
Sidereal days compared to solar days on other planets
Of the eight solar planetPlanet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s, all but Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...
and Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...
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 and Uranus, however, have retrograde
Retrograde motion
Retrograde motion is motion in the direction opposite to the movement of something else, and is the contrary of direct or prograde motion. This motion can be the orbit of one body about another body or about some other point, or the rotation of a single body about its axis, or other phenomena such...
rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is
or equivalently
On the other hand, the formula in the case of retrograde rotation is
or equivalently
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 .997 . But the situation is quite different for Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
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
- Earth rotationEarth rotationEarth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates towards the east. As viewed from the North Star Polaris, the Earth turns counter-clockwise.- Rotation period :...
- Sidereal month
- Synodic daySynodic dayA synodic day is the period of time it takes for a planet to rotate once in relation to the body it is orbiting ....
- Anti-sidereal timeAnti-sidereal timeAnti-sidereal time and extended-sidereal time are artificial time scales used to analyze the daily variation in the number of cosmic rays received on Earth. Anti-sidereal time has about 364.25 days per year, one day less than the number of days in a year of solar time, 365.25. Thus each...
- Nocturnal (instrument)Nocturnal (instrument)A nocturnal is an instrument used to determine the time based on the position of a certain star in the night sky. Sometimes called a "horologium nocturnum" or nocturlabe , it is closely related to the sun dial. A nocturnal is typically a navigational instrument...
- Transit instrumentTransit instrumentIn astronomy, transit instruments are used for the precise observation of star positions. The instruments can be divided into three groups:- Meridian instruments :for observation of star transits in the exact direction of South or North:...
External links
- Web based Sidereal time calculator
- For more details, see the article on sidereal time from Jason Harris' Astroinfo.