Sidereal time // 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 coordinates in the night sky. Briefly, sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars".
Viewed from the same location, 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 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 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 sidereal time roughly follows 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 and both celestial poles, and is usually expressed in hours, minutes, and seconds.Common time on a typical clock 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 is approximately 86164.0905 seconds (23 h 56 min 4.0905 s or 23.9344696 h).
(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 26,000 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 period of rotation relative to the fixed stars. The slightly longer "true" sidereal period is measured as the Earth Rotation Angle (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, 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.
Solar time is measured by the apparent diurnal motion of the Sun, and 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 (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 Earth once per year. Therefore, there is one fewer solar day per year than there are sidereal days. This makes a sidereal day approximately 365.24/ times the length of the 24-hour solar day, giving approximately 23 h 56 min 4.1 s (86,164.1 s).
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 to 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 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 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, 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.
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 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 the meridian of the observatory at 0 hours local sidereal time.
Beginning in the 1970s the radio astronomy methods very long baseline interferometry (VLBI) and pulsar timing overtook optical instruments for the most precise astrometry. This led to the determination of UT1 (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.
The Earth Rotation Angle (ERA) measures the rotation of the Earth from an origin on the celestial equator, the Celestial Intermediate Origin, that has no instantaneous motion along the equator; it was originally referred to as the non-rotating origin. ERA replaces Greenwich Apparent Sidereal Time (GAST). The origin on the celestial equator for GAST, called the true equinox, 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.
ERA, measured in radians, is related to UT1 by the expression
where tU is the Julian UT1 date − 2451545.0.
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″.
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, less precisely called the Greenwich, or Prime meridian. There are two varieties, mean sidereal time if the mean equator and equinox of date are used, or apparent sidereal time if the apparent equator and equinox of date are used. The former ignores the effect of astronomical nutation 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, EPREC is the accumulated precession, and E0 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.
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.
Of the eight solar planets, 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:
But do note, when calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign. Because the orbit will be going the opposite way around the object.
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 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.
In astronomy, declination 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 celestial equator, along the hour circle passing through the point in question.
The ecliptic is the plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.
An equinox is commonly regarded as the instant of time when the plane of Earth's equator passes through the geometric center of the Sun's disk. This occurs twice each year, around 20 March and 23 September. In other words, it is the moment at which the center of the visible Sun is directly above the equator.
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.
A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.
Universal Time (UT) is a time standard based on Earth's rotation. There are several versions of Universal Time, which differ by up to a few seconds. The most commonly used are Coordinated Universal Time (UTC) and UT1. All of these versions of UT, except for UTC, are based on Earth's rotation relative to distant celestial objects, but with a scaling factor and other adjustments to make them closer to solar time. UTC is based on International Atomic Time, with leap seconds added to keep it within 0.9 second of UT1.
The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.
The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence, it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It equals 365.256 363 004 Ephemeris days for the J2000.0 epoch.
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning-top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.
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. Two types of solar times are apparent solar time and mean solar time.
Lunar precession is the change in orientation of the lunar rotational axis with respect to a reference plane, following the normal rules of precession followed by spinning objects. The orbit of the Moon undergoes two important types of precessional motion: apsidal and nodal. The axis of the Moon also experiences precession.
The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconcile a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion. Apparent solar time can be obtained by measurement of the current position of the Sun, as indicated by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.
The rotation period of a celestial object is the time that the object takes to complete a single revolution around its axis of rotation relative to the background stars. It differs from the object's solar day, which may differ by a fractional rotation to accommodate the portion of the object's orbital period during one day.
Earth's rotation is the rotation of planet Earth around its own axis. Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counterclockwise.
The Moon orbits Earth in the prograde direction and completes one revolution relative to the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,600 km (2,900 mi) from Earth's center. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's center, which corresponds to about 60 Earth radii or 1.282 light-seconds.
In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. Although there are two intersections of the ecliptic with the celestial equator, by convention, the equinox associated with the Sun's ascending node is used as the origin of celestial coordinate systems and referred to simply as "the equinox". In contrast to the common usage of spring/vernal and autumnal equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.
A tropical year is the 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. This differs from the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars by about 20 minutes because of the precession of the equinoxes.
This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.
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. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.
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