Editing Sidereal time (section)

==Modern definitions==
During the past, time was measured by observing stars with instruments such as [[Zenith telescope|photographic zenith tube]]s and [[André-Louis Danjon|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 [[Astronomical transit|transit]] the meridian of the observatory at 0 hours local sidereal time.{{Sfn|ES1|1961|loc=Ch 3, "Systems of Time Measurement"}}

Beginning during the 1970s, the [[radio astronomy]] methods [[very-long-baseline interferometry]] (VLBI) and [[Pulsar timing array|pulsar timing]] overtook optical instruments for the most precise [[astrometry]]. This resulted in 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 became effective 1 January 2003.{{Sfn|Urban|Seidelmann|2013|pages= 78–81, 112}}

===Earth rotation angle{{anchor|ERA}}===

The '''Earth rotation angle''' ('''ERA''') measures the rotation of the Earth from an origin on the celestial equator, the ''Celestial Intermediate Origin'', also termed the ''Celestial Ephemeris Origin'',<ref>{{cite dictionary |url=https://www.iers.org/IERS/EN/Service/Glossary/celestialIntermediateOrigin.html?nn=14894 |title=Celestial Intermediate Origin (CIO) |dictionary=Glossary of the [[IERS]] Conventions (2010)}}</ref> 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.<ref>{{cite dictionary |url=https://www.iers.org/IERS/EN/Service/Glossary/ceo.html?nn=14894 |title=Celestial Ephemeris Origin |dictionary=Glossary of the [[IERS]] Conventions (2010)}}</ref>

ERA, measured in [[radian]]s, is related to [[Universal time|UT1]] by a simple linear relation:{{sfn|Urban|Seidelmann|2013|page=78}}
<math display="block">\theta(t_U)=2\pi(0.779\,057\,273\,2640+1.002\,737\,811\,911\,354\,48\cdot t_U)</math>
where ''t<sub>U</sub>'' is the [[Julian day|Julian UT1 date]] (JD) minus 2451545.0.
The linear coefficient represents the [[Earth's rotation speed]] around its own axis.

ERA replaces ''Greenwich Apparent Sidereal Time'' (GAST). The origin on the celestial equator for GAST, termed the true [[Equinox (celestial coordinates)|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.{{Sfn|Urban|Seidelmann|2013|page=6}}

The ERA may be converted to other units; for example, the ''Astronomical Almanac for the Year 2017'' tabulated it in degrees, minutes, and seconds.{{Sfn|Astronomical Almanac|2016|pages=B21–B24}}

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″.{{Sfn|Astronomical Almanac|2016|page=B21}} Since [[Coordinated Universal Time]] (UTC) is within a second or two of UT1, this can be used as an anchor to give the ERA approximately for a given civil time and date.

===Mean and apparent varieties===
[[File:Sidereal Clock made for Sir George Augustus William Shuckburgh.jpg|thumb|One of the two known surviving sidereal angle clocks in the world, made by [[John Arnold (watchmaker)|John Arnold]] & Son. It was previously owned by Sir [[George Shuckburgh-Evelyn]]. It is on display in the [[Royal Observatory, Greenwich]], London.]]

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 use Greenwich sidereal time (GST), which is sidereal time on the [[IERS Reference Meridian]], less precisely termed the Greenwich, or [[Prime meridian (Greenwich)|Prime meridian]]. 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]] 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 are true:{{Sfn|Urban|Seidelmann|2013|page=80}}
{{block indent|1=local mean sidereal time = GMST + east longitude}}
{{block indent|1=local apparent sidereal time = GAST + east longitude}}

The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are:
<math display="block">\mathrm{GMST}(t_U,t)=\theta(t_U)-E_\mathrm{PREC}(t)</math>
<math display="block">\mathrm{GAST}(t_U,t)=\theta(t_U)-E_0(t)</math>

such that ''θ'' is the Earth Rotation Angle, ''E''<sub>PREC</sub> is the accumulated precession, and ''E''<sub>0</sub> is equation of the origins, which represents accumulated precession and nutation.{{Sfn|Urban|Seidelmann|2013|pages=78–79}} 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″ (6 h 42 m 28.8291 s). 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.{{Sfn|Astronomical Almanac|2016|page=B21}}

===Relationship between solar time and sidereal time intervals===
[[File:ConantClock.png|thumb|upright|This [[astronomical clock]] has dials showing both sidereal time and [[mean solar time]].]]
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:
<math display="block">\frac{I_\mathrm{mean\,sidereal}}{I_\mathrm{UT1}}=r'=1.002\,737\,379\,093\,507\,95 + 5.9006\times10^{-11}t - 5.9\times10^{-15}t^2</math>

such that ''t'' represents the number of Julian centuries elapsed since noon 1 January 2000 [[Terrestrial Time]].{{Sfn|Urban|Seidelmann|2013|page=81}}