Since the advent of atomic time in 1955 there has been a steady transition from reliance on the earth's rotation to the use of atomic time as the primary standard. Before atomic time, the closest approximation to a uniform time was Ephemeris Time (ET), which used the best available theory of the earth's rotation to remove its known changes in rotation rate. The use of Ephemeris Time continued until 1984. It was the time independent variable for planetary ephemerides until then.

Several important time scales still follow the rotation of the earth, most notably civil and sidereal time, but of these are now derived from atomic time through a combination of earth rotation theory and actual measurements of the earth's rotation and orientation. Chapter 2 of the most recent Explanatory Supplement to the Astronomical Almanac [ref 1] gives an extensive summary of time standards and a list of original literature references. The kinds of time typically encountered in astronomy are briefly described below.

You will notice that many of the time acronyms are reversed from
their full English names. That's because they are acronyms from French (TAI
= *Temps Atomique International*) since France has a long and
continuing history as a primary source of time standards, now through the
*Bureau International des Poids et Measures*.

UTC = TAI - (number of leap seconds)Before UTC, the time broadcast by WWV and other services was a close approximation to Greewich Mean Time (GMT) [ref 2]. GMT is an earth rotation time and is now called UT1 or simply UT.

TT = TAI + 32.184 = UTC + (number of leap seconds) + 32.184There is a subtle relativistic distinction between coordinate time and dynamic time, which is not significant for most practical purposes. The counterpart to TT is Geocentric Coordinate Time (TCG) which differs in rate from TT by about 0.7 parts per billion [ref 3]. TT and TCG were coincident on January 1, 1977 and now differ by 0.42 seconds. The rate difference from TT can be important to long term measurements, so make sure you know which time is being used when comparing observations. Some physical constants are different in coordinate time. You are not likely to encounter TCG in the literature.

TDB = TT + 0.001658 sin( g ) + 0.000014 sin( 2g ) seconds where g = 357.53 + 0.9856003 ( JD - 2451545.0 ) degreesand JD is the Julian Date. A more accurate formula, with adds terms smaller than 20 microseconds, is given in the Explanatory Supplement to the Astronomical Almanac [ref 4]. Planetary motions are now computed using TDB.

There is a subtle relativistic distinction between coordinate time and dynamic time, which is not significant for most practical purposes. The counterpart to TDB is Barycentric Coordinate Time (TCB) which differs in rate from TDB by about 15.5 parts per billion [ref 5]. TDB and TCB were coincident on January 1, 1977 and now differ by 9.3 seconds. The rate difference from TDB can be important to long term measurements, so make sure you know which time is being used when comparing observations. Some physical constants are different in coordinate time. You are not likely to encounter TCB in the literature.

Since the earth's rotation is not uniform, the rate of UT1 is not constant, and its offset from atomic time is continually changing in a not completely predictable way. As of December 1995, UT1 was drifting about 0.8 seconds per year with respect to atomic time (TAI or UTC). Since UTC is intentionally incremented by integer seconds (leap seconds) to stay within 0.7 seconds of UT1, the difference between UT1 and UTC is never greater than this. The difference, DUT1 = UT1 - UTC is monitored by the International Earth Rotation Service and published weekly in IERS Bulletin A along with predictions for a number of months into the future.

UT1 = UTC + DUT1 (from the IERS Bulletin A)Note that when a leap second is added to or subtracted from UTC, the value of DUT1 is discontinuous by one second. UT1 is continuous, and UTC is incremented or decremented by integer seconds to stay witin 0.7 seconds of UT1.

From ref [7]

UT0 = UT1 + tan(lat) * (x * sin(long) + y * cos(long))where

UT2 = UT1 + 0.022 * sin(2 * Pi * t) - 0.012 * cos(2 * Pi * t) - 0.006 * sin(4 * Pi * t) + 0.007 * cos(4 * Pi * t)where

t = 2000.0 + (MJD - 51544.03) / 365.2422is the Besselian day fraction, and MJD is the Modified Julian Date (Julian Date - 2400000.5). See ref [6] and the Explanatory Supplement to IERS Bulletins A and B.

By convention, the reference points for Greenwich Sidereal Time are the Greenwich Meridian and the vernal equinox (the intersection of the planes of the earth's equator and the earth's orbit, the ecliptic). The Greenwich sidereal day begins when the vernal equinox is on the Greenwich Meridian. Greenwich Mean Sidereal Time (GMST) is the hour angle of the average position of the vernal equinox, neglecting short term motions of the equinox due to nutation.

In conformance with IAU conventions for the motion of the earth's equator and equinox [ref 7] GMST is linked directly to UT1 through the equation

GMST (in seconds at UT1=0) = 24110.54841 + 8640184.812866 * T + 0.093104 * T^2 - 0.0000062 * T^3where

T = d / 36525 d = JD - 2451545.0It might seem strange that UT1, a solar time, is determined by measuring the earth's rotation with respect to distant celestial objects, and GMST, a sidereal time, is derived from it. This oddity is mainly due our choice of solar time in defining the atomic time second. Hence, small variations of the earth's rotation are more easily published as (UT1 - Atomic Time) differences. In practice, of course, some form of sidereal time is involved in measuring UT1.

GAST = GMST + (equation of the equinoxes)

LMST = GMST + (observer's east longitude)

Hour Angle = LST - Right Ascensionwhere the right ascension can be specified in one of the catalog coordinate systems B1950 (FK4) or J2000 (FK5), for example. In practice, LST is used more loosely to mean either LMST or "Local Apparent Sidereal Time" = GAST + (equation of the equinoxes). The operational definition probably varies from one observatory to the next.

Last updated January, 30, 1996, Rick Fisher (NRAO).

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