# Time Reference Frames

CASA supported time reference frames

CASA supported time reference frames:

Acronym Name Description
ET Ephemeris Time  The time scale used prior to 1984 as the independent variable in gravitational theories of the solar system. In 1984, ET was replaced by dynamical time (see TDB, TT).
GAST Greenwich Apparent Sidereal Time  The Greenwich hour angle of the true equinox  of date.
GMST Greenwich Mean Sidereal Time

The Greenwich hour angle of the mean equinox  of date, defined as the angular distance on the celestial sphere measured westward along the celestial equator from the Greenwich meridian to the hour circle that passes through a celestial object or point.

GMST (in seconds at UT1=0) = 24110.54841 + 8640184.812866 * T
+ 0.093104 * T$^2$ - 0.0000062 * T$^3$
where T is in Julian centuries from 2000 Jan. 1 12h UT1:
T = d / 36525
d = JD - 2451545.0

GMST1    GMST calculated specifically with reference to UT1
IAT International Atomic Time (a.k.a. TAI en Francais):  The continuous time scale resulting from analysis by the Bureau International des Poids et Mesures of atomic time standards in many countries. The fundamental unit of TAI is the SI second  on the geoid  , and the epoch is 1958 January 1.
LAST Local Apparent Sidereal Time

LAST is derived from LMST by applying the equation of equinoxes  or nutation of the mean pole of the Earth from mean to true position yields LAST.

http://tycho.usno.navy.mil/sidereal.html

LMST Local Mean Sidereal Time

Sidereal time is the hour angle of the vernal equinox, the ascending node of the ecliptic on the celestial equator. The daily motion of this point provides a measure of the rotation of the Earth with respect to the stars, rather than the Sun. It corresponds to the coordinate right ascension of a celestial body that is presently on the local meridian.
LMST is computed from the current GMST plus the local offset in longitude measured positive to the east of Greenwich, (converted to a sidereal offset by the ratio 1.00273790935 of the mean solar day to the mean sidereal day.)
LMST = GMST + (observer's east longitude)

TAI International Atomic Time (a.k.a. TAI en Francais) see IAT
TCB Barycentric Coordinate Time  The coordinate time of the Barycentric Celestial Reference System (BCRS), which advances by SI seconds  within that system. TCB is related to TCG and TT by relativistic transformations that include a secular term.
TCG
TDB Barycentric Dynamical Time A time scale defined by the IAU (originally in 1976; named in 1979; revised in 2006) used in barycentric ephemerides and equations of motion. TDB is a linear function of TCB that on average tracks TT over long periods of time; differences between TDB and TT evaluated at the Earth's surface remain under 2 ms for several thousand years around the current epoch. TDB is functionally equivalent to Teph, the independent argument of the JPL planetary and lunar ephemerides DE405/LE405.
TDT Terrestrial Dynamical Time  The time scale for apparent geocentric ephemerides defined by a 1979 IAU resolution. In 1991 it was replaced by TT.
TT Terrestrial Time  An idealized form of International Atomic Time (TAI) with an epoch offset; in practice TT = TAI + 32s.184. TT thus advances by SI seconds on the geoid 
UT Universal Time  Loosely, mean solar time on the Greenwich meridian (previously referred to as Greenwich Mean Time). In current usage, UT refers either to UT1 or to UTC.
UT1    UT1 is formally defined by a mathematical expression that relates it to sidereal time. Thus, UT1 is observationally determined by the apparent diurnal motions of celestial bodies, and is affected by irregularities in the Earth's rate of rotation.
UT2

Before 1972 the time broadcast services kept their time signals within 0.1 seconds  of UT2, which is UT1 with annual and semiannual variations in the earth's rotation removed. The formal relation between UT1 and UT2 is

UT2 = UT1 + 0.022 * sin(2 * Pi * t) - 0.012 * cos(2 * Pi * t)

UTC Coordinated Universal Time UTC is based on IAT but is maintained within 0s.9 of UT1 by the introduction of leap seconds when necessary.
Footnote Number 1 mean equator and equinox v. true equator and equinox: The mean equator and equinox are used for the celestial coordinate system defined by the orientation of the Earth's equatorial plane on some specified date together with the direction of the dynamical equinox on that date, neglecting nutation. Thus, the mean equator and equinox moves in response only to precession. Positions in a star catalog have traditionally been referred to a catalog equator and equinox that approximate the mean equator and equinox of a standard epoch. The true equator and equinox are affected by both precession and nutation. The Equation of the Equinoxes is the difference (apparent sidereal time minus mean sidereal time). Equivalently, the difference between the right ascensions of the true and mean equinoxes, expressed in time units.
 FootnoteNumber 2 The Systeme International (SI) second is defined as the duration of 9,192,631,770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of caesium 133.
Footnote Number 3 The geoid is an equipotential surface that coincides with mean sea level in the open ocean. On land it is the level surface that would be assumed by water in an imaginary network of frictionless channels connected to the ocean.