# Systems of Time

*"Now let me see," the Golux said. "If you can touch the clocks and never start them, then you can start the clocks and never touch them. That's logic, as I know and use it...." *

-- James Thurber, "The 13 Clocks"

**Atomic Time**, with the unit of duration the*Systeme International (SI) second*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 cesium 133.**TAI**is the International Atomic Time scale, a statistical timescale based on a large number of atomic clocks.**Universal Time (UT)**is counted from 0 hours at midnight, with unit of duration the*mean solar day*, defined to be as uniform as possible despite variations in the rotation of the Earth.**UT0**is the rotational time of a particular place of observation. It is observed as the diurnal motion of stars or extraterrestrial radio sources.**UT1**is computed by correcting UT0 for the effect of polar motion on the longitude of the observing site. It varies from uniformity because of the irregularities in the Earth's rotation.

**Coordinated Universal Time (UTC)**differs from TAI by an integral number of seconds. UTC is kept within 0.9 seconds of UT1 by the introduction of one-second steps to UTC, the**"leap second."**To date these steps have always been positive. UTC has replaced Greenwich Mean Time (GMT) as an international standard.**Dynamical Time**replaced*ephemeris time*as the independent argument in dynamical theories and ephemerides. Its unit of duration is based on the orbital motions of the Earth, Moon, and planets.**Terrestrial Time (TT)**, (or Terrestrial Dynamical Time,**TDT**), with unit of duration 86400 SI seconds on the geoid, is the independent argument of apparent*geocentric*ephemerides. TDT = TAI + 32.184 seconds.**Barycentric Dynamical Time (TDB)**, is the independent argument of ephemerides and dynamical theories that are referred to the*solar system barycenter*. TDB varies from TT only by periodic variations.

**Geocentric Coordinate Time (TCG)**is a*coordinate time*having its spatial origin at the center of mass of the Earth. TCG differs from TT as: TCG - TT = Lg x (JD -2443144.5) x 86400 seconds, with Lg = 6.969291e-10.**Barycentric Coordinate Time (TCB)**is a*coordinate time*having its spatial origin at the solar system barycenter. TCB differs from TDB in rate. The two are related by: TCB - TDB = iLb x (JD -2443144.5) x 86400 seconds, with Lb = 1.550505e-08.**Sidereal Time**, with unit of duration the period of the Earth's rotation with respect to a point nearly fixed with respect to the stars, is the*hour angle of the vernal equinox*.

**Delta T** is the difference between Earth rotational time (UT1) and dynamical time (TDT). Predicted values of **UT1 - UTC **are provided as an **Earth Orientation Product**. An example showing the variation of the length of the day to late 2008 is shown below. Units are milliseconds.

**Julian Day Number** is a count of days elapsed since Greenwich mean noon on 1 January 4713 B.C., Julian proleptic calendar. The **Julian Date** is the Julian day number followed by the fraction of the day elapsed *since the preceding noon*.

We frequently make use of the **Modified Julian Date (MJD)**, which is defined as MJD = JD - 2400000.5. An MJD day thus begins and ends at midnight. Julian dates can be expressed in UT, TAI, TDT, etc. and so for precise applications the timescale should be specified, *e.g.* MJD 49135.3824 TAI.

To see the current MJD, click this link: MJD