Dynamical time
 
Both mean solar time and sidereal time are based on the rotation of the Earth on its axis. Until comparatively recently, it was thought that, apart from a slow secular increase in the rotation period due to tidal friction, the Earth’s period of rotation was constant. Tidal friction, due to the Moon’s gravitational effect, acts as a break on the Earth’s rotation.
The development and use of very accurate clocks revealed that other variations occur in the period of the Earth’s rotation. These small changes in general take place abruptly and are not predictable. Since UT is based on observations of the transits of celestial objects made from the irregularly rotating Earth, it must differ from a theoretical time that flows on uniformly. This time is the Newtonian time of celestial mechanics, that branch of astronomy which deals with and predicts the movements of the Sun, Moon and planets. Hence, their positions as published in ephemerides (tables of predicted positions) based on celestial mechanics theories are bound to Terrestrial Dynamical Time, this replacing Ephemeris Time in 1984.
The value of (Terrestrial) Dynamical Time at a given instant is obtained by very accurate observations of abrupt variations in the longitudes of the Sun, Moon and planets due to corresponding variations in the Earth’s rate of rotation. It is estimated that to define Dynamical Time correctly to one part in 1010 , observations of the Moon are required over five years. In practice, laboratory atomic clocks may be used to give approximate values of Dynamical Time, their readings being subsequently

Figure 1. The geographical zones.
corrected by long series of astronomical observations. The quantity that is in fact determined is T , where
ΔT = Dynamical Time − Universal Time.
This quantity is tabulated in The Astronomical Almanac. At present (2000) its value is about 66^s, increasing at about 1 second per year. The relationship between Dynamical Time and International Atomic Time (TAI), based on careful analysis of atomic processes, is, for practical purposes, taken to be
TDT = TAI + 32·^s184.
International Atomic Time (TAI) is the most precisely determined time scale available for astronomical use. TAI has the SI second as its fundamental unit. It is defined as the duration of 9 192 631 770 cycles of the radiation from the transition between two hyperfine levels in the ground state of caesium (¹³³Cs). There are 86 400 SI seconds in the mean solar day.