USNO Circular 179 - U.S. Naval Observatory

Chapter 2
Time Scales
Relevant IAU resolutions: A4.III, A4.IV, A4.V, A4.VI of 1991; C7 of 1994; B1.3, B1.5, B1.7, B1.8,
B1.9, and B2 of 2000
Summary The IAU has not established any new time scales since 1991, but more
recent IAU resolutions have redefined or clarified those already in use, with no loss of
continuity. There are two classes of time scales used in astronomy, one based on the
SI (atomic) second, the other based on the rotation of the Earth. The SI second has
a simple definition that allows it to be used (in practice or in theory) in any reference
system. Time scales based on the SI second include TAI and TT for practical applications,
and TCG and TCB for theoretical developments. The latter are to be used
for relativistically correct dynamical theories in the geocentric and barycentric reference
systems, respectively. Closely related to these are two time scales, TDB and Teph,
used in the current generation of ephemerides. Time scales based on the rotation of
the Earth include mean and apparent sidereal time and UT1. Because of irregularities
in the Earth’s rotation, and its tidal deceleration, Earth-rotation-based time scales do
not advance at a uniform rate, and they increasingly lag behind the SI-second-based
time scales. UT1 is now defined to be a linear function of a quantity called the Earth
Rotation Angle, θ. In the formula for mean sidereal time, θ now constitutes the “fast
term”. The widely disseminated time scale UTC is a hybrid: it advances by SI seconds
but is subject to one-second corrections (leap seconds) to keep it within 0. s 9 of UT1.
That procedure is now the subject of debate and there is a movement to eliminate leap
seconds from UTC.
2.1 Different Flavors of Time
The phrase time scale is used quite freely in astronomical contexts, but there is sufficient confusion
surrounding astronomical times scales that it is worthwhile revisiting the basic concept. A time scale
is simply a well defined way of measuring time based on a specific periodic natural phenomenon.
The definition of a time scale must provide a description of the phenomenon to be used (what
defines a period, and under what conditions), the rate of advance (how many time units correspond
to the natural period), and an initial epoch (the time reading at some identifiable event). For
example, we could define a time scale where the swing of a certain kind of pendulum, in vacuum at
sea level, defines one second, and where the time 00:00:00 corresponds to the transit of a specified
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