USNO Circular 179 - U.S. Naval Observatory

10 TIME SCALES
were computed in a barycentric reference system and are distributed with the independent argument
being a coordinate time scale called Teph (Chapter 4 describes the JPL ephemerides). Teph differs
in rate from that of TCB, the IAU recommended time scale for barycentric developments; the rate
of Teph matches that of TT, on average, over the time span of the ephemerides. One may treat
Teph as functionally equivalent to Barycentric Dynamical Time (TDB), defined by the IAU in 1976
and 1979. Both are meant to be “time scales for equations of motion referred to the barycenter of
the solar system” yet (loosely speaking) match TT in average rate. The original IAU definition of
TDB specified that “there be only periodic variations” with respect to what we now call TT (the
largest variation is 0.0016 s with a period of one year). It is now clear that this condition cannot be
rigorously fulfilled in practice; see Standish (1998a) for a discussion of the issue and the distinction
between TDB and Teph. Nevertheless, space coordinates obtained from the JPL ephemerides are
consistent with TDB, and it has been said that “Teph is what TDB was meant to be.” Therefore,
barycentric and heliocentric data derived from the JPL ephemerides are often tabulated with TDB
shown as the time argument (as in The Astronomical Almanac), and TDB is the specified time
argument for many of the equations presented in this circular. 2 Because Teph (≈TDB) is not based
on the SI second, as is TCB, the values of parameters determined from or consistent with the JPL
ephemerides will, in general, require scaling to convert them to SI-based units. This includes the
length of the astronomical unit. Dimensionless quantities such as mass ratios are unaffected.
The problem of defining relativistic time scales in the solar system has been treated by Brumberg
& Kopeikin (1990); the paper is quite general but pre-dates the current terminology.
2.3 Time Scales Based on the Rotation of the Earth
Time scales that are based on the rotation of the Earth are also used in astronomical applications,
such as telescope pointing, that depend on the geographic location of the observer. Greenwich
sidereal time is the hour angle of the equinox measured with respect to the Greenwich meridian.
Local sidereal time is the local hour angle of the equinox, or the Greenwich sidereal time plus the
longitude (east positive) of the observer, expressed in time units. Sidereal time appears in two
forms, mean and apparent, depending on whether the mean or true equinox is the reference point.
The position of the mean equinox is affected only by precession while the true equinox is affected by
both precession and nutation. The difference between true and mean sidereal time is the equation
of the equinoxes, which is a complex periodic function with a maximum amplitude of about 1 s.
Of the two forms, apparent sidereal time is more relevant to actual observations, since it includes
the effect of nutation. Greenwich (or local) apparent sidereal time can be observationally obtained
from the right ascensions of celestial objects transiting the Greenwich (or local) meridian.
Universal Time (UT) is also widely used in astronomy, and now almost always refers to the
specific time scale UT1. Historically, Universal Time (formerly, Greenwich Mean Time) has been
obtained from Greenwich sidereal time using a standard expression. In 2000, the IAU redefined
UT1 to be a linear function of the Earth Rotation Angle, θ, which is the geocentric angle between
two directions in the equatorial plane called, respectively, the Celestial Intermediate Origin (CIO)
2 The IAU Working Group on Nomenclature for Fundamental Astronomy is considering a recommendation to
correct the definition of TDB so that a distinction between TDB and Teph would no longer be necessary; TDB would
be a linear function of TCB with a rate as close to that of TT as possible over the time span of the ephemeris to
which it applies.