It is not hard to see why such time scales are necessary.
UTC would clearly be unsuitable as the argument of an
ephemeris because of leap seconds.
A solar-system ephemeris based on UT1 or sidereal time would somehow
have to include the unpredictable variations of the Earth's rotation.
TAI would work, but in principle
the ephemeris and the ensemble of atomic clocks would
eventually drift apart.
In effect, the ephemeris *is* a clock, with the bodies of
the solar system the hands from which the ephemeris time is read.

Only two of the dynamical time scales are of any great importance to observational astronomers, TT and TDB.

*Terrestrial Time,* TT, is
the theoretical time scale of apparent geocentric ephemerides of solar
system bodies. It applies to clocks at sea-level, and for practical purposes
it is tied to
Atomic Time TAI through the formula TT TAI
.
In practice, therefore, the units of TT are ordinary SI seconds, and
the offset of
with respect to TAI is fixed.
The SLALIB function
sla_DTT
returns TTUTC for a given UTC
(*n.b.* sla_DTT
calls
sla_DTT,
and the latter must be an up-to-date version if recent leap seconds are
to be taken into account).

*Barycentric Dynamical Time,* TDB, is a
*coordinate time,* suitable
for labelling events that are most simply described in a context
where the bodies of the solar system
are absent. Applications include
the emission of pulsar radiation and the motions of the
solar-system bodies themselves. When the readings of the
observer's TT clock are labelled using such a
coordinate time, differences
are seen because the clock is affected by its
speed in the barycentric coordinate system
and the gravitational potential in which it is immersed. Equivalently,
observations of pulsars
expressed in TT would display similar variations (quite
apart from the familiar light-time effects).

TDB is defined in such a way that it keeps close to TT on the average, with the relativistic effects emerging as quasi-periodic differences of maximum amplitude rather less than 2ms. This is negligible for many purposes, so that TT can act as a perfectly adequate surrogate for TDB in most cases, but unless taken into account would swamp long-term analysis of pulse arrival times from the millisecond pulsars.

Most of the variation between TDB and TT comes from the ellipticity of the Earth's orbit; the TT clock's speed and gravitational potential vary slightly during the course of the year, and as a consequence its rate as seen from an outside observer varies due to transverse Doppler effect and gravitational redshift. The main component is a sinusoidal variation of amplitude ; higher harmonics, and terms caused by Moon and planets, lie two orders of magnitude below this dominant annual term. Diurnal (topocentric) terms, a function of UT, are s or less.

The IAU 1976 resolution defined TDB by stipulating that TDBTT consists of periodic terms only. This provided a good qualitative description, but turned out to contain hidden assumptions about the form of the solar-system ephemeris and hence lacked dynamical rigour. A later resolution, in 1991, introduced new coordinate time scales, TCG and TCB, and identified TDB as a linear transformation of one of them (TCB) with a rate chosen not to drift from TT on the average. Unfortunately even this improved definition has proved to contin ambiguities. The SLALIB sla_RCC function implements TDB in the way that is most consistent with the 1976 definition and with existing practice. It provides a model of TDBTT accurate to a few nanoseconds.

Unlike TDB, the IAU 1991 coordinate time scales TCG and TCB (not supported by SLALIB functions at present) do not have their rates adjusted to track TT and consequently gain on TT and TDB, by about /year and /year respectively.

As already pointed out, the distinction between TT and TDB is of no practical importance for most purposes. For example when calling sla_PRENUT to generate a precession-nutation matrix, or when calling sla_EVP or sla_EPV to predict the Earth's position and velocity, the time argument is strictly TDB, but TT is entirely adequate and will require much less computation.

The time scale used by the JPL solar-system ephemerides is called and is numerically the same as TDB.

Predictions of topocentric solar-system phenomena such as
occultations and eclipses require solar time UT as well as dynamical
time. TT/TDB/ET is all that is required in order to compute the geocentric
circumstances, but if horizon coordinates or geocentric parallax
are to be tackled UT is also needed. A rough estimate
of
is
available via the function
sla_DT.
For a given epoch (*e.g.* 1650) this returns an approximation
to
in seconds.

Starlink User Note 67

P. T. Wallace

19 December 2005

E-mail:starlink@jiscmail.ac.uk

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