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<H3><A NAME="SECTION000515400000000000000">
Dynamical Time: TT, TDB</A>
</H3>
Dynamical time is the independent variable in the theories
which describe the motions of bodies in the solar system. When
you use published formulae which model the position of the
Earth in its orbit, for example, or look up
the Moon's position in a precomputed ephemeris, the date and time
you use must be in terms of one of the dynamical timescales. It
is a common but understandable mistake to use UT directly, in which
case the results will be about 1 minute out (in the present
era).
<P>
It is not hard to see why such timescales 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 eventually
the ephemeris and the ensemble of atomic clocks would drift apart.
In effect, the ephemeris <I>is</I> a clock, with the bodies of
the solar system the hands.
<P>
Only two of the dynamical timescales are of any great importance to
observational astronomers, TT and TDB. (The obsolete
timescale ET, ephemeris time, was more or less the same as TT.)
<P><I>Terrestrial Time</I> TT is
the theoretical timescale of apparent geocentric ephemerides of solar
system bodies. It applies, in principle,
to an Earthbound clock, at sea-level, and for practical purposes
it is tied to
Atomic Time TAI through the formula TT = TAI + <IMG WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img311.gif"
ALT="$32^{\rm s}\hspace{-0.3em}.184$">.In practice, therefore, the units of TT are ordinary SI seconds, and
the offset of <IMG WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img311.gif"
ALT="$32^{\rm s}\hspace{-0.3em}.184$"> with respect to TAI is fixed.
The SLALIB routine
sla_DTT
returns TT-UTC for a given UTC
(<I>n.b.</I> sla_DTT
calls
sla_DAT,
and the latter must be an up-to-date version if recent leap seconds are
to be taken into account).
<P><I>Barycentric Dynamical Time</I> TDB differs from TT by an amount which
cycles back and forth by a millisecond or two due to
relativistic effects. The variation is
negligible for most purposes, but unless taken into
account would swamp
long-term analysis of pulse arrival times from the
millisecond pulsars. It is a consequence of
the TT clock being on the Earth rather than in empty
space: the ellipticity of
the Earth's orbit means that 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. By definition, TDB and TT differ only
by periodic terms, and the main effect
is a sinusoidal variation of amplitude <IMG WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img312.gif"
ALT="$0^{\rm s}\hspace{-0.3em}.0016$">; the
largest planetary terms are nearly two orders of magnitude
smaller. The SLALIB routine
sla_RCC
provides a model of
TDB-TT accurate to a few nanoseconds.
There are other dynamical timescales, not supported by
SLALIB routines, which include allowance also for the secular terms.
These timescales gain on TT and TDB by about <IMG WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img313.gif"
ALT="$0^{\rm s}\hspace{-0.3em}.0013$">/day.
<P>
For most purposes the more accessible TT is the timescale to use,
for example when calling
sla_PRENUT
to generate a precession/nutation matrix or when calling
sla_EVP
to predict the
Earth's position and velocity. For some purposes TDB is the
correct timescale, for example when interrogating the JPL planetary
ephemeris (see <I>Starlink User Note 87</I>), though in most cases
TT will be near enough and will involve less computation.
<P>
Investigations of topocentric solar-system phenomena such as
occultations and eclipses require solar time 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 <IMG WIDTH="117" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img314.gif"
ALT="$\Delta {\rm T} = {\rm ET} - {\rm UT}$"> is
available via the routine
sla_DT.
For a given epoch (<I>e.g.</I> 1650) this returns an approximation
to <IMG WIDTH="28" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img315.gif"
ALT="$\Delta {\rm T}$"> in seconds.
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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