Dynamical Time: TT, TDB

From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node221.html | 158 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 158 insertions(+) create mode 100644 src/slalib/sun67.htx/node221.html (limited to 'src/slalib/sun67.htx/node221.html') diff --git a/src/slalib/sun67.htx/node221.html b/src/slalib/sun67.htx/node221.html new file mode 100644 index 0000000..926f2ce --- /dev/null +++ b/src/slalib/sun67.htx/node221.html @@ -0,0 +1,158 @@ + + + + +Dynamical Time: TT, TDB + + + + + + + + + + + +

+ +

+
+ Next: Calendars +
+Up: Timescales +
+ Previous: Sidereal Time: GMST, LAST +

+Dynamical Time: TT, TDB +

+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). +

+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 is a clock, with the bodies of +the solar system the hands. +

+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.) +

Terrestrial Time 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 + $32^{\rm s}\hspace{-0.3em}.184$ .In practice, therefore, the units of TT are ordinary SI seconds, and +the offset of $32^{\rm s}\hspace{-0.3em}.184$ with respect to TAI is fixed. +The SLALIB routine +sla_DTT +returns TT-UTC for a given UTC +(n.b. 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). +

Barycentric Dynamical Time 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 $0^{\rm s}\hspace{-0.3em}.0016$ ; 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 $0^{\rm s}\hspace{-0.3em}.0013$ /day. +

+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 Starlink User Note 87), though in most cases +TT will be near enough and will involve less computation. +

+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 $\Delta {\rm T} = {\rm ET} - {\rm UT}$ is +available via the routine +sla_DT. +For a given epoch (e.g. 1650) this returns an approximation +to $\Delta {\rm T}$ in seconds. +

+ +

+
+ Next: Calendars +
+Up: Timescales +
+ Previous: Sidereal Time: GMST, LAST +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit