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| author | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
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| committer | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
| commit | d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch) | |
| tree | afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node221.html | |
| download | calfuse-d54fe7c1f704a63824c5bfa0ece65245572e9b27.tar.gz | |
Initial commit
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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 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) + by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds +* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan +* with significant contributions from: + Jens Lippman, Marek Rouchal, Martin Wilck and others --> +<HTML> +<HEAD> +<TITLE>Dynamical Time: TT, TDB</TITLE> +<META NAME="description" CONTENT="Dynamical Time: TT, TDB"> +<META NAME="keywords" CONTENT="sun67"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"> +<LINK REL="STYLESHEET" HREF="sun67.css"> +<LINK REL="previous" HREF="node220.html"> +<LINK REL="up" HREF="node217.html"> +<LINK REL="next" HREF="node222.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2663" HREF="node222.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2661" HREF="node217.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2657" HREF="node220.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2664" HREF="node222.html">Calendars</A> +<BR> +<B>Up:</B> <A NAME="tex2html2662" HREF="node217.html">Timescales</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2658" HREF="node220.html">Sidereal Time: GMST, LAST</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<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. +<P> +<BR> <HR> +<A NAME="tex2html2663" HREF="node222.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2661" HREF="node217.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2657" HREF="node220.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2664" HREF="node222.html">Calendars</A> +<BR> +<B>Up:</B> <A NAME="tex2html2662" HREF="node217.html">Timescales</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2658" HREF="node220.html">Sidereal Time: GMST, LAST</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<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> +</ADDRESS> +</BODY> +</HTML> |