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<H2><A NAME="SECTION0004150000000000000000">SLA_RCC - Barycentric Coordinate Time</A>
<A NAME="xref_SLA_RCC"> </A><A NAME="SLA_RCC"> </A>
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<DL>
<DT><STRONG>CALL:</STRONG>
<DD><TT>D = sla_RCC (TDB, UT1, WL, U, V)</TT>
<DT><STRONG>ACTION:</STRONG>
<DD>The relativistic clock correction TDB-TT, the
difference between <I>proper time</I>
on Earth and <I>coordinate time</I> in the solar system barycentric
space-time frame of reference. The proper time is TT; the
coordinate time is <I>an implementation</I> of TDB.
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TDB</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>coordinate time (MJD: JD-2400000.5)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>UT1</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>universal time (fraction of one day)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>WL</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>clock longitude (radians west)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>U</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>clock distance from Earth spin axis (km)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>clock distance north of Earth equatorial plane (km)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>sla_RCC</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>TDB-TT (sec)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>TDB may be considered to
be the coordinate time in the solar system barycentre frame of
reference, and TT is the proper time given by clocks at mean sea
level on the Earth.
<DT>2.
<DD>The result has a main (annual) sinusoidal term of amplitude
approximately 1.66ms, plus planetary terms up to about
20<IMG WIDTH="12" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img146.gif"
ALT="$\mu$">s, and lunar and diurnal terms up to 2<IMG WIDTH="12" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img146.gif"
ALT="$\mu$">s. The
variation arises from the transverse Doppler effect and the
gravitational red-shift as the observer varies in speed and
moves through different gravitational potentials.
<DT>3.
<DD>The argument TDB is, strictly, the barycentric coordinate time;
however, the terrestrial proper time (TT) can in practice be used.
<DT>4.
<DD>The geocentric model is that of Fairhead & Bretagnon (1990),
in its full
form. It was supplied by Fairhead (private communication)
as a Fortran subroutine. A number of coding changes were made to
this subroutine in order
match the calling sequence of previous versions of the present
routine, to comply with Starlink programming standards and to
avoid compilation problems on certain machines. On the supported
computer types,
the numerical results are essentially unaffected by the
changes. The topocentric model is from Moyer (1981) and Murray (1983).
During the interval 1950-2050, the absolute accuracy of the
geocentric model is better than <IMG WIDTH="23" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img147.gif"
ALT="$\pm3$"> nanoseconds
relative to direct numerical integrations using the JPL DE200/LE200
solar system ephemeris.
<DT>5.
<DD>The IAU definition of TDB is that it must differ from TT only by
periodic terms. Though practical, this is an imprecise definition
which ignores the existence of very long-period and secular effects
in the dynamics of the solar system. As a consequence, different
implementations of TDB will, in general, differ in zero-point and
will drift linearly relative to one other.
</DL></DL>
<P> <DL>
<DT><STRONG>REFERENCES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Fairhead, L. &
Bretagnon, P., 1990. <I>Astr.Astrophys.</I> <B>229</B>, 240-247.
<DT>2.
<DD>Moyer, T.D., 1981. <I>Cel.Mech.</I> <B>23</B>, 33.
<DT>3.
<DD>Murray, C.A., 1983, <I>Vectorial Astrometry</I>, Adam Hilger.
</DL></DL>
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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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