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\write 0 {4.  NUMERICAL STANDARDS \noexpand\dotfill
\the\pageno\noexpand\break}
\noindent {\large CHAPTER 4} {\bf NUMERICAL STANDARDS}
\bigskip

     Table 4.1 listing numerical standards is organized into 5
columns:  item, value, uncertainty, reference, comment.  All
values are given in terms of SI units ({\it Le Syst\`eme International
d'Unit\'es (SI)}, 1991).  The SI second, the basic unit of the TT
time scale, is specifically assumed.  If the TDB time scale is used, 
new units of time, $t_{TDB}$, and length, $\ell_{TDB}$, are implicitly
defined by the expressions (Seidelmann and Fukushima, 1992)

$$t_{TDB} = t/(1-L_B), {\rm and}$$
$$\ell _{TDB} = \ell /(1-L_B),$$
                                    
\noindent where t and $\ell$ are the SI units and $L_B$ is a 
derived constant given in Table 4.1.  Chapter 11 provides 
further details on the transformations between time scales. 

     The 1976 IAU System of Astronomical Constants ({\it Astronomical
Almanac for the Year 1984}) is adopted for all astronomical constants 
which do not appear in Table 4.1.


\noindent {\bf References}

\item{[8]}
{\it Astronomical Almanac for the Year 1984}, U.S. Government
     Printing Office, Washington, DC.

\item{[1]}
Bur\v sa, M., 1995, Report of the I.A.G. Special Commission SC3,
     Fundamental Constants, XXI, I.A.G. General Assembly.

\item{[2]}
Cohen, E. R. and Taylor, B. N., 1973, {\it J. Phys. Chem. Ref.
     Data}, {\bf 2}, p. 663.

\item{[3]}
Cohen, E. R. and Taylor, B. N., 1986, ``The 1986 Adjustment of
     the Fundamental Physical Constants,"  CODATA Bulletin, Bureau
     International des Poids et Mesures.

\item{[4]}
Fukushima, T., 1994, ``Time Ephemeris," {\it Astron. Astrophys.},
     {\bf 294}, pp. 895--906.

\item{[5]}
Herring, T., 1996, ``KSV\_1996\_3 Precession/Nutation," personal 
     communication.

\item{}\kern-2pc
{\it Le Syst\`eme International d'Unit\'es (SI)}, 1991, Bureau 
     International des Poids et Mesures, S\`evres, France.

\item{}\kern-2pc
Seidelmann, P. K. and Fukushima, T., 1992, ``Why New Time Scales?"
     {\it Astron. Astrophys.}, {\bf 265}, pp. 833--838.

\item{[6]}
Standish, E. M., 1994, Report of the IAU WGAS Sub-group on Numerical
     Standards.

\item{[7]}
Standish, E. M., Newhall, X X, Williams, J. G., and Folkner, W. F., 
     1995 ``JPL Planetary and Lunar Ephemerides, DE403/LE403," JPL IOM 
     314.10--127 to be submitted to {\it Astron. Astrophys.}

\vfil\eject

\noindent Table 4.1.  IERS Numerical Standards.
\hrule
\smallskip
\halign{#\hfil&\kern.4pc#\hfil&\kern.4pc#\hfil&\kern.3pc\hfil#\hfil&\kern.4pc#\hfil\cr
ITEM&VALUE&UNCERTAINTY&REF.&COMMENTS\cr
$c$&$299 792 458 ms^{-1}$&Defining&[2]&Speed of light\cr
$L_B$&$1.550 519 748\times 10^{-8}$&$4\times 10^{-17}$&[4]&Average value of\cr
&&&&d(TCB)/d(TT)-1\cr
$L_C$&$1.480 826 845 7\times 10^{-8}$&$1\times 10^{-17}$&[4]&Average value of\cr
&&&&d(TCB)/d(TCG)-1\cr
$L_G$&$6.969 290 23\times 10^{-10}$&$1\times 10^{-17}$&[1]&Average value of\cr
&&&&d(TCG)/d(TT)-1\cr
$W_0$&$626 368 56.85 m^2s^{-2}$&$1.0 m^2s^{-2}$&[1]&Potential of the geoid\cr
$\tau_A$&$499.004 783 8061s$&$ 0.000 000 02 s$&[7]&Astronomical unit in seconds\cr
$c\tau_A$&$149 597 870 691 m$&$30 m$&[7]&Astronomical unit in meters\cr
$P$&$5 029\qd096 6 /century$&$0\qd3 /century$&[8]&General precession in\cr
&&&&longitude at J2000.0\cr
$\epsilon_0$&$84 381\qd412$&$0\qd005$&[7]&Obliquity of the ecliptic\cr
&&&&at J2000.0\cr
$a_E$&$6 378 136.49 m$&$0.10 m$&[1]&Equatorial radius of the Earth\cr
$1/f$&$298.256 42$&$0.00001$&[1]&Flattening factor of the Earth\cr
$J_{2\oplus}$&$1.082 635 9\times 10^{-3}$&$ 1.0\times 10^{-10}$&[1]&Dynamical form-factor\cr
&&&&of the Earth\cr
$G$&$6.672 59\times 10^{-11} m^3kg^{-1}s^{-2}$&$8.54\times 10^{-15} m^3kg^{-1}s^{-2}$&[3]&Constant of gravitation\cr
$GM_\oplus$&$3.986 004 418\times 10^{14} m^3s^{-2}$&$ 8\times 10^5 m^3s^{-2}$&[1]&Geocentric gravitational\cr
&&&&constant\cr
$\mu$&$0.0123 000 345$&$5\times 10^{-10}$&[7]&Moon-Earth mass ratio\cr
$\omega$&$7.292 115\times 10^{-5} rad s^{-1}$&variable&[1]& Nominal mean angular\cr
&&&&velocity of the Earth\cr
$GM_\odot$&$1.327 124\times 10^{20} m^3s^{-2}$&&[6]&Heliocentric gravitational\cr
&&&&constant\cr
$g_e$&$9.78 0327 ms^{-2}$&$1\times 10^{-6} ms^{-2}$&[1]&Mean equatorial gravity\cr
$R_0=GM_\oplus/W_0$&$6 363 672.461 m$&$0.1 m$&[1]&Geopotential scale factor\cr}
\hrule
 
     Some geodetic parameters are affected by tidal variations (see
Chapter 3).  The values given in Table 4.1 are in the zero-tide system
so that they correspond to a realistic time-averaged crust.  This is 
done to be consistent with XVIII IAG General Assembly Resolution 16.  

\vfil\eject
