\documentstyle{article}

\title{The need and opportunity to develop more accurate 4000-year ephemerides,
using lunar and spacecraft ranging and ancient eclipse and planetary data$^*$}
\author{Kevin D. Pang, Kevin K.C. Yau \\
Jet Propulsion Laboratory\\
M/S 230-101, 4800 Oak Grove Dr., Pasadena, California 91109 USA\\
\and Hung-hsiang Chou\\
East Asian Languages and Cultures\\
University of California, Los Angeles, Calif. 90024 USA}
\date{}

\begin{document}
\maketitle

The initial conditions of the JPL DE102, BDL VSOP and ELP2000 ephemerides were
based on observations up tp 1977. Much more tracking data have been collected
since. Lunar laser ranging has also given an accurate $\dot n_{moon}$ of $-25.9
\pm 0.5^{"}/cen^2$ (EOS {\bf 73}, No43, 126). The lack of $\Delta T$ values
before 700 BC had left the early timescale of the ephemerides unconstrained
(Morrison, {\it Observ.{\bf 112}, 289}). We summarize our effort to solve this
problem here.

Since $\Delta T = ct^2$ (t is cen before 1800) the oldest data have the most
weight. The {\it Bamboo Annals}, entombed in 299 BC and unearthed in AD 281,
states that "in the 1st year of King Yi of the W Zhou dynasty the day dawned
twice at Zheng ($34.5^{\circ}N, 109.8^{\circ}E$)." {\it Kayuan zhanjing} [AD
724] adds that "in the 2nd (actually 12th) year of Sheng Ping reign period of
King Shang (actually King Xi) the day began twice at Zheng." Matching these
records with the 4/21/899 BC and 4/4AD 368 sunrise eclipses gives $\Delta T$
values of$5.8\pm 0.15$ and $1.7\pm 0.1$ hr [{\it Vistas Astron.}{\bf 31}, 833;
{\it EOS} {\bf 73}, No 43,62]. Analysis of Shang dynasty oracle bone eclipse
records gives $\Delta T$ values of 7.3-7.2 hrfor 14-12 th cen BC [{\it Bull. Am.
Astron. Soc.} {\bf 21}, 753; {\it EOS} {\bf 71}, No43, 1269]. Our best-fit
equation is $\Delta T = ( 30 \pm 2.5 ) t^2$.

From this we get an $\dot{\omega}/\omega$ of $-(19\pm1.6).10^{-11}/yr$.
Substracting a tidal $\dot{\omega}/\omega$ of $-(27.8).10^{-11}/yr$
[Lambeck, 1980] gives a nontidal $\dot{\omega}/\omega$ of
$(9\pm1.6).10^{-11}/yr$ [$J_2$ of $-(4.5 \pm 0.8).10^{-11}/yr$]. The historical
and present $J_2$ from satellite laser ranging, $-3.10^{-11}/yr$ are consistent
with postglacial rebound from an upper mantle of viscosity $10^{21}Pa s$, and
lower mantle of $(2-4).10^{21}Pa s$, deformed by Pleistocene ice sheet loading.
The bounceback to  its less oblate interglacial shape makes the Earth spin
faster, overcomming a third of tidal bracking. The net effect has been
lengthening the day by $1.64 \pm 0.14 msec/cen$. Successful matching of Chinese
records with the 9/24/1912 BC sunset eclipse, and late 3rd millenium BC lunar
eclipses wuth Babylonian cuneiform tablets, shows that our model holds back to
then [{\it Eos} {\bf 75}, No. 44, 75]. We conclude that conditions are ripe for
producing more accurate 4000-year ephemerides, which would be og great value to
the analysis of ancient astronomical records. 


*We thank J. Bangert. 





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