Oral, Tuesday, May 6, 2003, 8:30-10:50am,

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*T. Fukushima (NAOJ)*

We adapted J.G. Williams' expression of the precession and
nutation by the 3-1-3-1 rotation (Williams 1994) to an
arbitrary inertial frame of reference. The new expression of
the precession matrix is P = R_{1}(-\epsilon) R_{3}(-\psi)
R_{1}(\varphi) R_{3}(\gamma) while that of precession-nutation
matrix is NP = R_{1}(-\epsilon-\Delta \epsilon)
R_{3}(-\psi-\Delta \psi) R_{1}(\varphi) R_{3}(\gamma). Here
\gamma and \varphi are the new planetary precession
angles, \psi and \epsilon are the new luni-solar
precession angles, and \Delta \psi and \Delta \epsilon
are the usual nutations. The modified formulation avoids a
singularity caused by finite pole offsets near the epoch. By
adopting the latest planetary precession formula determined
from DE405 (Harada 2003) and by using a recent theory of the
forced nutation of the non-rigid Earth, SF2001 (Shirai and
Fukushima 2001), we analysed the celestial pole offsets
observed by VLBI for 1979-2000 and compiled by USNO and
determined the best-fit polynomials of the new luni-solar
precession angles. Then we translated the results into the
classic precessional quantities as \sin \pi_{A} \sin \Pi_{A},
\sin \pi_{A} \cos \Pi_{A}, \pi_{A}, \Pi_{A}, p_{A}, \psi_{A}, \omega_{A},
\chi_{A}, \zeta_{A}, z_{A}, and \theta_{A}. Also we evaluated the
effect of the difference in the ecliptic definition between
the inertial and rotational senses. The combination of these
formulas and the periodic part of SF2001 serves as a good
approximation of the precession-nutation matrix in the ICRF.
As a by-product, we determined the mean celestial pole
offset at J2000.0 as X_{0} = -(17.12 ±0.01) mas and Y_{0}
= -(5.06 ±0.02) mas. Also we estimated the speed of
general precession in longitude at J2000.0 as p =
(5028.7955 ±0.0003)''/Julian century, the mean obliquity
at J2000.0 in the rotational sense as \epsilon_{0} =
(84381.40955 ±0.00001)'', and the dynamical flattening
of the Earth as H_{d} = (0.0032737804 ±0.0000000003).
Further, we established a fast way to compute the
precession-nutation matrix and provided a best-fit
polynomial of s, an angle to specify the mean CEO.

The author(s) of this abstract have provided an email address for comments about the abstract: Toshio.Fukushima@nao.ac.jp

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.