34th Meeting of the AAS Division on Dynamical Astronomy, May 2003
7 Space Missions, Astrometry, and Observables
Oral, Tuesday, May 6, 2003, 8:30-10:50am,

## [7.05] New Precession Formulas

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 = R1(-\epsilon) R3(-\psi) R1(\varphi) R3(\gamma) while that of precession-nutation matrix is NP = R1(-\epsilon-\Delta \epsilon) R3(-\psi-\Delta \psi) R1(\varphi) R3(\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 \piA \sin \PiA, \sin \piA \cos \PiA, \piA, \PiA, pA, \psiA, \omegaA, \chiA, \zetaA, zA, and \thetaA. 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 X0 = -(17.12 ±0.01) mas and Y0 = -(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 \epsilon0 = (84381.40955 ±0.00001)'', and the dynamical flattening of the Earth as Hd = (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.