AbstractRecent progress in the determinations of astronomical constants is reviewed. First is the latest estimation of the general relativistic scale constants,LC, LG, andLB(Irwin and Fukushima, 1999). By reestimating the uncertainty, the value of the first constant is given asLC= 1.480 826 867 4 × 10–8± 1.4 × 10–17. Also noted is the rigorous relation among these three,LB=LC+ LG– LCLG. Based on the latest determination of the geoidal potentialW0in the IAG 1999 Best Estimate of Geodetic

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... s (Groten, 1999),LGandLBwere reevaluated asLG= 6.969 290 09 × 10–10± 6 × 10–18andLB= 1.550 519 767 3 × 10–8± 2.0 × 10–17. SinceLGis roughly related toW0, a proposal to fix its numerical value is presented in order to remove the geophysical ambiguity in its evaluation in the future. In that case,LGbecomes a defining constant for the scale difference between the geocentric and terrestrial coordinate systems. WhileLCandLBremain as a primary and derived constant, respectively. Next is the correction to the current precession constant, Δp. The recent estimates of Δpbased on Very Long Baseline Interferometry (VLBI) observation seem to converge to a value close to –0.30″/cy (Mathewset al., 2000; Petrov, 2000; Shirai and Fukushima, 2000; Vondrák and Ron, 2000). Unfortunately this is significantly different from –0.34″/cy, the latest value determined from the Lunar Laser Ranging (LLR) data (Chaprontet al., 1999). The difference is roughly ten times larger than the sum of their formal uncertainties. Since the cause of this difference is not clear, we first arranged the best estimates based on VLBI and LLR techniques, respectively, then took a simple mean of these two best estimates, and recommend it as the current best estimate. The value derived isp= 5 028.78 ± 0.03 ″/cy. Similar estimates were given for some other quantities related to the precession formula; namely the correction to the obliquity rate of the IAU 1976 precession formula (Lieskeet al., 1977), Δε1= (–0.024 5 ± 0.002 5) ″/cy, and the offsets of the Celestial Ephemeris Pole of the International Celestial Reference System, Δψ0sinε0= (–17.5 ± 0.8) mas and Δε0= (–5.2 ± 0.4) mas. As a result, the obliquity of the ecliptic at the epoch J2000.0 was estimated asε0= 23°26′21.″405 6 ± 0.″000 5. The draft IAU 2000 File of Current Best Estimates of astronomical constants, that is to replace the 1994 version (Standish, 1995) or maybe even the formal IAU 1976 System of Astronomical Constants (Duncombeet al., 1977), after discussion at the 24th General Assembly of the IAU is presented.