Meeting Mathematics of Gravitation II
Warsaw, September 1 – 10, 2003
Toruñ
Radio Astronomy Observatory
Centre
for Astronomy
Nicolaus Copernicus University
Toruñ, Poland
• On the new paradigm officially implemented in astronomy and space geodesy since 2003
• Two programs developed independently, by Pia Astone and myself, for the purpose of referring the data to an inertial frame
• Comparison of outputs from these programs allowed us to correct flaws down to centimeter level (subsequently confirmed by comparison with newest IAU/IERS software)
—— Transformations ——
Frames
[EB] — a vector in the terrestrial frame (ITRF)
[SSB] — the same position/velocity in BCRF
[Terra] — the Earth position/velocity in BCRF

where we have the following time dependent matrices (R_{i} being a rotation around ith axis):_{ }
B = R_{3}(da_{o})·R_{2}(dx)·R_{1}(dh) — bias,
P — precession (4 or 5 rotations),
N — nutation (3 rotations),
R = R_{3}(GAST) — Earth diurnal rotation,
W = R_{1}(v)·R_{2}(u)·R_{3}(s') — polar motion
(wobble),
BPNR' =
R_{3}(E)·R_{2}(d)·R_{3}(qEs)
— new idea
Classical:
UTC Û UT1 Û
UT1R Û GMST Û GAST
UTC Û TAI Û TDT/TT/ET
Û TDB
New:
UTC Û UT1 Û UT1S
Û ERA
UTC Û TAI Û
TT/T_{eph}
Û TCG Û TCB
Type Diurnal Earth rotation Precession Nutation Dy, De corr. eq. eqx. corr. FCN geodesic nutation Polar motion Leap second in UTC UT1 – UTC UT1S – UT1 (zonal tides) UT1 corr. ocean tides PM corr. tides < 1 d Solid Earth tides Polar tides_{ } Plate motion Local site displacements: ocean loading atmospheric loading postglacial rebound Site^{ }coordinates error Earth ephemeris (JPL) TT – UTC (TDT – UT1) TDB/TCB – TDT/ET T_{eph} – TT 
Magnitude 360 °/d 50 "/y 9 " 0.03 " 0.0027 " 0.001 " 0.00015 " 0.55 " 1 s 0.9 s 0.17 s 0.0001 s 0.001 " <76 cm 25_{r} ´ 7_{h} mm 2 °/My a few cm 0.9 mm/mbar ±0.01^{ }° = 36 " ±0.1–0.3 km/y 65 s (now) 0.0017 s 0 s 
Displacement 6378 km 1500 m/y 280 m 0.9 m 8 cm 3 cm 0.5 cm 17 m 450 m 400 m 76 m 4.5 cm 3 cm 22 cm _{ } 2.6 cm 3 cm/y 3 cm 3 cm 1 cm/y ±1100 m ^{ } ±1–5 km 2000^{ }km 50 m 0 m 
Atmospheric refraction Diurnal aberration Stellar aberration Deflection of light Refraction in the solar corona Light time (planets) 
35' 0.32" 20" 2" negl. D/c 
—–Old vs. New Paradigm—–
Old FK5 Bright stars Moving reference frame Newtonian CEP Equinox (precessing) IAU1976 precession IAU1980 nutation Sidereal time: GAST = a + b·UT1 + + c·UT1^{2} + d·UT1^{3} + + Dy cose + corr. 
New ICRS Extragalactic sources Fixed reference frame Relativistic CIP CEO (stable) IAU2000A/B PN theory Earth rotation angle: q = a' + b'·UT1 
Greenwich & CIO TEO not defined (u,v) 
Greenwich & CIO TEO on CIP equator (u,v,s') 
Gains
• Higher accuracy (marcseconds level)
• Simplified ideas and procedures
• Relativistic relation between BCRS and GCRS
• Reference frame is fixed — coordinates of defining objects in ICRF essentially epoch independent
• The frame independent of the dynamics of the solar system
• Computer routines made readily available:
 IERS Conventions 2000 site,
 IAU SOFA
(Standards Of Fundamental Astronomy)
Problems
• Two paradigms coexisting in practice for long
• Complex practical procedures prepared by a few people (e.g. GST – ERA relation published 2 month back has been derived in 28 steps — will be difficult to check by independent parties)
• Delayed implementation (formally since 2003.0, Astron. Almanac for 2005)
• IAU2000A precessionnutation theory overdue complex:
 nearly 1400 terms down to 0.1 mas
 absolute accuracy 0.2 ÷ tens of mas (FCN)
 has errors (VLBI ® CIP offset, B matrix)
 possible replacement by SF2001 PN theory (Shirai & Fukushima) with 194 terms
• IAU2000B oversimplified (77 terms, 1 mas; Bangert)
• Terminology — numerous new terms and abbreviations (sometimes inconsistent, e.g. ERA or stellar angle, NRO or CEO, or lack of friendly names, e.g. s, s' quantities)
• Inadequately explained and popularised among common users; sources include:
 IAU resolutions (IAU Inf. Bull. 88)
 dispersed refereed papers
 Proc.
IERS Workshop Implem. New IAU Resolutions (2002)
 IERS Standards 1996
 IERS
Conventions 2000 (to appear this fall)
 Explanatory Supplement to the Astron. Almanac (2004?)
Differences in x coordinate of the EXPLORER detector position transformed to ICRF with the classical and new IAU procedures (data plotted every 1.7 days) Differences between 'observed' X,Y of the CIP and predicted values based on the IAU2000A developments (Capitaine et al. 2003, A&A 400,1145–1154) 
I would like to state with gratitude that the success of 'tuning'
my program to
the most uptodate IAU/IERS standards has been possible owing to
cooperation with Dr Pia Astone of the Istituto Nazionale di Fisica Nucleare (Rome).
This study and programming work behind it were supported through
the Polish National Committee for Scientific Research (KBN)
Grant No. 2 P03B 094 17 managed by Prof. Andrzej Królak of the Institute of Mathematics, Polish Academy of Sciences (Warsaw).