• General intoduction to transformations between reference frames

• On the new paradigm officially implemented in astronomy and space geodesy since 2003

• Search for gravitational waves in data from the Explorer detector (Królak et al., this Meeting; see also a dedicated web page)

• 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 ——

To express the position and velocity
in a (quasi)inertial reference frame
by means of rotations, translations and
scalings of coordinates and time

Frames

Terrestrial (ITRF) — pole and origin of longitudes
Celestial (ICRF) — CEP/CIP and equinox/CEO
  geocentric (GCRF) — Earth center of mass
  barycentric (BCRF) — solar system barycenter

[EB] — a vector in the terrestrial frame (ITRF)
[SSB] — the same position/velocity in BCRF
[Terra] — the Earth position/velocity in BCRF

[SSB] = [Terra] + P·N·R·W·[EB] — classical [SSB] = [Terra] + BPNR·W'·[EB] — new classical   [SSB] = [Terra] + BPNR'·W'·[EB] — IAU2000

where we have the following time dependent matrices (R_i being a rotation around i-th axis): 

B = R₃(da_o)·R₂(dx)·R₁(-dh) — bias,
P — precession (4 or 5 rotations),
N — nutation (3 rotations),
R = R₃(-GAST) — Earth diurnal rotation,
W = R₁(-v)·R₂(u)·R₃(-s') — polar motion (wobble),
BPNR' = R₃(E)·R₂(d)·R₃(q-E-s) — new idea

E = arctan(Y/X) — 'intermediate right ascension' of the CIP,
d = arctan(Ö{X²+Y²}/Z) — 'i. co-declination' of the CIP,
q — Earth rotation angle (ERA or stellar angle),
s/s' — describes current position of the CEO/TEO

  Classical:
UTC Ű UT1 Ű UT1R Ű GMST Ű GAST
UTC Ű TAI Ű TDT/TT/ET Ű TDB
  New:
UTC Ű UT1 Ű UT1S Ű ERA
UTC Ű TAI Ű TT/T_eph Ű TCG Ű 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    Teph – 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 25r ´ 7h 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·UT12 + d·UT13 +   + 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 precession-nutation 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)