Meeting Mathematics of Gravitation II
Warsaw, September 1 10, 2003

Referring a Detector
to the Solar System Barycenter

Kazimierz Borkowski

Toru Radio Astronomy Observatory
Centre for Astronomy
Nicolaus Copernicus University
Toru, Poland




Scope of this presentation

General intoduction to transformations between reference frames

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




Background

Search for gravitational waves in data from the Explorer detector (Krlak 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



Purpose
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



Transformation of coordinates

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


[SSB] = [Terra] + PNRW[EB] classical [SSB] = [Terra] + BPNRW'[EB] new classical   [SSB] = [Terra] + BPNR'W'[EB] IAU2000

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

B = R3(dao)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({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



Transformations of time

  Classical:
UTC UT1 UT1R GMST GAST
UTC TAI TDT/TT/ET TDB
  New:
UTC UT1 UT1S ERA
UTC TAI TT/Teph TCG TCB



Effects to account for

  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 "
0.10.3 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    
15 km
2000 km
  50 m
    0 m



EM propagation effects

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



Some properties

    Old
FK5
Bright stars
Moving reference frame  
Newtonian
CEP
Equinox (precessing)
IAU1976 precession
IAU1980 nutation
Sidereal time:
  GAST = a + bUT1 +
  + cUT12 + dUT13 +
  + 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?)



FCN component and the IAU2000 system

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)

(50kB) - FCN in X
(28kB) Capitaine et al. 2003, A&A <b>400</b>,
1145

Differences between 'observed' X,Y of the CIP and predicted values based on the IAU2000A developments (Capitaine et al. 2003, A&A 400,11451154)



  Acknowledgements

  I would like to state with gratitude that the success of 'tuning' my program to the most up-to-date 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 Krlak of the Institute of Mathematics, Polish Academy of Sciences (Warsaw).