J/A+A/408/387 Transformation between ICRS and ITRS (Bretagnon+, 2003)
On transformation between International Celestial and
Terrestrial Reference systems.
Bretagnon P., Brumberg V.A.
<Astron. Astrophys. 408, 387 (2003)>
=2003A&A...408..387B 2003A&A...408..387B
ADC_Keywords: Earth
Keywords: relativity - reference systems - time
Abstract:
Based on the current IAU hierarchy of the relativistic reference
systems, practical formulae for the transformation between barycentric
(BCRS) and geocentric (GCRS) celestial reference systems are derived.
BCRS is used to refer to ICRS, International Celestial Reference
System. This transformation is given in four versions, dependent on
the time arguments used for BCRS (TCB or TDB) and for GCRS (TCG or
TT). All quantities involved in these formulae have been tabulated
with the use of the VSOP theories (IMCCE theories of motion of the
major planets). In particular, these formulae may be applied to
account for the indirect relativistic third-body perturbations in
motion of Earth's satellites and Earth's rotation problem. We propose
to use the SMART theory (IMCCE theory of Earth's rotation) in
constructing the Newtonian three-dimensional spatial rotation
transformation between GCRS and ITRS, the International Terrestrial
Reference System. This transformation is compared with two other
versions involving extra angular variables currently used by IERS, the
International Earth Rotation Service. It is shown that the comparison
of these three forms of the same transformation may be greatly
simplified by using the proposed composite rotation formula.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tables.dat 88 230 *Parameters
tables.tex 121 427 LaTeX version of the tables
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Note on tables.dat: xEi, vEi, c-2aE1, c-2UE(t,xE),
c-2Ap, c-2ApvEi, c-2Fi, and c-2{dot}(F)i (i=1,2,3) in
function of t=TDB (Barycentric Dynamical Time) as computed with VSOP
(Variations Seculaires des Orbites Planetaires) theories.
All values are given using the astronomical unit as the unit of length and
1000 Julian years (365250 Julian days) as the unit of time.
All series are presented in form of (31), i.e.
xE1(t)=
{Sum on alpha}talpha *
[{Sum on k}(Xik)alpha * cos((psik)alpha + (nuk)alpha*t]
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See also:
VI/79 : Lunar Solution ELP 2000-82B (Chapront-Touze+, 1998)
J/A+A/400/1145 : Celestial Intermediate Pole + Ephemeris Origin
(Capitaine+, 2003)
Byte-by-byte Description of file: tables.dat
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Bytes Format Units Label Explanations
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1- 2 I2 --- Tab Table number (1)
4- 5 I2 --- Term Ordinal number of the term
7 I1 rad l1 Mean longitude of Mercury
9 I1 rad l2 Mean longitude of Venus
11- 13 I3 rad l3 Mean longitude of Earth
15- 16 I2 rad l4 Mean longitude of Mars
18- 19 I2 rad l5 Mean longitude of Jupiter
21- 22 I2 rad l6 Mean longitude of Saturne
24 I1 rad l7 Mean longitude of Uranus
26 I1 rad l8 Mean longitude of Neptune
28- 29 I2 rad D Delaunay D argument of lunar theory (2)
31- 32 I2 rad F Delaunay F argument of lunar theory (2)
34- 35 I2 rad l Delaunay l argument of lunar theory (2)
38- 51 E14.9 --- X X coefficient
55- 68 E14.9 rad psi Phase angle of the argument
72- 85 E14.9 10-3rad/yr nu Frequency of the argument,
expressed in rad/(1000 Julian year)
88 I1 --- alpha Exposant alpha of power of t
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Note (1): Parameters associated to the tables:
01: xE1, 02: xE2, 03: xE3
04: vE1, 05: vE2, 06: vE3
07: c-2aE1, 08: c-2aE2, 09: c-2aE3
10: c-2UE(t,xE)
11: c-2Ap
12: c-2ApvE1, 13: c-2ApvE2, 14: c-2ApvE3
15: c-2F1, 16: c-2F2, 17: c-2F3
18: c-2{dot}(F)1, 19: c-2{dot}(F)2, 20: c-2{dot}(F)3
The truncation level is as follows:
0.5E-03 au over 1000 yrs for xEi (Tables 1-3),
0.5AU/1000 yrs over 1000 yrs for vEi (Tables 4-6),
0.4E-12 over 1000 yrs for c-2aEi (Tables 7-9),
0.15E-12 over 1000 yrs for c-2UE(t,xE) (Table 10)
0.5E-16 over 1000 yrs for c-2Ap (Table 11),
0.8E-12 over 1000 yrs for c-2ApvEi (Tables 12-14)
0.1E-12 over 1000 yrs for c-2Fi (Tables 15-17)
0.1E-8 over 1000 yrs for c-2{dot}(F)i (Tables 18-20)
Note (2): Delaunay's arguments:
D = w1 - l3 + 180°, F = w1 - w3 ; l = w1 - w2
where w1, w2, and w3 are respectively the secular mean lunar
longitude, the mean longitude of the perigee and the mean longitude
of the node. l3 is the mean longitude of the Earth
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Acknowledgements: Victor Brumberg
References:
Arais et al., IRCS Servive 1995A&A...303..604A 1995A&A...303..604A
Seidelmann & Kovalesky, Definitions (ICRS, CIP and CEO) 2002A&A...392..341S 2002A&A...392..341S
(End) Patricia Bauer [CDS] 19-Jun-2003