J/A+A/406/1135 UT1 definitions in IAU 2000 (Capitaine+, 2003)
Expressions to implement the IAU 2000 definition of UT1.
Capitaine N., Wallace P.T., McCarthy D.D.
<Astron. Astrophys. 406, 1135 (2003)>
=2003A&A...406.1135C 2003A&A...406.1135C
ADC_Keywords: Earth ; Ephemerides
Keywords: astrometry - reference systems - ephemerides - time
Abstract:
This paper provides expressions to be used to implement the new
definition of UT1 corresponding to the IAU 2000 resolutions either
in the new (CEO-based) or classical (equinox-based) transformations
between the International Terrestrial Reference System (ITRS) and
the Geocentric Celestial Reference System (GCRS). The new expression
for Greenwich Sidereal Time (GST) has to be in agreement at the
micro-arcsecond level, for one century, with the IAU 2000 expressions
for the Earth Rotation Angle (ERA) and for the quantity s positioning
the Celestial Ephemeris Origin (CEO) on the equator of the CIP.
The computations of the new expressions using the IAU 2000
precession-nutation model are performed in such a manner as to ensure
that there is no discontinuity in UT1 on 1 January 2003 and that there
is equivalence of the classical and new transformations between the
ITRS and GCRS relative to the rotation about the axis of the CIP when
these expressions are used. The equinox offset that is considered in
the computations refers to the dynamical mean equinox of J2000.0. The
resulting expressions have been included in the IERS Conventions 2000.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tablea.dat 112 1600 Expression (IAU 2000A) of the X coordinate of
the CIP in the GCRS provided by N. Capitaine
tableb.dat 112 1275 Expression (IAU 2000A) of the Y coordinate of
the CIP in the GCRS provided by N. Capitaine
tablec.dat 112 66 Expression (IAU 2000A) of the s(t)+XY/2 quantity
provided provided by N. Capitaine
tablef.dat 112 34 Expression for Greenwich Sidereal Time based on
the IAU2000A precession-nutation model
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Description of file: table[abcf].dat
The expressions for the X and Y coordinates of the CIP in the GCRS and
the quantity s(t)+XY/2 are based on the IAU2000A precession-nutation
model. They are in the form : polynomial part + non-polynomial part
In the non-polynomial part, ARG being for various combination of the
fundamental arguments of the nutation theory)
The expressions for the fundamental arguments appearing in columns 6
to 10 (luni-solar part) and in columns 11 to 19 (planetary part) are
those of the IERS Conventions 2000
X expression (tablea.dat):
Polynomial part (unit microarcsecond)
-16616.99 + 2004191742.88t - 427219.05t2 - 198620.54t3 - 46.05t4
+ 5.98t5
Non-polynomial part (unit microarcsecond)
Sumi[a{s,0})_i*sin(ARG) + a{c,0})i*cos(ARG)]
+ Sum_i)j=1,4 [a{s,j})i*tj*sin(ARG) + a{c,j})i*cos(ARG)]*tj]
Y expression (tableb.dat):
Polynomial part (unit microarcsecond)
-6950.78 - 25381.99t - 22407250.99t2 + 1842.28t3 + 1113.06t4 + 0.99t5
Non-polynomial part (unit microarcsecond)
Sumi[b{c,0})_i*cos(ARG) + b{s,0})i*sin(ARG)]
+ Sum_i)j=1,4 [b{c,j})i*tj*cos(ARG) + b{s,j})i*sin(ARG)]*tj]
s + XY/2 expression (tablec.dat):
Polynomial part (unit microarcsecond)
94.0 + 3808.35t - 119.94t2 - 72574.09t3 + 27.70t4 + 15.61t5
Non-polynomial part (unit microarcsecond)
Sumi[C{s,0})_i*sin(ARG) + C{c,0})i*cos(ARG)]
+ Sum_i)j=1,4 [C{s,j})i*tj*sin(ARG) + C{c,j})i*cos(ARG)]*tj]
Updated Table (12/11/2003) for ensuring continuity of UT1 on 1st January 2003
Cutoff (0.1 microarcsecond and periods less than 500 years)
GST expression (tablef.dat):
Expression ensuring continuity of UT1 on 1st January 2003
GST = Theta(UT1) + polynomial part + DeltaPsi*cos(epsilon_A)
+ non-polynomial part
Theta(UT1) = 2*Pi*(0.7790572732640 + 1.00273781191135448.Tu)
where Tu = Julian UT1 date - 2451545.0, and UT1 = UTC + (UT1 - UTC)
Polynomial part (unit arcsecond)
0.014506 + 4612.15739966t + 1.39667721t2 - 0.00009344t3 + 0.00001882t4
DeltaPsi*cos(epsilon_A) = classical expression for the equation of the
Non-polynomial part (unit microarcsecond)
Sumi[C{s,0})_i*sin(ARG) + C{c,0})i*cos(ARG)]
+ Sumi[C{s,1})_i*t*sin(ARG) + C{c,1})i*cos(ARG)]*t]
Cutoff (0.1 microarcsecond and periods less than 500 years)
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See also:
J/A+A/355/398 : Celestial Ephemeris Origin definition (Capitaine+, 2000)
J/A+A/400/1145 : Celestial Intermediate Pole + Ephemeris Origin
(Capitaine+, 2003)
Byte-by-byte Description of file: table?.dat
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Bytes Format Units Label Explanations
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1 I1 --- j [0/4] Number j
3- 6 I4 --- nj Number of terms (i) for j
9- 12 I4 --- i Number i (range [0 .. nj])
17- 27 F11.2 --- i(s,j) a{s,j})i (X), b{s,j})i (Y) or
c{s,j})i (S(t)+XY/2) coefficient
33- 42 F10.2 --- i(c,j) a{c,j})i (X), b{c,j})i (Y) or
c{c,j})i (S(t)+XY/2) coefficient
47 I1 --- l Mean anomaly of the Moon coefficient
51- 52 I2 --- l' Mean anomaly of the Sun coefficient
56- 57 I2 --- F L - Omega (L: Mean longitude of the Moon)
coefficient
61- 62 I2 --- D Mean elongation from the Moon to the Sun
coefficient
66- 67 I2 --- Omega Mean longitude of the ascending node of the
Moon coefficient
71- 72 I2 --- LMe Mean longitude of Mercure coefficient
75- 77 I3 --- LVe Mean longitude of Venus coefficient
80- 82 I3 --- LE Mean longitude of the Earth coefficient
85- 87 I3 --- LMa Mean longitude of Mars coefficient
91- 92 I2 --- LJ Mean longitude of Jupiter coefficient
96- 97 I2 --- LSa Mean longitude of Saturn coefficient
101-102 I2 --- LU Mean longitude of Uranus coefficient
106-107 I2 --- LNe Mean longitude of Neptune coefficient
111-112 I2 --- pA General precession in longitude coefficient
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History:
Copied at http://maia.usno.navy.mil/ch5tables.html
(End) Patricia Bauer [CDS] 30-Jul-2003