ERA-based expression for Greenwich Sidereal Time (GST) based on the IAU 2006 precession
and IAU 2000A_R06 nutation
(updated on 15/10/2009)
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Expression ensuring continuity of UT1 on 1st January 2003
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GST = ERA(UT1) - EO, EO being the "equation of the origins", can be written as:
GST = ERA(UT1) + polynomial part + DeltaPsi*cos(epsilon_A) + non-polynomial additional part
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ERA(UT1) = 2*Pi*(0.7790572732640 + 1.00273781191135448.T_u)
where T_u = Julian UT1 date - 2451545.0, and UT1 = UTC + (UT1 - UTC)
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Polynomial part (unit arcsecond)
warning: typo for the signs of the t^4 and t^5 terms corrected on 15/10/2009 (*)
0.014506 + 4612.156534 t + 1.3915817 t^2 - 0.00000044 t^3 - 0.000029956 t^4 - 0.0000000368 t^5
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DeltaPsi*cos(epsilon_A) : IAU 2000A_R06 expression for the classical "equation of the equinoxes"
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Non-polynomial additional part (unit microarcsecond)
(ARG being for various combination of the fundamental arguments of the nutation theory)
Sum_i[C'_{s,0})_i * sin(ARG) + C'_{c,0})_i * cos(ARG)]
+ Sum_i[C'_{s,1})_i * t * sin(ARG) + C'_{c,1})_i * cos(ARG)] * t]
The Table below provides the values for C'_{s,j})_i and C'_{c,j})_i
Cutoff (0.1 microarcsecond and periods less than 500 years)
The expressions for the fundamental arguments appearing in columns 4 to 8 (luni-solar part)
and in columns 6 to 17 (planetary part) are those of the IERS Conventions 2003
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i C'_{s,j})_i C'_{c,j})_i l l' F D Om L_Me L_Ve L_E L_Ma L_J L_Sa L_U L_Ne p_A
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j = 0 Number of terms = 33
1 2640.96 -0.39 0 0 0 0 1 0 0 0 0 0 0 0 0 0
2 63.52 -0.02 0 0 0 0 2 0 0 0 0 0 0 0 0 0
3 11.75 0.01 0 0 2 -2 3 0 0 0 0 0 0 0 0 0
4 11.21 0.01 0 0 2 -2 1 0 0 0 0 0 0 0 0 0
5 -4.55 0.00 0 0 2 -2 2 0 0 0 0 0 0 0 0 0
6 2.02 0.00 0 0 2 0 3 0 0 0 0 0 0 0 0 0
7 1.98 0.00 0 0 2 0 1 0 0 0 0 0 0 0 0 0
8 -1.72 0.00 0 0 0 0 3 0 0 0 0 0 0 0 0 0
9 -1.41 -0.01 0 1 0 0 1 0 0 0 0 0 0 0 0 0
10 -1.26 -0.01 0 1 0 0 -1 0 0 0 0 0 0 0 0 0
11 -0.63 0.00 1 0 0 0 -1 0 0 0 0 0 0 0 0 0
12 -0.63 0.00 1 0 0 0 1 0 0 0 0 0 0 0 0 0
13 0.46 0.00 0 1 2 -2 3 0 0 0 0 0 0 0 0 0
14 0.45 0.00 0 1 2 -2 1 0 0 0 0 0 0 0 0 0
15 0.36 0.00 0 0 4 -4 4 0 0 0 0 0 0 0 0 0
16 -0.24 -0.12 0 0 1 -1 1 0 -8 12 0 0 0 0 0 0
17 0.32 0.00 0 0 2 0 0 0 0 0 0 0 0 0 0 0
18 0.28 0.00 0 0 2 0 2 0 0 0 0 0 0 0 0 0
19 0.27 0.00 1 0 2 0 3 0 0 0 0 0 0 0 0 0
20 0.26 0.00 1 0 2 0 1 0 0 0 0 0 0 0 0 0
21 -0.21 0.00 0 0 2 -2 0 0 0 0 0 0 0 0 0 0
22 0.19 0.00 0 1 -2 2 -3 0 0 0 0 0 0 0 0 0
23 0.18 0.00 0 1 -2 2 -1 0 0 0 0 0 0 0 0 0
24 -0.10 0.05 0 0 0 0 0 0 8 -13 0 0 0 0 0 -1
25 0.15 0.00 0 0 0 2 0 0 0 0 0 0 0 0 0 0
26 -0.14 0.00 2 0 -2 0 -1 0 0 0 0 0 0 0 0 0
27 0.14 0.00 1 0 0 -2 1 0 0 0 0 0 0 0 0 0
28 -0.14 0.00 0 1 2 -2 2 0 0 0 0 0 0 0 0 0
29 0.14 0.00 1 0 0 -2 -1 0 0 0 0 0 0 0 0 0
30 0.13 0.00 0 0 4 -2 4 0 0 0 0 0 0 0 0 0
31 -0.11 0.00 0 0 2 -2 4 0 0 0 0 0 0 0 0 0
32 0.11 0.00 1 0 -2 0 -3 0 0 0 0 0 0 0 0 0
33 0.11 0.00 1 0 -2 0 -1 0 0 0 0 0 0 0 0 0
j = 1 Number of terms = 1
34 -0.87 0.00 0 0 0 0 1 0 0 0 0 0 0 0 0 0
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(*): typo mentioned to the IERS by Jose-Ramon Garcia, GMV Aerospace and Defence S.A., Madrid, Spain on 12/10/2009
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