| EARTH ROTATION VARIATIONS DUE TO ZONAL TIDES |
UT1, hence the duration of the day Δ
and the Earth's rotation rate Ω are subject to variations
under the effect of zonal tides. We report here below the model of the IERS
96 conventions. It includes 62 periodic components, with periods ranging from
5.6 days to 18.6 years. They are 41 components with period under 35 days (Table
A) and 27 above (Table B).
- R = Σ A'i cos ξi ω - ωR = Σ A"i cos ξi Table A - WITH PERIODS UP TO 35 DAYS |
ARGUMENT (ξi) PERIOD UT1-UT1R Δ - ΔR Ω - ΩR
N l l' F D Ω DAYS Ai A'i A"i
1 1 0 2 2 2 5.64 -0.024 0.26 -0.22
2 2 0 2 0 1 6.85 -0.040 0.37 -0.31
3 2 0 2 0 2 6.86 -0.099 0.90 -0.76
4 0 0 2 2 1 7.09 -0.051 0.45 -0.38
5 0 0 2 2 2 7.10 -0.123 1.09 -0.92
6 1 0 2 0 0 9.11 -0.039 0.27 -0.22
7 1 0 2 0 1 9.12 -0.411 2.83 -2.39
8 1 0 2 0 2 9.13 -0.993 6.83 -5.76
9 3 0 0 0 0 9.18 -0.018 0.12 -0.10
10 -1 0 2 2 1 9.54 -0.082 0.54 -0.45
11 -1 0 2 2 2 9.56 -0.197 1.30 -1.10
12 1 0 0 2 0 9.61 -0.076 0.50 -0.42
13 2 0 2 -2 2 12.81 0.022 -0.11 0.09
14 0 1 2 0 2 13.17 0.025 -0.12 0.10
15 0 0 2 0 0 13.61 -0.299 1.38 -1.17
16 0 0 2 0 1 13.63 -3.208 14.79 -12.48
17 0 0 2 0 2 13.66 -7.757 35.68 -30.11
18 2 0 0 0 -1 13.75 0.022 -0.10 0.08
19 2 0 0 0 0 13.78 -0.338 1.54 -1.30
20 2 0 0 0 1 13.81 0.018 -0.08 0.07
21 0 -1 2 0 2 14.19 -0.024 0.11 -0.09
22 0 0 0 2 -1 14.73 0.047 -0.20 0.17
23 0 0 0 2 0 14.77 -0.734 3.12 -2.64
24 0 0 0 2 1 14.80 -0.053 0.22 -0.19
25 0 -1 0 2 0 15.39 -0.051 0.21 -0.17
26 1 0 2 -2 1 23.86 0.050 -0.13 0.11
27 1 0 2 -2 2 23.94 0.101 -0.26 0.22
28 1 1 0 0 0 25.62 0.039 -0.10 0.08
29 -1 0 2 0 0 26.88 0.047 -0.11 0.09
30 -1 0 2 0 1 26.98 0.177 -0.41 0.35
31 -1 0 2 0 2 27.09 0.435 -1.01 0.85
32 1 0 0 0 -1 27.44 0.534 -1.22 1.03
33 1 0 0 0 0 27.56 -8.261 18.84 -15.90
34 1 0 0 0 1 27.67 0.544 -1.24 1.04
35 0 0 0 1 0 29.53 0.047 -0.10 0.08
36 1 -1 0 0 0 29.80 -0.055 0.12 -0.10
37 -1 0 0 2 -1 31.66 0.118 -0.23 0.20
38 -1 0 0 2 0 31.81 -1.824 3.60 -3.04
39 -1 0 0 2 1 31.96 0.132 -0.26 0.22
40 1 0 -2 2 -1 32.61 0.018 -0.03 0.03
41 -1 -1 0 2 0 34.85 -0.086 0.15 -0.13
Table B- WITH PERIODS LONGER THAN 35 DAYS
(Based on Yoder et al.(1981),with K/C = 0.94).
ARGUMENT (ξi) PERIOD UT1-UT1R Δ - ΔR Ω - ΩR
N l l' F D Ω DAYS Ai A'i A"i
42 0 2 2 -2 2 91.31 -0.057 0.04 -0.03
43 0 1 2 -2 1 119.61 0.033 -0.02 0.01
44 0 1 2 -2 2 121.75 -1.885 0.97 -0.82
45 0 0 2 -2 0 173.31 0.251 -0.09 0.08
46 0 0 2 -2 1 177.84 1.170 -0.41 0.35
47 0 0 2 -2 2 182.62 -48.247 16.60 -14.01
48 0 2 0 0 0 182.63 -0.194 0.07 -0.06
49 2 0 0 -2 -1 199.84 0.049 -0.02 0.01
50 2 0 0 -2 0 205.89 -0.547 0.17 -0.14
51 2 0 0 -2 1 212.32 0.037 -0.01 0.01
52 0 -1 2 -2 1 346.60 -0.045 0.01 -0.01
53 0 1 0 0 -1 346.64 0.092 -0.02 0.01
54 0 -1 2 -2 2 365.22 0.828 -0.14 0.12
55 0 1 0 0 0 365.26 -15.359 2.64 -2.23
56 0 1 0 0 1 386.00 -0.138 0.02 -0.02
57 1 0 0 -1 0 411.78 0.035 -0.01 0.00
58 2 0 -2 0 0 1095.17 -0.137 -0.01 0.01
59 -2 0 2 0 1 1305.47 0.422 -0.02 0.02
60 -1 1 0 1 0 3232.85 0.040 0.00 0.00
61 0 0 0 0 2 -3399.18 7.900 0.15 -0.12
62 0 0 0 0 1 -6790.36 -1617.268 -14.95 12.62
Delaunay arguments :
following approximate expressions are sufficient for computing zonal tides effects :
l = 134°.96 + 13°.064993(MJD-51544.5) Mean anomaly of the Moon
l ' = 357°.53 + 0°.985600(MJD-51544.5) Mean anomaly of the Sun
F = 93°.27 + 13°.229350(MJD-51544.5) L - Ω with L : mean longitude of the Moon
D = 297°.85 + 12°.190749(MJD-51544.5) Mean elongation of the Moon from the Sun
Ω = 125°.04 - 0°.052954(MJD-51544.5) Mean longitude of the ascending node of the Moon