POLAR MOTION INDUCED BY LUNI-SOLAR GRAVITATIONAL TIDES
Table with the harmonic development of the model of polar
motion due to the lunisolar torque on the triaxial Earth, corresponding to that
what is frequently referred to as high-frequency nutation. The coefficients
have been computed for the model of non-rigid Earth and refer to the conventional
intermediate pole (CIP) which was defined by Resolution B1.7 of the last IAU
General Assembly. This table is based on the discussion and comparisons done
during the last 3 months by the Sub-WG "Subdiurnal Nutations" of the
IAU Commission 19 WG on Nutation. Two models for non-rigid Earth were taken
into account in this discussion, one by Mathews and Bretagnon (2002, Proc. JSR
2001) and the other one by Brzezinski (2001, Proc. JSR 2000), Brzezinski and
Capitaine (2002, Proc. JSR 2001). The papers describing these theories are in
preparation and should be soon submitted for publication in the reviewed international
journals. After discussing several details and introducing all the necessary
corrections, Sonny and myself could reach a consensus on the attached table. Aleksander Brzezinski, July 2002.
Coefficients in microarcseconds
Cut-off: 0.5 muas on the amplitude defined as the
square root of the sin and cos coefficients of PM X or PM Y, whichever is larger
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Degree| Argument |Doodson | Period | PM X | PM Y
n |chi l l' F D Om | number | (days) | sin cos | sin cos
----------------------------------------------------------------------
4 0 0 0 0 0 -1 055.565 6798.3837 -.03 .63 -.05 -.55
3 0 -1 0 1 0 2 055.645 6159.1355 1.46 .00 -.18 .11
3 0 -1 0 1 0 1 055.655 3231.4956 -28.53 -.23 3.42 -3.86
3 0 -1 0 1 0 0 055.665 2190.3501 -4.65 -.08 .55 -.92
3 0 1 1 -1 0 0 056.444 438.35990 -.69 .15 -.15 -.68
3 0 1 1 -1 0 -1 056.454 411.80661 .99 .26 -.25 1.04
3 0 0 0 1 -1 1 056.555 365.24219 1.19 .21 -.19 1.40
3 0 1 0 1 -2 1 057.455 193.55971 1.30 .37 -.17 2.91
3 0 0 0 1 0 2 065.545 27.431826 -.05 -.21 .01 -1.68
3 0 0 0 1 0 1 065.555 27.321582 0.89 3.97 -.11 32.39
3 0 0 0 1 0 0 065.565 27.212221 0.14 .62 -.02 5.09
3 0 -1 0 1 2 1 073.655 14.698136 -.02 .07 .00 .56
3 0 1 0 1 0 1 075.455 13.718786 -.11 .33 .01 2.66
3 0 0 0 3 0 3 085.555 9.1071941 -.08 .11 .01 .88
3 0 0 0 3 0 2 085.565 9.0950103 -.05 .07 .01 .55
2 1 -1 0 -2 0 -1 135.645 1.1196992 -.44 .25 -.25 -.44
2 1 -1 0 -2 0 -2 135.655 1.1195149 -2.31 1.32 -1.32 -2.31
2 1 1 0 -2 -2 -2 137.455 1.1134606 -.44 .25 -.25 -.44
2 1 0 0 -2 0 -1 145.545 1.0759762 -2.14 1.23 -1.23 -2.14
2 1 0 0 -2 0 -2 145.555 1.0758059 -11.36 6.52 -6.52 -11.36
2 1 -1 0 0 0 0 155.655 1.0347187 .84 -.48 .48 .84
2 1 0 0 -2 2 -2 163.555 1.0027454 -4.76 2.73 -2.73 -4.76
2 1 0 0 0 0 0 165.555 0.9972696 14.27 -8.19 8.19 14.27
2 1 0 0 0 0 -1 165.565 0.9971233 1.93 -1.11 1.11 1.93
2 1 1 0 0 0 0 175.455 0.9624365 .76 -.43 .43 .76
Rate of secular polar motion (muas/yr) due to the zero frequency tide
4 4 0 0 0 0 0 555.555 -3.80 -4.31
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Legend:
1. "Degree" means degree of the tidal potential.
2. "chi" denotes GMST+pi
3. The responsible geopotential terms are
U31 - long periodic waves, 3-rd order tidal potential
U41 - long periodic waves and linear trend, 4-th order tidal potential
U22 - prograde diurnal waves
The corresponding Stokes coefficients were taken from the model JGM-3
4. Each pair of the prograde and retrograde long periodic waves has been
merged into a single elliptical wave with increasing argument.
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