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
--------------------------------------------------------------------- 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 ------------------------------------------------------------------------ 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.