Table 3: Theoretical contributions (from W94, Williams (1995) and MHB) to the precession rates, $r_{\psi }$ and $r_{\epsilon }$, of the equator used in the present paper.
Source of the effect $\epsilon $ dependence Contribution in longitude at J2000 Contribution in obliquity at J2000
    $\mu$as/cy $\mu$as/cy2 $\mu$as/cy3 $\mu$as/cy $\mu$as/cy2 $\mu$as/cy3
Luni-solar & Planetary torque              
    Luni-solar 1st order $\cos\epsilon$ (r0)1 -3395 -6 0 0 0
    Luni-solar 2d order(a) $6\cos^2\epsilon-1$ -33 100 0 0 0 0 0
    Luni-solar 2d order(b) $3\cos^2\epsilon-1$ -13 680 0 0 0 0 0
    Luni-solar J4 $\cos\epsilon\left(4-7\sin^2\epsilon\right)$ +2600 0 0 0 0 0
    Planetary 1st order $\cos\epsilon$ +31 367 0 0 -1400 0 0
J2 and planetary tilts              
    J2 and planetary tilt(a) $\cos2\epsilon/\sin\epsilon$ -269 430 +1074 0 0 0 0
    planetary tilt(b) $\cos\epsilon$ 0 0 0 (u0)1 -44 +3
Tides              
    tides(a) $\cos^2\epsilon$ 0 -102 0 0 0 0
    tides(b) $\cos^3\epsilon$ 0 -133 0 0 0 0
    tides(c) $\sin\epsilon \cos\epsilon$ 0 0 0 +2400 0 0
J2 rate $\cos\epsilon$ 0 -14 000 0 0 0 0
Non-linear effect 1 -21 050 0 0 0 0 0
Geodesic precession 1 -1 919 883 +3 +1 -1 0 +5
Total   (r0)1 - 2 223 176 -16 553 -5 (u0)1 + 999 -44 +8


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