Contribution to the Earth's Obliquity Rate, Precession, and Nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J₂ perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The J(sub2) effects have generally been allowed for in past nutation theories and some procession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta phi plus out-of-phase contributions of 0.14 mas in Delta phi and -0.03 mas in Delta epsilon. The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C = 0.003 273 763 4 which, in combination with a satellite-derived J(sub2), gives a normalized polar moment of inertia C/MR(exp2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub2). Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.