nutation

Nutation (Latin nutare, "to nod") refers to the small, relatively rapid oscillations of a spinning body's axis of rotation about its mean, precessing orientation. For a rigid body precessing steadily under a constant torque, nutation is a transient effect set by initial conditions: the axis traces a cycloid-like curve rather than a smooth circle. In spinning tops, nutation is visible as a slight up-and-down wobble of the axis as it precesses around the vertical.

For astronomical bodies, nutation refers specifically to the small periodic changes in the Earth's rotation axis superimposed on its 26,000-year precession of the equinoxes. The largest component of Earth's nutation has an 18.6-year period and an amplitude of about 9 arcseconds, driven by the regression of the Moon's orbital nodes. Smaller components come from semi-annual and semi-monthly variations of the lunar and solar gravitational torques on the Earth's equatorial bulge. James Bradley discovered the lunar nutation observationally in 1728.

Modern nutation theory, based on Very Long Baseline Interferometry observations of quasars, catalogues hundreds of nutation components with amplitudes down to microarcseconds. Each corresponds to a specific periodic feature of the Earth-Moon-Sun geometry and is predictable from gravitational celestial mechanics. The fact that the theory and observations agree to microarcseconds is one of the most sensitive demonstrations that Newtonian gravitation applied to rigid-body mechanics remains an extraordinarily good description of solar-system motions.