precession: one construct, many systems

Precession of the equinoxes is the slow, roughly 26,000-year drift of Earth's rotation axis, which traces a cone against the stars and gradually moves the points where the Sun crosses the celestial equator. Hipparchus of Nicaea first detected it around 150 BCE by comparing his own star positions with earlier records, and the effect was set down in Ptolemy's Almagest around 150 CE; Copernicus treated it in De revolutionibus (1543) and Newcomb (1906) gave a rigorous quantitative account. Here the referent is the orientation of a whole planet's spin axis over millennia, tracked as a shift of celestial coordinates, not the axis of a laboratory top or the orientation of a nuclear magnetic moment.[1][2][3]

Unit

One full circuit of the axis around the celestial pole, about 25,800 years

Recovery means

Not applicable

Measured by

Determined from the observed shift of stellar coordinates and the general precession constant, historically about 50 arcseconds per year

Gyroscopic precession is the way the spin axis of a rotating rigid body responds to an applied torque by turning perpendicular to it, so a spinning top under gravity sweeps its axis around the vertical instead of toppling. Euler's Theoria motus corporum solidorum (1765) laid out the rigid-body equations that govern this motion, and Goldstein's Classical Mechanics (1980) is the standard modern derivation relating the precession rate to the applied torque and the spin angular momentum. The referent here is any spinning rigid object in a laboratory or engineered setting, described by its angular momentum and the torque acting on it, in contrast to the specific case of a whole planet's axis or the orientation of a magnetic moment in a field.[4][5]

Unit

An angular rate at which the spin axis sweeps out its cone, in radians per second

Recovery means

Not applicable

Measured by

Computed as the ratio of the applied torque to the spin angular momentum, and observed as the steady circulation of the axis

Larmor precession is the circulation of a magnetic moment, such as that of an electron or a nuclear spin, around the direction of an applied magnetic field, at a rate proportional to the field strength. Larmor (1897) derived the frequency of this motion while studying the magnetic influence on spectral lines, and Bloch's Nuclear Induction (1946) made it the working principle of nuclear magnetic resonance by describing how a population of nuclear moments precesses and can be detected. The referent is the orientation of a magnetic moment in a field, read off as a resonant frequency in hertz, and it is a magnetic rather than a mechanical or astronomical instance of the word.[6][7]

Unit

A resonant angular frequency, the Larmor frequency, scaled per unit of field strength

Recovery means

Not applicable

Measured by

Measured as the resonance frequency in magnetic resonance experiments, equal to the gyromagnetic ratio times the field strength