Precession and Nutation

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+Precession and Nutation +

+Right ascension and declination, ( $[\,\alpha,\delta\,]$ ), are the names +of the longitude and latitude in a spherical +polar coordinate system based on the Earth's axis of rotation. +The zero point of $\alpha$ is the point of intersection of +the celestial +equator and the ecliptic (the apparent path of the Sun +through the year) where the Sun moves into the northern +hemisphere. This point is called the +first point of Aries, +the vernal equinox (with apologies to +southern-hemisphere readers) or simply the equinox. +

+This simple picture is unfortunately +complicated by the difficulty of defining +a suitable equator and equinox. One problem is that the +Sun's apparent motion is not completely regular, due to the +ellipticity of the Earth's orbit and its continuous disturbance +by the Moon and planets. This is dealt with by +separating the motion into (i) a smooth and steady mean Sun +and (ii) a set of periodic corrections and perturbations; only the former +is involved in establishing reference frames and timescales. +A second, far larger problem, is that +the celestial equator and the ecliptic +are both moving with respect to the stars. +These motions arise because of the gravitational +interactions between the Earth and the other solar-system bodies. +

+By far the largest effect is the +so-called ``precession of the equinoxes'', where the Earth's +rotation axis sweeps out a cone centred on the ecliptic +pole, completing one revolution in about 26,000 years. The +cause of the motion is the torque exerted on the distorted and +spinning Earth by the Sun and the Moon. Consider the effect of the +Sun alone, at or near the northern summer solstice. The Sun +`sees' the top (north pole) of the Earth tilted towards it +(by about $23^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$ , the obliquity of the +ecliptic), +and sees the nearer part of the Earth's equatorial bulge +below centre and the further part above centre. +Although the Earth is in free fall, +the gravitational force on the nearer part of the +equatorial bulge is greater than that on the further part, and +so there is a net torque acting +as if to eliminate the tilt. Six months later the same thing +is happening in reverse, except that the torque is still +trying to eliminate the tilt. In between (at the equinoxes) the +torque shrinks to zero. A torque acting on a spinning body +is gyroscopically translated +into a precessional motion of the spin axis at right-angles to the torque, +and this happens to the Earth. +The motion varies during the +year, going through two maxima, but always acts in the +same direction. The Moon produces the same effect, +adding a contribution to the precession which peaks twice +per month. The Moon's proximity to the Earth more than compensates +for its smaller mass and gravitational attraction, so that it +in fact contributes most of the precessional effect. +

+The complex interactions between the three bodies produce a +precessional motion that is wobbly rather than completely smooth. +However, the main 26,000-year component is on such a grand scale that +it dwarfs the remaining terms, the biggest of +which has an amplitude of only $17\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and a period of +about 18.6 years. This difference of scale makes it convenient to treat +these two components of the motion separately. The main 26,000-year +effect is called luni-solar precession; the smaller, +faster, periodic terms are called the nutation. +

+Note that precession and nutation are simply +different frequency components of the same physical effect. It is +a common misconception that precession is caused +by the Sun and nutation is caused by the Moon. In fact +the Moon is responsible for two-thirds of the precession, and, +while it is true that much of the complex detail of the nutation is +a reflection of the intricacies of the lunar orbit, there are +nonetheless important solar terms in the nutation. +

+In addition to and quite separate +from the precession/nutation effect, the orbit of the Earth-Moon system +is not fixed in orientation, a result of the attractions of the +planets. This slow (about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ per year) +secular rotation of the ecliptic about a slowly-moving diameter is called, +confusingly, planetary +precession and, along with the luni-solar precession is +included in the general precession. The equator and +ecliptic as affected by general precession +are what define the various ``mean'' $[\,\alpha,\delta\,]$ reference frames. +

+The models for precession and nutation come from a combination +of observation and theory, and are subject to continuous +refinement. Nutation models in particular have reached a high +degree of sophistication, taking into account such things as +the non-rigidity of the Earth and the effects of +the planets; SLALIB's nutation +model (IAU 1980) involves 106 terms in each of $\psi$ (longitude) +and $\epsilon$ (obliquity), some as small as + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0001$ . +

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+SLALIB support for precession and nutation +

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+ Next: SLALIB support for precession and nutation +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Celestial Coordinate Systems +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit