# Precession of the Equinoxes

### earth equator space ecliptic

The precession of the equinoxes (sometimes simply called precession), is a movement of the celestial equator, the projection of the earth's equator into space, with respect to the fixed stars and the ecliptic, the path of the Sun's motion in space as viewed from the earth. These two great circles in space are inclined to one another by an angle of approximately 23.5°, called the obliquity. Their intersection defines the equinox. The equator moves from east to west—in the same direction as the daily motion of the Sun—at a rate of about 50.°2 per year.

Ancient Greed astronomer Hipparchus (ca. 150 B.C.) discovered precession when he compared positions of stars for his epoch with observations made 150 years earlier by Timocharis (early third century B.C.). Hipparchus determined that the precession was at least 36" per year and probably in the range 45-46," close to the modern value (although the value is not the same in all parts of the sky).

Although precession was discovered in antiquity, its cause was unexplained until formulated in the seventeenth century. In his Principia Mathematica, Sir Issac Newton (1643-1727) demonstrated that precession results from the nonspherical shape of the earth. Consider the motion of another nonspherical object, a spinning top. If the top were not spinning, but merely balanced on its axis, a slight push would topple it over because the gravitational pull on one side would exceed that on the Figure 1. The precessional motion of a top. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 2. The precessional motion of the earth. Illustration by Hans & Cassidy. Courtesy of Gale Group. other. But with the top spinning, the force generated by the spin prevents the top from falling, moving it in a direction perpendicular to the line of gravitational pull. The top's axis then precesses and traces a cone in space.

The same occurs with the earth. The earth is slightly flattened, with the distance from its center to the equator being 0.3% greater than the distance from its center to the poles. Both the Sun, moving in the ecliptic, and the Moon, whose orbit is inclined 5° to the ecliptic, generate gravitational pulls on the equatorial bulge. If the earth were not spinning, its equator would eventually line up near the ecliptic. But because of its daily rotation, the earth, like a top, precesses; its axis of rotation traces a cone in space with a period of (360° × 60' × 60")/50. 2" per year or 25,800 years (also called a Platonic year). The precession generated by the gravitational pulls of the Sun and the Moon is called luni-solar precession and amounts to some 50.3" per year, two-thirds of which is caused by the Moon.

But the precessional motion is actually more complicated. The earth moves in its orbit, coinciding with the ecliptic, but it is subject to the gravitational pull of the other planets called the planetary precession. These gravitational forces cause the ecliptic, and hence the equinox, to precess at a rate of 0.12" per year, much smaller than the luni-solar precession. The luni-solar and planetary precession together constitute the general precession. The plane of the Moon's orbit does not remain stationary in space; it oscillates around a mean value and rotates with a period of 18.6 years. These changes cause small oscillations in the precession, constituting an astronomical nutation, with an amplitude 9.2" and a period of 18.6 years. English astronomer James Bradley (1693-1762) announced the discovery of nutation in 1748.

Astronomical observations of the positions of celestial bodies must be corrected to account for the effects of precession and nutation. The displacement caused by precession appears negligible during the span of a human life, but the resulting movements become significant over the course of several centuries. In our time the bright star Polaris in the constellation Ursa Minor lies within 1° of the north celestial pole and offers a convenient guide, as in celestial navigation, for ascertaining the northern direction. But at the time of the Egyptian Second Dynasty (ca. 2800 B.C.) Polaris was more than 26° from the pole, whereas the star Thuban in the Draco constellation (currently 25° from the pole), was situated less than 2' from the pole. In the year A.D. 13,400 the very bright star Vega in the Lyra constellation, currently over 61° from the pole, will be located less than 5° from the pole. At that time the seasons in the two hemispheres will be reversed. The Northern Hemisphere will receive the most sunshine in December, and the least in June. December, January, and February will become summer months and June, July, and August winter months; the reverse will be true in the Southern Hemisphere. December, January, and February, currently summer months, will become winter months.

## Resources

### Books

Murray, C.A. Vectorial Astrometry. Bristol, U.K.: Adam Hilger Ltd., 1983.

Newcomb, S. Compendium of Spherical astronomy. Dover, New York: 1960.

### Periodicals

Krzeminski, Z.S. "How Precession Changes the Coordinates of a Star." Sky & Telescope (October 1991): 408.

Richard L. Branham,

## KEY TERMS

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Celestial equator

—The projection into space of the earth's equator.

Ecliptic

—Apparent path of the Sun in the sky or, alternatively, the plane of the earth's orbit in space.

Equinox

—Intersection of the celestial equator (the projection of Earth's equator into space) and the ecliptic (the path of the Sun's motion in space as viewed from the earth).

General precession

—Combined luni-solar and planetary precession.

Luni-solar precession

—Precession caused by the gravitational pull of the Sun and the Moon on the earth's equator.

Nutation

—Periodic oscillation in the precession caused principally by the Moon.

Obliquity

—The angle formed by the intersection of the celestial equator and the ecliptic.

Planetary precession

—Precession caused by the gravitational pull of the planets on the earth as a whole.