Precession of the equinoxes

The Earth goes through one complete precession cycle in a period of approximately 25,920 years, during which the positions of stars as measured in the equatorial coordinate system will slowly change; the change is actually due to the change of the coordinates. Over this cycle the Earth's north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of 23 degrees 27 arcminutes [1], or about 23.5 degrees (pythagorean comma?). The shift is 1 degree in 180 years (the angle is taken from the observer, not from the center of the circle).

The explanation of this is: The axis of the Earth undergoes precession due to a combination of the Earth's nonspherical shape (it is an oblate spheroid, bulging outward at the equator) and the gravitational tidal forces of the Moon and Sun applying torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. The portion of the precession due to the combined action of the Sun and the Moon is called lunisolar precession.

A changing north star

Polaris is not particularly well-suited for marking the north celestial pole, as its visual magnitude, which is variable, hovers around 2.1, fairly far down the list of brightest stars in the sky. On the other hand, in 3000 BC the faint star Thuban in the constellation Draco was the pole star; at magnitude 3.67 it is only one-fifth as bright as Polaris; today it is all but invisible in light-polluted urban skies. The brightest star known to have been North Star or to be predictable as taking that role in the future is the brilliant Vega in the constellation Lyra, which was the pole star around 12000 BC and will be again around the year AD 14,000. When viewed looking down onto the Earth from the north, the direction of precession is clockwise. When standing on Earth looking outward, the axis appears to move counter-clockwise across the sky. This sense of precession, against the sense of Earth's own axial rotation, is opposite to the precession of a top on a table. The reason is that the torques imposed on the Earth by the Sun and Moon act in the sense of trying to align its axis normal to the ecliptic, i.e. to stand up more vertically in regard to the ecliptic plane, while the torque on a top spinning on a hard surface acts in the sense of trying to make the top fall over, rather than to stand up straighter.

Polaris is not exactly at the pole; any long-exposure unguided photo will show it having a short trail. It is close enough for most practical purposes, though. The south celestial pole precesses too, always remaining exactly opposite the north pole. The south pole is in a particularly bland portion of the sky, and the nominal south pole star is Sigma Octantis, which, while fairly close to the pole, is even weaker than Thuban -- magnitude 5.5, which is barely visible even under a properly dark sky. The precession of the Earth is not entirely regular due to the fact that the Sun and Moon are not in the same plane and move relative to each other, causing the torque they apply to Earth to vary. This varying torque produces a slight irregular motion in the poles called nutation.

Precession of the Earth's axis is a very slow effect, but at the level of accuracy at which astronomers work, it does need to be taken into account. Note that precession has no effect on the inclination ("tilt") of the plane of the Earth's equator (and thus its axis of rotation) on its orbital plane. It is 23.5 degrees and precession does not change that. The inclination of the equator on the ecliptic does change due to gravitational torque, but its period is different (main period about 41000 years).
The following figure illustrates the effects of axial precession on the seasons, relative to perihelion and aphelion. The precession of the equinoxes can cause periodic climate change (see Milankovitch cycles), because the hemisphere that experiences summer at perihelion and winter at aphelion (as the southern hemisphere does presently) is in principle prone to more severe seasons than the opposite hemisphere.

Hipparchus first estimated Earth's precession around 130 BC, adding his own observations to those of Babylonian and Chaldean astronomers in the preceding centuries. In particular they measured the distance of the stars like Spica to the Moon and Sun at the time of lunar eclipses, and because he could compute the distance of the Moon and Sun from the equinox at these moments, he noticed that Spica and other stars appeared to have moved over the centuries.

Precession causes the cycle of seasons (tropical year) to be about 20.4 minutes less than the period for the earth to return to the same position with respect to the stars as one year previously (sidereal year). This results in a slow change (one day per 58 calendar years) in the position of the sun with respect to the stars at an equinox. It is significant for calendars and their leap year rules.

Precession of planetary orbits

The revolution of a planet in its orbit around the Sun is also a form of rotary motion. (In this case, the combined system of Earth and Sun is rotating.) So the axis of a planet's orbital plane will also precess over time.
The major axis of each planet's elliptical orbit also precesses within its orbital plane, in response to perturbations in the form of the changing gravitational forces exerted by other planets. This is called perihelion precession. Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately.

It is generally understood that the gravitational pulls of the sun and the moon cause the precession of the equinoxes on Earth which operate on cycles of 23,000 and 19,000 years. The precession of the orbit of the Earth is an important part of the astronomical theory of ice ages.

Precession is also an important consideration in the dynamics of atoms and molecules.

Zodiac in Astronomy

In astronomy, the zodiac is the region of the sky close to the circle on which the orbital plane of our solar system intersects the celestial sphere. It includes the apparent path of the sun across the sky, known as the ecliptic, and the apparent paths of the naked eye planets which move in a zone just above and below this. It is a useful region of the sky to define, because it has practical implications for observations from the earth's surface. A bright object lying outside of the zodiacal region cannot be a planet. Polar observatories cannot easily observe the planets, because the zodiac is too close to the horizon.

The zodiac is traditionally thought of as comprising a certain set of constellations. The constellations of both zodiacs are shown in the table below, including Ophiuchus, which was recognised as a zodiacal constellation at least as far back as Ptolemy's Almagest in the 2nd century.
Most of Ophiuchus is north of the ecliptic — however, there are a few stars of Ophiuchus which are south of the ecliptic. Ptolemy recognised 4 of them, which are today known as 36 Oph, 42 θ Oph, 44 Oph and 51 Oph, and he recognised that they were south of the path of the sun through the sky. Thus, although the 1930 decision by the International Astronomical Union to adopt constellation boundaries is a common reason given by astrologers for the inconsistency, Ophiuchus as a recognised zodiacal constellation predates this IAU decision by at least 1,700 years.

In modern astronomy, the zodiacal constellations, like all constellations, are recognized as chance visual groupings of stars, with no natural significance. In most cases they are not groupings of stars in three-dimensional space. In a few cases, parts of constellations are made up of stars that are close in space as well as in the sky. We see the sky without any perception of its depth; two stars that are neighbours in a constellation are usually three-dimensionally not close to each other. Star clusters and star systems are exceptions.

Zodiac as a Calendar

The concept of the zodiac was originated by the Babylonians certainly before 2000 BC as a method of visualizing the passage of time. The zodiac worked as a symbolic calendar. It was divided into twelve parts as suggested by the appearance of 12 moons in a year. The signs are geometric divisions of the celestial sphere, each corresponding to one twelfth of a year.

The signs of the zodiac, as enumerated by Egyptian astronomer, Ptolemy, in the 2nd-century AD, are the ones we know today. The same names are used for both signs in astrology and for constellations in astronomy, but it's important to make a distinction between signs and constellations. Signs are geometric sections, each 30° wide, corresponding with particular periods of time of the year, but which don't necessarily physically correspond with the constellations of the same name.

By the time of Ptolemy the zodiac was already at least two thousand years old. But together with its burgeoning astrological use the basic function and structure of the "calendar of the zodiac" remained. The sign of Aries marks the beginning of the year at the Northern Hemisphere vernal equinox. The retreating crab in Cancer represents the retreat of the Sun from its farthest northern point at the time of the Northern Hemisphere summer solstice. Leo, the symbol of fire, represents summer heat. The scales of Libra signify the balance between day and night at the autumnal equinox. The decline of the sun's power is represented in Scorpio by the scorpion, the symbol of darkness. The water-bearer, Aquarius, represents the rainy season which, in Egypt, meant the yearly flooding of the Nile. The fishes of Pisces, symbolize the return of life and the resumption of agriculture.

The concept of the zodiac spread from Babylonia to Greece and, from there, to Egypt where the Egyptians substituted their own symbolism. Aries became the Fleece. Two Sprouting Plants replaced the twins of Gemini. Cancer was re-named Scarabaeus. Leo became the Knife and Libra the Mountain of the Sun. Sagittarius was reduced to just an arrow. Capricorn became the image of life, represented by a mirror. Scorpio became a serpent. Aquarius became simply water, while Taurus, Virgo and Pisces were not changed.

Western Tropical astrology uses the signs fixed to the seasons but because of the precession of the Earth's equinoxes since the time of Ptolemy the Sun's position in the actual zodiac constellations is now approx 22 days out of alignment and this difference is increasing. Hindu astrologers maintained a tradition of actual sky observation and have continually adjusted their zodiac to approximately align with the stars and so have abandoned the link between the zodiac and the calendar. During the twentieth century some western Sidereal astrologers began to realign their work to the actual stars and also abandoned the link with the calendar.

Since Ptolemy's time there has been significant settlement in the Southern hemisphere and for people in this region the symbolism of the signs is at odds with their actual experience of the seasons.


A Sphinx is an iconic image of a recumbent lion with a human head, invented by the Egyptians of the Old Kingdom, but a cultural import in archaic Greek mythology, where it received its name (Greek Σφινξ, "strangler"). The best known is the Great Sphinx of Giza.

Egyptian Sphinx

The Egyptian sphinx is an ancient iconic mythical creature usually comprised of a recumbent lion – an animal with sacred solar associations – with a human head, usually that of a pharaoh.

The largest and most famous is the Great Sphinx of Giza, sited on the Giza Plateau on the west bank of the Nile River, facing due east, with a small temple between its paws. The face of the Great Sphinx is believed to be the head of the pharaoh Khafra (often known by the Hellenized, transformed by the Greeks, version of his name, Chephren), which would date its construction to the Fourth Dynasty (2723 BCE – 2563 BCE). However, there are some alternative theories that re-date the Sphinx to pre-Old Kingdom – and, according to one hypothesis, to prehistoric – times. Other famous Egyptian sphinxes include the alabaster sphinx of Memphis, currently located within the open-air museum at that site; and the ram-headed sphinxes (criosphinxes), representing the god Amun, that line either side of the three-kilometer route linking the complexes of Luxor Temple and Karnak in Luxor (ancient Thebes), of which there were originally some nine hundred.
What names ancient Egyptians called the statues is unknown. The Arabic name of the Great Sphinx, Abu al-Hôl, translates as "Father of Terror". The Greek name "Sphinx" was applied to it in Antiquity though it has the head of a man, not a woman.

Greek Sphinx

There was a single Sphinx in Greek mythology, a unique demon of destruction and bad luck, according to Hesiod a daughter of the Chimaera and Orthrus, or, according to others, of Typhon and Echidna— all of these chthonic figures. She was represented in vase-painting and bas-reliefs most often seated upright rather than recumbent, as a winged lion with a woman's head; or she was a woman with the paws, claws and breasts of a lion, a serpent's tail and birdlike wings. Hera or Ares sent the Sphinx from her Ethiopian homeland (for the Greeks remembered the Sphinx's foreign origins) to sit outside Thebes and ask all passersby history's most famous riddle: "Which creature in the morning goes on four feet, at noon on two, and in the evening upon three?" She strangled anyone unable to answer. The word "sphinx" comes from the Greek Σφινξ, Sphinx, apparently from the verb σφινγω, sphingo, meaning "to strangle". Oedipus solved the riddle: man – he crawls on all fours as a baby, then walks on two feet as an adult, and walks with a cane in old age. Bested at last, the Sphinx then threw herself from her high rock and died. Other versions tell that she devoured herself. In fact, the exact riddle asked by the Sphinx was not specified by early tellers of the story and was not standardized as the one given above until much later in Greek history.

Thus Oedipus can be recognized as a liminal or "threshold" figure, helping effect the transition between the old religious practices, represented by the Sphinx, and new, Olympian ones.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Precession", Wikipedia article "Zodiac" and Wikipedia article "Sphinx".