Open Course : Astronomy : Introduction : Lecture 3 : Motion of the Earth Look in the calendar, and bring me word. -- Shakespeare, Julius Caesar 3.1 The Solar System Viewpoint (Discovering the Universe, 5th ed., §1-4, §1-6) We now know that the diurnal motion of the stars and the Sun is due to the Earth's rotation. In addition, the movement of the Sun along the ecliptic is actually because of the Earth's revolution around the Sun. Let's now consider the point of view where we are fixed with respect to the stars, located above (north of) the Earth, looking down on it and observing these motions. First we notice that, looking down on the Earth's north pole, it is rotating counterclockwise. Such a rotation is essentially a definition of a "north pole". The side of the Earth facing the Sun is in daylight, and the side away from the Sun is at night. Twelve noon would be halfway through the daylight portion, and twelve midnight would be on the opposite side of the Earth, halfway through the night portion. The Sun sets around 6 P.M.

as we are carried into the dark side, and rises around 6 A.M. as we are carried back into daylight. Since the Sun rises in the east and sets in the west, these directions must be defined in terms of the rotation: east is in the direction of rotation and west is opposite to that direction, no matter where we stand on the surface of the Earth. Continuing further "north", we are able to see the Earth's orbit around the Sun. The Earth's orbit is very nearly circular, and it defines a plane in space called the plane of the ecliptic. As the Earth moves around the orbit, we say that the Earth revolves around the Sun (to distinguish this motion from rotation). The Earth's revolution is in the same counterclockwise direction as its rotation. Because of the revolution of the Earth, stars shift their position relative to the Sun. For example, in the picture at the right (representing the passage of about two months' time), a star which was overhead at midnight (i.e. directly opposite the Sun) is now overhead at a different time. Question: about what time is it in the second position?

As a result of the Earth's revolution, from day to day a particular star will transit (or rise, or set) at earlier and earlier times. This is the same 4 min/day differentiating the sidereal day from the synodic day . 3.2 The Tilt of the Earth's Axis (Discovering the Universe, 5th ed., §1-6) Moving from directly above the Earth's orbit down outside one edge of the orbit, we can get a perspective view. We then observe that, with respect to the perpendicular to the ecliptic plane (which points to orbital north), the Earth's axis is tilted at an angle of 23.5°: Equivalently, we can say that the Earth's equator is at an angle of 23.5° to the ecliptic plane. The tilt angle is fixed, so the Earth's axis maintains the same orientation with respect to the stars as the Earth revolves around the Sun. When the Earth's north pole is tilted directly towards the Sun, the latter is highest in the sky (in the northern hemisphere), which is what we called the summer solstice .

Here in Atlanta, the Sun is 33.4° - 23.5° = 10.2° away from the zenith at the summer solstice. When the north pole is tilted directly away from the Sun, the latter is lowest in the sky (in the northern hemisphere), which is the winter solstice . Here in Atlanta, the Sun is 33.4° + 23.5° = 57.2° away from the zenith at the winter solstice. As before, the intermediate positions are the vernal and autumnal equinoxes. Here in Atlanta, the Sun is 33.7° away from the zenith at the equinoxes. Note that (in the northern hemisphere) daytime (the light part of the circle the person is standing on) is longest at the summer solstice, and it is shortest at the winter solstice. Question: what effect will this have on daily temperature? Daytime and nighttime have roughly equal length at the equinoxes, hence the name,which means "equal night".

3.3 Precession (Discovering the Universe, 5th ed., §1-7) The Earth is not a perfect sphere; instead, it is slightly oblate, i.e. it bulges in the middle along the equator. This bulge is due to its rotation and the fact that it is not completely rigid. As a result, the equatorial diameter is 43 Km greater than the polar diameter, a difference of 0.34%. Because the force of gravity weakens with distance, the Sun and Moon have non-uniform gravitational forces on the Earth, pulling harder on the near side of the bulge than on the far side. This differential gravitational force is called a tidal force. Basically, the Sun and Moon try to "straighten" the rotation axis to bring it in line with the orbital axis. However, instead of straightening, the Earth's rotation axis precesses, i.e. it exhibits a slow, conical motion around the orbital axis. Precession is the same effect you see with a top. As long as it is spinning, the top does not fall over, and likewise the Earth's axis won't straighten.

The Earth's precession is a very small effect; it takes 26,000 years for the axis to make one full circle! Currently the Earth's axis points within a degree of the star Polaris , and it will slowly get closer until around the year 2100, when it reaches a minimum separation of 27 minutes of arc. Almost 5000 years ago the Earth's axis pointed towards the star Thuban in the constellation of Draco, and this star was used by the ancient Egyptians as their pole star. In 6,000 years the Earth's axis will point towards the star Alderamin in Cepheus, and in 12,000 years it will be near Vega in Lyra. The Earth's precession can be easily observed by standing at the Earth's north pole, where the north celestial pole is at the zenith, and watching how that point changes over time (note the year in the lower-left corner): The circle traced out by the north celestial pole can also be observed on the celestial sphere. Two different positions, now and 13,000 years in the future, are noted in the picture at the right.

As the precession of the axis occurs, the orientation of the celestial equator will also change, since it is necessarily perpendicular to the axis. However, the ecliptic is fixed on the sphere. As a result, the intersections between the celestial equator and the ecliptic, the equinoxes, move along the ecliptic 50 arc sec (3.3 sec R.A.) per year. The vernal equinox moves in the direction shown. Currently, the vernal equinox is in Pisces; 2000 years ago it was in Aries; in another 1000 years, it will move into Aquarius. This movement of the celestial equator relative to the ecliptic is called precession of the equinoxes. Obviously, this effect is so slow that it is only observable over many years. Precession was discovered by the Greek astronomer Hipparchus , who had access to several centuries of Greek and Babylonian records. 3.4 The Calendar (Discovering the Universe, 5th ed., §1-5) The sidereal year is defined to be the time for the Sun to return to the same position against the stars.

The sidereal year is equal to 365.25 d + 9 min 10s. The tropical year is the time for the Sun to return to the same position relative to the Earth's axis, e.g. summer solstice to summer solstice. Because of precession, the tropical year is 20 min 24 s shorter than the sidereal year, equal to 365.25 d - 11 min 14 s. Neither of these is an integer number of days. The early Roman calendar (~300 B.C.) had 365 days per year, so it was short by roughly one day every four years. As a result, the date of the equinoxes and solstices moved forward on the calendar. In the original Roman calendar the vernal equinox was on March 24. By 45 B.C. it had moved into late May, so the first Roman Emperor Julius Caesar subtracted 63 days from the calendar to bring the equinoxes back to their traditional dates (more than two months were therefore "redone").

To keep the equinoxes fixed, Caesar decreed that every four years an extra leap day would be added to the calendar, at the end of the year (February). A year with a leap day added is called a leap year, and this calendar is known as the Julian Calendar. Then, the calendar was too long by 11 min 14 s /year. Even this small amount can build up with time, and the vernal equinox began to move backward on the calendar, about 1 day every 128 years. By 325 A.D. the vernal equinox had moved three days to its current location on March 21. At this time the Roman Emperor Constantine I convened the Council of Nicaea, to establish dates for the Christian holidays. Easter, in particular, was based on the date of the vernal equinox. The vernal equinox continued to move backward on the calendar. By 1582 the vernal equinox had moved another ten days. On the advice of astronomers, Pope Gregory established a new calendar system which accounted for the extra 11 min 14 s.

In the Julian calendar, century years had always been leap years; in the new calendar, that would no longer be true, except in years divisible by 400: 1600 leap year 1700 not a leap year 1800 not a leap year 1900 not a leap year 2000 leap year 2100 not a leap year .... Precession of the Equinoxes - Age of Aquarius - Crystalinks Precession of the Equinoxes In astronomy, axial precession is a gravity-induced, slow and continuous change in the orientation of an astronomical body's rotational axis. In particular, it refers to the gradual shift in the orientation of Earth's axis of rotation, which, like a wobbling top, traces out a pair of cones joined at their apices in a cycle of approximately 26,000 years (called a Great or Platonic Year in astrology). The term "precession" typically refers only to this largest secular motion; other changes in the alignment of Earth's axis - nutation and polar motion - are much smaller in magnitude.

Earth's precession was historically called precession of the equinoxes because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the motion of the Sun along the ecliptic. This term is still used in non-technical discussions, that is, when detailed mathematics are absent. Historically, Hipparchus is credited with discovering precession of the equinoxes. The exact dates of his life are not known, but astronomical observations attributed to him by Ptolemy date from 147 BC to 127 BC. With improvements in the ability to calculate the gravitational force between planets during the first half of the 19th century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession instead of precession of the equinoxes. Lunisolar precession is caused by the gravitational forces of the Moon and Sun on Earth's equatorial bulge, causing Earth's axis to move with respect to inertial space.

Planetary precession (actually an advance) is due to the small angle between the gravitational force of the other planets on Earth and its orbital plane (the ecliptic), causing the plane of the ecliptic to shift slightly relative to inertial space. Lunisolar precession is about 500 times larger than planetary precession. In addition to the Moon and Sun, the other planets also cause a small movement of Earth's axis in inertial space, making the contrast in the terms lunisolar versus planetary misleading, so in 2006 the International Astronomical Union recommended that the dominant component be renamed the precession of the equator and the minor component be renamed precession of the ecliptic, but their combination is still named general precession. Causes The precession of the equinoxes is caused by the gravitational forces of the Sun and the Moon, and to a lesser extent other bodies, on the Earth. It was first explained by Sir Isaac Newton. Axial precession is similar to the precession of a spinning top. In both cases, the applied force is due to gravity. For a spinning top, this force tends to be almost parallel to the rotation axis.

For the Earth, however, the applied forces of the Sun and the Moon are nearly perpendicular to the axis of rotation. The Earth is not a perfect sphere but an oblate spheroid, with an equatorial diameter about 43 kilometers larger than its polar diameter. Because of the Earth's axial tilt, during most of the year the half of this bulge that is closest to the Sun is off-center, either to the north or to the south, and the far half is off-center on the opposite side. The gravitational pull on the closer half is stronger, since gravity decreases with distance, so this creates a small torque on the Earth as the Sun pulls harder on one side of the Earth than the other. The axis of this torque is roughly perpendicular to the axis of the Earth's rotation so the axis of rotation precesses. If the Earth were a perfect sphere, there would be no precession. This average torque is perpendicular to the direction in which the rotation axis is tilted away from the ecliptic pole, so that it does not change the axial tilt itself. The magnitude of the torque from the sun (or the moon) varies with the gravitational object's alignment with the Earth's spin axis and approaches zero when it is orthogonal.

Although the above explanation involved the Sun, the same explanation holds true for any object moving around the Earth, along or close to the ecliptic, notably, the Moon. The combined action of the Sun and the Moon is called the lunisolar precession. In addition to the steady progressive motion (resulting in a full circle in about 25,700 years) the Sun and Moon also cause small periodic variations, due to their changing positions. These oscillations, in both precessional speed and axial tilt, are known as the nutation. The most important term has a period of 18.6 years and an amplitude of less than 20 seconds of arc. In addition to lunisolar precession, the actions of the other planets of the solar system cause the whole ecliptic to rotate slowly around an axis which has an ecliptic longitude of about 174� measured on the instantaneous ecliptic. This so-called planetary precession shift amounts to a rotation of the ecliptic plane of 0.47 seconds of arc per year (more than a hundred times smaller than lunisolar precession). The sum of the two precessions is known as the general precession.

Effects The precession of the Earth's axis has a number of observable effects. First, the positions of the south and north celestial poles appear to move in circles against the space-fixed backdrop of stars, completing one circuit in 25,772 Julian years (2000 rate). Thus, while today the star Polaris lies approximately at the north celestial pole, this will change over time, and other stars will become the "north star". The south celestial pole currently lacks a bright star to mark its position, but over time precession will also cause bright stars to become south stars. As the celestial poles shift, there is a corresponding gradual shift in the apparent orientation of the whole star field, as viewed from a particular position on Earth. Secondly, the position of the Earth in its orbit around the Sun at the solstices, equinoxes, or other time defined relative to the seasons, slowly changes. For example, suppose that the Earth's orbital position is marked at the summer solstice, when the Earth's axial tilt is pointing directly towards the Sun.

One full orbit later, when the Sun has returned to the same apparent position relative to the background stars, the Earth's axial tilt is not now directly towards the Sun: because of the effects of precession, it is a little way "beyond" this. In other words, the solstice occurred a little earlier in the orbit. Thus, the tropical year, measuring the cycle of seasons (for example, the time from solstice to solstice, or equinox to equinox), is about 20 minutes shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars. Note that 20 minutes per year is approximately equivalent to one year per 25,772 years, so after one full cycle of 25,772 years the positions of the seasons relative to the orbit are "back where they started". (In actuality, other effects also slowly change the shape and orientation of the Earth's orbit, and these, in combination with precession, create various cycles of differing periods; see also Milankovitch cycles.

The magnitude of the Earth's tilt, as opposed to merely its orientation, also changes slowly over time, but this effect is not attributed directly to precession.) For identical reasons, the apparent position of the Sun relative to the backdrop of the stars at some seasonally fixed time, say the vernal equinox, slowly regresses a full 360� through all twelve traditional constellations of the zodiac, at the rate of about 50.3 seconds of arc per year (approximately 360 degrees divided by 25,772), or 1 degree every 71.6 years. Age of Aquarius We are allegedly in the Age of Aquarius. According to astrological mysticism, there will be unusual harmony and understanding in the world. Those who follow that belief system see it as a turning point in human consciousness in which balance is restored by consciously moving beyond the physical body. The Aquarius symbol is metaphoric in content - meaning 'closure in water'. Water represents the collective unconsciousness or consciousness hologram which creates the grid programs of our physical reality.

Many connect the Age of Aquarius with the return of the goddess, priestess, or feminine energies - those that vibrate above/faster than physical frequency. This is the return to higher consciousness, the awakening of higher mind and thought in the alchemy of time. The Age of Aquarius is the polar opposite of the Age of Leo - in the bipolar reality in which we experience the physical experiment of time and illusion through the consciousness projection of the eye or All Seeing Eye. Age of Leo -> approximately 13,000 years later -> Age of Aquarius History Hellenistic World Hipparchus Though there is still-controversial evidence that Aristarchus of Samos possessed distinct values for the sidereal and tropical years as early as c. 280 BC, the discovery of precession is usually attributed to Hipparchus (190-120 BC) of Rhodes or Nicaea, a Greek astronomer. According to Ptolemy's Almagest, Hipparchus measured the longitude of Spica and other bright stars.

Comparing his measurements with data from his predecessors, Timocharis (320-260 BC) and Aristillus (~280 BC), he concluded that Spica had moved 2° relative to the autumnal equinox. He also compared the lengths of the tropical year (the time it takes the Sun to return to an equinox) and the sidereal year (the time it takes the Sun to return to a fixed star), and found a slight discrepancy. Hipparchus concluded that the equinoxes were moving ("precessing") through the zodiac, and that the rate of precession was not less than 1° in a century, in other words completing a full cycle in no more than 36000 years. Virtually all Hipparchus' writings are lost, including his work on precession. They are mentioned by Ptolemy, who explains precession as the rotation of the celestial sphere around a motionless Earth. It is reasonable to assume that Hipparchus, like Ptolemy, thought of precession in geocentric terms as a motion of the heavens.

Ptolemy The first astronomer known to have continued Hipparchus' work on precession is Ptolemy in the 2nd century. Ptolemy measured the longitudes of Regulus, Spica, and other bright stars with a variation of Hipparchus' lunar method that did not require eclipses. Before sunset, he measured the longitudinal arc separating the Moon from the Sun. Then, after sunset, he measured the arc from the Moon to the star. He used Hipparchus' model to calculate the Sun's longitude, and made corrections for the Moon's motion and its parallax (Evans 1998, pp. 251-255). Ptolemy compared his own observations with those made by Hipparchus, Menelaus of Alexandria, Timocharis, and Agrippa. He found that between Hipparchus' time and his own (about 265 years), the stars had moved 2°40', or 1° in 100 years (36" per year; the rate accepted today is about 50" per year or 1° in 72 years).

He also confirmed that precession affected all fixed stars, not just those near the ecliptic, and his cycle had same period of 36000 years as found by Hipparchus. Other Authors Most ancient authors did not mention precession and perhaps did not know of it. Besides Ptolemy, the list includes Proclus, who rejected precession, and Theon of Alexandria, a commentator on Ptolemy in the 4th century, who accepted Ptolemy's explanation. Theon also reports an alternate theory: According to certain opinions ancient astrologers believe that from a certain epoch the solstitial signs have a motion of 8° in the order of the signs, after which they go back the same amount. . . . (Dreyer 1958, p. 204) Instead of proceeding through the entire sequence of the zodiac, the equinoxes "trepidated" back and forth over an arc of 8°. The theory of trepidation is presented by Theon as an alternative to precession. Alternative Theories Babylonians Various assertions have been made that other cultures discovered precession independent of Hipparchus.

At one point it was suggested that the Babylonians may have known about precession. According to Al-Battani, the Chaldean astronomers had distinguished the tropical and sidereal year (the value of precession is equivalent to the difference between the tropical and sidereal years). He stated that they had, around 330 BC, an estimation for the length of the sidereal year to be SK = 365 days 6 hours 11 min (= 365.258 days) with an error of (about) 2 min. It was claimed by P. Schnabel in 1923 that Kidinnu theorized about precession in 315 BC. Otto Neugebauer's work on this issue in the 1950s superseded Schnabel's (and earlier, Kugler's) theory of a Babylonian discoverer of precession. In recent decades, the hypothesis was revived and amplified in de Santillana and von Dechend's Hamlet's Mill (Harvard University Press, 1969).

In an application of extreme Panbabylonism to archaeoastronomy, they proposed that a Babylonian mythological account of the precession gave rise via diffusion to similar myths around the world, even as far away as China, Polynesia, and North America. While their theory has not been widely accepted in academia, it anticipated the recent popular revival of interest in precessional archeoastronomy. Ancient Egyptians Similar claims have been made that precession was known in Ancient Egypt prior to the time of Hipparchus, but these remain controversial. Some buildings in the Karnak temple complex, for instance, were allegedly oriented towards the point on the horizon where certain stars rose or set at key times of the year. A few centuries later, when precession made the orientations obsolete, the temples would be rebuilt. However, the observation that a stellar alignment has grown wrong does not mean that the Egyptians understood that the stars moved across the sky at the rate of about one degree per 72 years. Nonetheless, they kept accurate calendars and if they recorded the date of the temple reconstructions it would be a fairly simple matter to plot the rough precession rate.

The Dendera Zodiac, a star-map from the Hathor temple at Dendera from a late (Ptolemaic) age, supposedly records precession of the equinoxes (Tompkins 1971). In any case, if the ancient Egyptians knew of precession, their knowledge is not recorded in surviving astronomical texts. Michael Rice wrote in his Egypt's Legacy, "Whether or not the ancients knew of the mechanics of the Precession before its definition by Hipparchos the Bithynian in the second century BC is uncertain, but as dedicated watchers of the night sky they could not fail to be aware of its effects." (p. 128) Rice believes that "the Precession is fundamental to an understanding of what powered the development of Egypt" (p. 10), to the extent that "in a sense Egypt as a nation-state and the king of Egypt as a living god are the products of the realization by the Egyptians of the astronomical changes effected by the immense apparent movement of the heavenly bodies which the Precession implies." (p.

56) Following Carl Jung, Rice says that "the evidence that the most refined astronomical observation was practiced in Egypt in the third millennium BC (and probably even before that date) is clear from the precision with which the Pyramids at Giza are aligned to the cardinal points, a precision which could only have been achieved by their alignment with the stars. This fact alone makes Jung's belief in the Egyptians' knowledge of the Precession a good deal less speculative than once it seemed." (p. 31) The Egyptians also, says Rice, were "to alter the orientation of a temple when the star on whose position it had originally been set moved its position as a consequence of the Precession, something which seems to have happened several times during the New Kingdom." (p. 170) The notion that an ancient Egyptian priestly elite tracked the precessional cycle over many thousands of years plays a central role in the theories expounded by Robert Bauval and Graham Hancock in their 1996 book "Keeper of Genesis.' The authors claim that the ancient Egyptians' monumental building projects functioned as a map of the heavens, and that associated rituals were an elaborate earthly acting-out of celestial events.

In particular, the rituals symbolized the "turning back" of the precessional cycle to a remote ancestral time known as Zep Tepi ("first time") which, the authors calculate, dates to around 10,500 BC. Mayans There has been speculation that the Mesoamerican Long Count calendar is somehow calibrated against the precession, but this view is not held by professional scholars of Mayan civilization. Hindu A 12th century text by Bhaskara II says: "sampat revolves negatively 30000 times in a Kalpa of 4320 million years according to Suryasiddhanta, while Munjala and others say ayana moves forward 199669 in a Kalpa, and one should combine the two, before ascertaining declension, ascensional difference, etc." Lancelot Wilkinson translated the last of these three verses in a too concise manner to convey the full meaning, and skipped the portion combine the two which the modern Hindi commentary has brought to the fore.

According to the Hindi commentary, the final value of period of precession should be obtained by combining +199669 revolutions of ayana with -30000 revolutions of sampaat to get +169669 per Kalpa, i.e. one revolution in 25461 years, which is near the modern value of 25771 years. Moreover, Munjala's value gives a period of 21636 years for ayana's motion, which is the modern value of precession when anomalistic precession is also taken into account. The latter has a period of 136000 years now, but Bhaskar-II gives its value at 144000 years (30000 in a Kalpa), calling it sampan. Bhaskar-II did not give any name of the final term after combining the negative sampan with the positive ayana. But the value he gave indicates that by ayana he meant precession on account of the combined influence of orbital and anomalistic precessions, and by sampan he meant the anomalistic period, but defined it as equinox.

His language is a bit confused, which he clarified in his own Vasanabhashya commentary Siddhanta Shiromani]by saying that Suryasiddhanta was not available and he was writing on the basis of hearsay. Bhaskar-II did not give his own opinion, he merely cited Suryasiddhanta, Munjala and unnamed "others". Yu Xi Yu Xi (4th century CE) was the first Chinese astronomer to mention precession. He estimated the rate of precession as 1° in 50 years (Pannekoek 1961, p. 92). Middle Ages and Renaissance In medieval Islamic astronomy, the Zij-i Ilkhani compiled at the Maragheh observatory set the precession of the equinoxes at 51 arc seconds per annum, which is very close to the modern value of 50.2 arc seconds. In the Middle Ages, Islamic and Latin Christian astronomers treated "trepidation" as a motion of the fixed stars to be added to precession. This theory is commonly attributed to the Arab astronomer Thabit ibn Qurra, but the attribution has been contested in modern times.

Nicolaus Copernicus published a different account of trepidation in De revolutionibus orbium coelestium (1543). This work makes the first definite reference to precession as the result of a motion of the Earth's axis. Copernicus characterized precession as the third motion of the earth. Modern Day Over a century later precession was explained in Isaac Newton's Philosophiae Naturalis Principia Mathematica (1687) to be a consequence of gravitation (Evans 1998, p. 246). However, Newton's original precession equations did not work and were revised considerably by Jean le Rond d'Alembert and subsequent scientists. Hipparchus' Discovery Hipparchus gave an account of his discovery in On the Displacement of the Solsticial and Equinoctial Points (described in Almagest III.1 and VII.2). He measured the ecliptic longitude of the star Spica during lunar eclipses and found that it was about 6° west of the autumnal equinox.

By comparing his own measurements with those of Timocharis of Alexandria (a contemporary of Euclid who worked with Aristillus early in the 3rd century BC), he found that Spica's longitude had decreased by about 2° in about 150 years. He also noticed this motion in other stars. He speculated that only the stars near the zodiac shifted over time. Ptolemy called this his "first hypothesis" (Almagest VII.1), but did not report any later hypothesis Hipparchus might have devised. Hipparchus apparently limited his speculations because he had only a few older observations, which were not very reliable. Why did Hipparchus need a lunar eclipse to measure the position of a star? The equinoctial points are not marked in the sky, so he needed the Moon as a reference point. Hipparchus had already developed a way to calculate the longitude of the Sun at any moment. A lunar eclipse happens during Full moon, when the Moon is in opposition. At the midpoint of the eclipse, the Moon is precisely 180° from the Sun. Hipparchus is thought to have measured the longitudinal arc separating Spica from the Moon.

To this value, he added the calculated longitude of the Sun, plus 180° for the longitude of the Moon. He did the same procedure with Timocharis' data (Evans 1998, p. 251). Observations like these eclipses, incidentally, are the main source of data about when Hipparchus worked, since other biographical information about him is minimal. The lunar eclipses he observed, for instance, took place on April 21, 146 BC, and March 21, 135 BC (Toomer 1984, p. 135 n. 14). Hipparchus also studied precession in On the Length of the Year. Two kinds of year are relevant to understanding his work. The tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). The sidereal year is the length of time that the Sun takes to return to the same position with respect to the stars of the celestial sphere.

Precession causes the stars to change their longitude slightly each year, so the sidereal year is longer than the tropical year. Using observations of the equinoxes and solstices, Hipparchus found that the length of the tropical year was 365+1/4-1/300 days, or 365.24667 days (Evans 1998, p. 209). Comparing this with the length of the sidereal year, he calculated that the rate of precession was not less than 1° in a century. From this information, it is possible to calculate that his value for the sidereal year was 365+1/4+1/144 days (Toomer 1978, p. 218). By giving a minimum rate he may have been allowing for errors in observation. To approximate his tropical year Hipparchus created his own lunisolar calendar by modifying those of Meton and Callippus in On Intercalary Months and Days (now lost), as described by Ptolemy in the Almagest III.1 (Toomer 1984, p. 139).

The Babylonian calendar used a cycle of 235 lunar months in 19 years since 499 BC (with only three exceptions before 380 BC), but it did not use a specified number of days. The Metonic cycle (432 BC) assigned 6,940 days to these 19 years producing an average year of 365+1/4+1/76 or 365.26316 days. The Callippic cycle (330 BC) dropped one day from four Metonic cycles (76 years) for an average year of 365+1/4 or 365.25 days. Hipparchus dropped one more day from four Callipic cycles (304 years), creating the Hipparchic cycle with an average year of 365+1/4-1/304 or 365.24671 days, which was close to his tropical year of 365+1/4-1/300 or 365.24667 days.

The three Greek cycles were never used to regulate any civil calendar - they only appear in the Almagest in an astronomical context. We find Hipparchus' mathematical signatures in the Antikythera Mechanism, an ancient astronomical computer of the 2nd century BC. The mechanism is based on a solar year, the Metonic Cycle, which is the period the Moon reappears in the same star in the sky with the same phase (full Moon appears at the same position in the sky approximately in 19 years), the Callipic cycle (which is four Metonic cycles and more accurate), the Saros cycle and the Exeligmos cycles (three Saros cycles for the accurate eclipse prediction). The study of the Antikythera Mechanism proves that the ancients have been using very accurate calendars based on all the aspects of solar and lunar motion in the sky. In fact the Lunar Mechanism which is part of the Antikythera Mechanism depicts the motion of the Moon and its phase, for a given time, using a train of four gears with a pin and slot device which gives a variable lunar velocity that is very close to the second law of Kepler, i.e.

it takes into account the fast motion of the Moon at perigee and slower motion at apogee. This discovery proves that Hipparchus mathematics were much more advanced than Ptolemy describes in his books, as it is evident that he developed a good approximation of Kepler's second law. Mithraism Mithraism was a mystery religion or school based on the worship of the god Mithras. Many underground temples were built in the Roman Empire from about the 1st century BC to the 5th century AD. Understanding Mithraism has been made difficult by the near-total lack of written descriptions or scripture; the teachings must be reconstructed from iconography found in mithraea (a mithraeum was a cave or underground meeting place that often contained bas reliefs of Mithras, the zodiac and associated symbols). Until the 1970s most scholars followed Franz Cumont in identifying Mithras with the Persian god Mithra. Cumont's thesis was re-examined in 1971, and Mithras is now believed to be a syncretic deity only slightly influenced by Persian religion.

Mithraism is recognized as having pronounced astrological elements, but the details are debated. One scholar of Mithraism, David Ulansey, has interpreted Mithras (Mithras Sol Invictus - the unconquerable sun) as a second sun or star that is responsible for precession. He suggests the cult may have been inspired by Hipparchus' discovery of precession. Part of his analysis is based on the tauroctony, an image of Mithras sacrificing a bull, found in most of the temples. According to Ulansey, the tauroctony is a star chart. Mithras is a second sun or hyper-cosmic sun and/or the constellation Perseus, and the bull is Taurus, a constellation of the zodiac. In an earlier astrological age, the vernal equinox had taken place when the Sun was in Taurus. The tauroctony, by this reasoning, commemorated Mithras-Perseus ending the "Age of Taurus" (about 2000 BC based on the Vernal Equinox � or about 11,500 BC based on the Autumnal Equinox).

The iconography also contains two torch bearing boys (Cautes and Cautopates) on each side of the zodiac. Ulansey, and Walter Cruttenden in his book Lost Star of Myth and Time, interpret these to mean ages of growth and decay, or enlightenment and darkness; primal elements of the cosmic progression. Thus Mithraism is thought to have something to do with the changing ages within the precession cycle or Great Year (Plato's term for one complete precession of the equinox). Changing Pole Stars Precession of Earth's axis around the north ecliptical pole Precession of Earth's axis around the south ecliptical pole A consequence of the precession is a changing pole star. Currently Polaris is extremely well-suited to mark the position of the north celestial pole, as it is about a half degree away from it and it is a moderately bright star (visual magnitude is 2.1 (variable)). On the other hand Thuban in the constellation Draco, which was the pole star in 3000 BC is much less conspicuous at magnitude 3.67 (one-fifth as bright as Polaris); today it is all but invisible in light-polluted urban skies.

The brilliant Vega in the constellation Lyra is often touted as the best Northstar, when it fulfilled that role around 12000 BC and will do so again around the year AD 14000. In reality it never comes closer than 5� to the pole. When Polaris will be the north star again around 27800 AD, due to its proper motion it will be farther away from the pole then than it is now, while in 23600 BC it came closer to the pole. To find the south celestial pole in the sky at this moment, one is less lucky, as that area is a particularly bland portion of the sky, and the nominal south pole star is Sigma Octantis, which with magnitude 5.5 is barely visible even under a properly dark sky. However that will change in the 80th to 90th century, when the south celestial pole travels through the False cross. It is also seen from the starmap that the south pole, nicely pointed to by the Southern cross for the last 2000 years or so, is moving towards that constellation.

By consequence it is now no longer visible from subtropical northern latitudes as it was in the time of the ancient Greeks. Still pictures like these, found in many astronomy books, are only first approximations as they do not take into account the variable speed of the precession, the variable obliquity of the ecliptic, the planetary precession (which makes not the ecliptic pole the centre, but a circle about 6� away from it) and the proper motions of the stars. Polar Shift and Equinoxes Shift Precessional movement as seen from 'outside' the celestial sphere. The rotation axis of the Earth describes over a period of about 25800 years a small circle (blue) among the stars, centred around the ecliptic northpole (blue E) and with an angular radius of about 23.4�: the angle known as the obliquity of the ecliptic. The orange axis was the Earth's rotation axis 5000 years ago when it pointed to the star Thuban. The yellow axis, pointing to Polaris is the situation now. Note that when the celestial sphere is seen from outside constellations appear in mirror image.

Also note that the daily rotation of the Earth around its axis is opposite to the precessional rotation. When the polar axis precesses from one direction to another, then the equatorial plane of the Earth (indicated with the circular grid around the equator) and the associated celestial equator will move too. Where the celestial equator intersects the ecliptic (red line) there are the equinoxes. As seen from the drawing, the orange grid, 5000 years ago one intersection of equator and ecliptic, the vernal equinox was close to the star Aldebaran of Taurus. By now (the yellow grid) it has shifted (red arrow) to somewhere in the constellation of Pisces. Note that this is an astronomical description of the precessional movement and the vernal equinox position in a given constellation may not imply the astrological meaning of an Age carrying the same name, as they (ages and constellations) only have an exact alignment in the "first point of Aries", meaning once in each ca. 25800 (Great Sidereal Year).

Same picture as above but now from (near) Earth perspective It might not be directly clear to the non-astronomer what the shift of the equinoxes has to do with the precession of the rotation axis of the Earth. The figures to the right try to explain that. The rotation axis of the Earth describes over a period of 25700 years a small circle (blue) among the stars, centred around the ecliptic northpole (blue E) and with an angular radius of about 23.4�: the angle known as the obliquity of the ecliptic. The orange axis was the Earth's rotation axis 5000 years ago when it pointed to the star Thuban. The yellow axis, pointing to Polaris is the situation now. Note that when the celestial sphere is seen from outside (as in the first drawing, an impossibilty of course) constellations appear in mirror image. Also note that the daily rotation of the Earth around its axis is opposite to the precessional rotation.

Of course when the polar axis precesses from one direction to another, then the equatorial plane of the Earth (indicated with the circular grid around the equator) and the associated celestial equator will move too. Where the celestial equator intersects the ecliptic (red line) there are the equinoxes. As seen from the drawing, the orange grid, 5000 years ago one intersection of equator and ecliptic, the vernal equinox was close to the star Aldebaran of Taurus. By now (the yellow grid) it has shifted (red arrow) to somewhere in the constellation of Pisces. This is why the equinoctial shift is a consequence of the precession of the rotation axis of the Earth and the other way around. The second drawing shows the perspective from a near Earth position as seen through a very wide angle lens (from which the apparent distortion). Explanation The precession as a consequence of the torque exerted on Earth by differential gravitation. The precession of the equinoxes is caused by the differential gravitation forces of Sun and Moon on Earth. In popular science books one often finds this explained with the analogy of the precession of a spinning top.

Indeed it is the same physical effect, however, some crucial details differ. In a spinning top it is gravity which causes the top to wobble which in its turn causes precession. The applied force is thus in the first instance parallel to the rotation axis. But for the Earth the applied forces of the Sun and Moon are in the first instance perpendicular to it. So how then can they cause it? The answer is that the forces do not work on the rotation axis. Instead they work on the equatorial bulge; due to its own rotation, the Earth is not a perfect sphere but an oblate spheroid, the equatorial diameter about 43 km larger than the polar. If the Earth were a perfect sphere, there would be no precession. The figure explains how this works. The Earth is given as a perfect sphere (so that all gravitational forces working on it can be taken equal as one force working on its center), and the bulge is approximated to be a torus of mass (blue) around its equator. Green arrows indicate the gravitational forces from the Sun on some extreme points. These forces are not parallel as they all point towards the centre of the Sun.

Therefore the forces working on the northernmost and southernmost parts of the equatorial bulge have a component perpendicular on the ecliptical plane and directed towards it. We find them (small cyan arrows) when the average gravitation force on the centre of the Earth is substracted (because this force will be used as the centripetal force for the Earth in its orbit around the Sun). In all cases in addition to these tangential components there will be also radial components, but they are not shown as they do not contribute to the precession (they contribute to the tides). It is now clear how these tangential forces create a torque (orange), and this torque added to the rotation (magenta) shifts the rotation axis slightly to a new position (yellow). Repeat this again and again, and one sees how the axis precesses along the white circle, which is centred around the ecliptic pole. It is important to note that the torque is always in the same direction, perpendicular onto the direction in which the rotation axis is tilted away from the ecliptic pole, so that it does not change the axial tilt itself.

It is also important to note that the torque is everywhere the same, whatever position of the Earth is in its orbit around the Sun. The precession is thus always steadily progressing and does not change with the seasons. Although the above explanation involved the Sun, the same story holds true for any object moving around the Earth along (or close to) the ecliptic, i.e. the Moon. The combined action of the Sun and the Moon is called the lunisolar precession. In addition to the steady progressive motion (resulting in a full circle in 25700 years) the Sun and Moon also cause small periodic variations, due to their changing positions. These oscillations, in both precessional speed and axial tilt are known as the nutation. The most important term has a period of 18.6 years and an amplitude of less than 20 arcseconds. In addition to lunisolar precession, the actions of the other planets of the solar system cause the whole ecliptic to slowly rotate around an axis which has an ecliptic longitude of about 174� measured on the instantaneous ecliptic.

This planetary precession shift is only 0.47 arcseconds per year (more than a hundred times smaller than lunisolar precession), and takes place along the instantaneous equator. The sum of the two precessions is known as the general precession. Effects of Axial Precession on the Seasons This 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 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 71 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 to Galileo The priests of ancient Babylonia and Egypt were also pioneer astronomers. They studied the heavens, mapped their constellations, identified the path of the Sun and estimated the periods of the Moon and Sun as they moved across the sky. But it was a Greek astronomer, Hipparchus of Nicea, who made the first major new discovery in astronomy. Comparing observations more than a century apart, Hipparchus proposed that the axis around which the heavens seemed to rotate shifted gradually, though very slowly. Viewed from Earth, the Sun moves around the ecliptic, one full circuit each year. Twice a year, at equinox, day and night are equal and the Sun rises exactly in the east and sets exactly in the west.

Ancient astronomers had no good clocks and could not tell when the day and night had the same length, but they could identify the equinox by the Sun rising exactly in the east and setting exactly in the west. At those times the Sun's position is at one of the intersections between the ecliptic and the celestial equator. Around the year 130 BC, Hipparchus compared ancient observations to his own and concluded that in the preceding 169 years those intersections had moved by 2 degrees. How could Hipparchus know the position of the Sun among the stars so exactly, when stars are not visible in the daytime? By using not the Sun but the shadow cast by the Earth on the moon, during an eclipse of the Moon! During an eclipse, Sun, Earth and Moon form a straight line, and therefore the center of the Earth's shadow is at the point on the celestial sphere which is exactly opposite that of the Sun. "The Dawning of the Age of Aquarius" Hipparchus concluded that the intersection marking the equinox slowly crept forward along the ecliptic, and called that motion "the precession of the equinoxes.

" The rate is about one full circle in 26 000 years. In ancient times the intersection marking the spring equinox was in the constellation of Aries, the ram, and for that reason the intersection (wherever it might be) is still sometimes called "the first point in Aries." Around the year 1 it moved into the constellation of Pisces (pronounced "pie-sees" in the US) and currently it is again in transition, to the constellation of Aquarius, the water carrier. If you ever heard the song "The dawning of the age of Aquarius" from the musical "Hair," that is what it is all about. To astronomers precession is mainly another factor to be taken into account when aiming a telescope or drawing a star chart; but to believers in astrology, the "dawning of the age of Aquarius" is a great portent and may mark the beginning of a completely new and different era . The Precession of the Earth's Axis What does this motion tell us about the Earth's motion in space? If you ever had a spinning top, you know that its axis tends to stay lined up in the same direction--usually, vertically, though in space any direction qualifies.

Precession of a spinning And would suffice Robert Frost Some 2000 years after Hipparchus, in the year 1840. Louis Agassiz, a Swiss scientist, published a book on glaciers, a familiar feature of his homeland--huge rivers of ice created by accumulated snowfall, filling valleys and slowly creeping downwards to their end points, lakes of meltwater (or, in some other countries, the sea). A glacier in Norway. Glaciers leave an imprint on the landscape: they scratch and grind down rocks, and carry loads of gravel, at times even big boulders, from the mountains to the plains, leaving them far from their origins, wherever the ice finally melts. Agassiz, who later became a distinguished professor at Harvard, noted that such imprints existed all over northern Europe, and suggested that the lands now inhabited by Germans, Poles, Russians and others used to be covered by enormous glaciers. America, too, had its glaciers; Cape Cod, for instance, is a left-over pile of glacial gravel. Later geological studies found evidence that such glaciers advanced and retreated several times in the last million years.

The last retreat, a rather abrupt one, occured about 12,000 years ago. The opposite is true south of the equator: the beginning of January occurs there in summer, and therefore one expects southern summers to be hotter, and southern winters colder, than those north of the equator. This effect is however greatly weakened, because by far most of the the southern hemisphere is covered by ocean, and the water tempers and moderates the climate. Right now, northern winter occurs in the part of the Earth's orbit where the north end of the axis points away from the Sun. However, since the axis moves around a cone, 13,000 years from now, in this part of the orbit, it will point towards the Sun, putting it in mid-summer just when the Earth is closest to the Sun. At that time one expects northern climate to be more extreme, and the oceans then have a much smaller effect, since the proportion of land in the northern hemisphere is much larger. Milankovich argued that because winters were colder, more snow fell, feeding the giant glaciers.

Furthermore, he said, since snow was white, it reflected sunlight, and with more severe winters, the snow-covered land warmed up less effectively once winter had ended. Climate is maintained by a delicate balance between opposing factors, and Milankovich argued that this effect alone was enough to upset that balance and cause ice ages. Milankovich was aware that this was just one of several factors, since it turns out that ice ages do not recur every 26,000 year, nor do they seem common in other geological epochs. The eccentricity of the Earth's orbit, which determines the closest approach to the Sun, also changes periodically, as does the inclination of the Earth's axis to the ecliptic. But overall the notion that ice ages may be linked to the motion of the Earth through space may be currently our best guess concerning the causes of ice ages. Postscript, 28 July 1999. The magnitude of the "Milankovich effect" depends on the difference between largest and smallest distances from the Sun.

That, in its turn, depends on the eccentricity of the Earth's orbit, which varies with a 100,000-year cycle, on which a 413,000-year cycle is superposed. J. Rial (Univ. of North Carolina) found signatures of those cycles in the oxygen isotope content of deep-sea sediments, in full agreement with the Milankovich theory. His work is in "Science," vol. 285, p. 564, 23 July 1999; a non-technical explanation "Why the Ice Ages Don't Keep Time " is on pages 503-504 of the same issue. Further note: The sea-bottom results have now been compared to hydrogen isotope ratios in deep boreholes in the ice sheets of Antarctica, which took nearly a million years to accumulate (Science, 11 June 2004, p. 1609). Deep-sea sediments show that in the last million years, but not before, the variation is dominated by a periodicity around 100,000 years.

Its origin, the article states, "is one of the unanswered, yet fundamental questions." Ice cores could help explain it. Exploring Further: Because of the precession of the equinoxes, the position among the stars of the celestial pole--the pivot around which the celestial sphere seems to rotate--traces a circle every 26,000 years of so. The celestial pole is now quite close to the pole star Polaris , but it will not be so in the future, and wasn't in the past. The ancient Egyptians regarded as pole star the star Thuban or "Alpha Draconis," the brightest star (=alpha) in the constellation Draco, the serpent. For more information about the motion of the pole, see here and here . A review article, primarily for scientists: Trends, Rhythms and Aberrations in Global Climate 65 Ma to the Present (Ma is million years), by James Zachos, Mark Pagani, Lisa Sloan, Ellen Thomas and Katharina Billups, "Science" vol 292, p. 686, 27 April 2001.

Goes beyond variations due to the precession of the equinoxes and also includes variations of orbit eccentricity, inclination between spin axis and the ecliptic and in the precession cycle itself. The full scoop on the Milankovich theory (including other periodicities).

Question: It takes roughly how long for the Earth's rotating axis to complete a full circle (precession)?
Answer: 26,000 years