Axial precession

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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, similar to a wobbling top, traces out a pair of cones joined at their apices in a cycle of approximately 26,000 years.[1] The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis – nutation and polar motion – are much smaller in magnitude.




Precession nomenclature[edit]

Etymologically, precession and procession are terms that relate to motion (derived from the Latin processio, “a marching forward, an advance”). Generally the term procession is used to describe a group of objects moving forward, whereas, the term precession is used to describe a group of objects moving backward. The stars viewed from Earth are seen to proceed in a procession from east to west daily, due to the Earth’s diurnal motion, and yearly, due to the Earth’s revolution around the Sun. At the same time the stars can be observed to move slightly retrograde, at the rate of approximately 50 arc seconds per year, a phenomenon known as the “precession of the equinox".

In describing this motion astronomers generally have shortened the term to simply “precession”. And in describing the cause of the motion physicists have also used the term “precession”, which has led to some confusion between the observable phenomenon and its cause, which matters because in astronomy, some precessions are real and others are apparent. This issue is further obfuscated by the fact that many astronomers are physicists or astrophysicists.



The relationship between the apses, seasons and precession of Earth's axis, as viewed from the north. The seasons indicated pertain to the Northern Hemisphere and are reversed for the Southern Hemisphere. The tilt of Earth's axis and the eccentricity of its orbit are exaggerated.



For identical reasons, the apparent position of the Sun relative to the backdrop of the stars at some seasonally fixed time 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. The constellation or house of the zodiac in front of which the Sun rises at the vernal equinox is therefore changed, and this is described as "the age of (the zodiac sign or house)," (e.g.; The Age of Aquarius). Various trends in mythological and religious beliefs are associated with the change of Ages and the different nature of the astrological sign associated with the zodiac constellation.[6]



Hellenistic world[edit]






Other authors[edit]

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 fourth century, who accepted Ptolemy's explanation. Theon also reports an alternate theory:



Alternative discovery theories[edit]



Ancient Egyptians[edit]

Similar claims have been made that precession was known in Ancient Egypt prior to the time of Hipparchus, but these claims remain controversial. Some buildings in the Karnak temple complex, for instance, allegedly were oriented toward 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. The observation that a stellar alignment has grown wrong, however, does not mean that the Egyptians understood that the stars moved across the sky at the specific 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 as such in surviving astronomical texts.


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 monumental building projects of the ancient Egyptians functioned as a map of the heavens, and that associated rituals were an elaborate earthly acting-out of celestial events. In particular, the rituals symbolised 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. The presumption is that this is when they believed their records began. Evidence from studies of prehistoric Egypt supports a major change at that time in the culture of the residents of Egypt from being hunter-gatherers that led to settled and agriculturally-based economies with centralized societies.[9] The change seems to have been brought about by climate changes and over-grazing.


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. Milbrath states, however, that "a long cycle 30,000 years involving the Pleiades ... may have been an effort to calculate the precession of the equinox."[10]

Indian views[edit]




Yu Xi[edit]


Middle Ages and Renaissance[edit]

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.[15]


Modern period[edit]


Hipparchus' discovery[edit]






Mithraic question[edit]


As far as axial precession is concerned, 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).

Ulansey's theory has not received much support from Mithraic scholars or from scholars of astrological beliefs.

Changing pole stars[edit]

Precession of Earth's axis around the north ecliptical pole
Precession of Earth's axis around the south ecliptical pole






This situation also is seen on a star map. The orientation of the south pole is moving toward the Southern Cross constellation. For the last 2,000 years or so, the Southern Cross has nicely pointed to the south pole. By consequence, the constellation is no longer visible from subtropical northern latitudes, as it was in the time of the ancient Greeks.

Polar shift and equinoxes shift[edit]

Precessional movement as seen from 'outside' the celestial sphere







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The precessional eras of each constellation, often known as Great Months, are approximately:[17]

Constellation Year entering Year exiting
Taurus 4500 BC 2000 BC
Aries 2000 BC 100 BC
Pisces 100 BC 2700 AD










The tidal force on Earth due to a perturbing body (Sun, Moon or planet) is expressed by Newton's law of universal gravitation, whereby the gravitational force of the perturbing body on the side of Earth nearest is said to be greater than the gravitational force on the far side by an amount proportional to the cube of the distance between the near and far sides. If the gravitational force of the perturbing body at the center of Earth (which provides the centripetal force causing the orbital motion) is subtracted from the gravitational force of the perturbing body everywhere on the surface of Earth, only the tidal force remains. For precession, this tidal force takes the form of two forces which only act on the equatorial bulge outside of a pole-to-pole sphere. This couple can be decomposed into two pairs of components, one pair parallel to Earth's equatorial plane toward and away from the perturbing body which cancel each other out, and another pair parallel to Earth's rotational axis, both toward the ecliptic plane.[19] The latter pair of forces creates the following torque vector on Earth's equatorial bulge:[4]

\overrightarrow{T} = \frac{3Gm}{r^3}(C-A)\sin\delta\cos\delta\begin{pmatrix}\sin\alpha\\-\cos\alpha\\0\end{pmatrix}


Gm = standard gravitational parameter of the perturbing body
r = geocentric distance to the perturbing body
C = moment of inertia around Earth's axis of rotation
A = moment of inertia around any equatorial diameter of Earth




T_x = \frac{3}{2}\frac{Gm}{a^3 (1-e^2)^{3/2}}(C-A)\sin\epsilon\cos\epsilon


a = semimajor axis of Earth's (Sun's) orbit or Moon's orbit
e = eccentricity of Earth's (Sun's) orbit or Moon's orbit

and 1/2 accounts for the average of the sine squared waveform, a^3 (1-e^2)^{3/2} accounts for the average distance cubed of the Sun or Moon from Earth over the entire elliptical orbit,[20] and \epsilon\,\! (the angle between the equatorial plane and the ecliptic plane) is the maximum value of δ for the Sun and the average maximum value for the Moon over an entire 18.6 year cycle.

Precession is:

\frac{d\psi}{dt} = \frac{T_x}{C\omega\sin\epsilon}


\frac{d\psi_S}{dt} = \frac{3}{2}\left[\frac{Gm}{a^3 (1-e^2)^{3/2}}\right]_S\left[\frac{(C-A)}{C}\frac{\cos\epsilon}{\omega}\right]_E

whereas that due to the Moon is:

\frac{d\psi_L}{dt} = \frac{3}{2}\left[\frac{Gm(1-1.5\sin^2 i)}{a^3 (1-e^2)^{3/2}}\right]_L\left[\frac{(C-A)}{C}\frac{\cos\epsilon}{\omega}\right]_E

where i is the angle between the plane of the Moon's orbit and the ecliptic plane. In these two equations, the Sun's parameters are within square brackets labeled S, the Moon's parameters are within square brackets labeled L, and the Earth's parameters are within square brackets labeled E. The term (1-1.5\sin^2 i) accounts for the inclination of the Moon's orbit relative to the ecliptic. The term (C−A)/C is Earth's dynamical ellipticity or flattening, which is adjusted to the observed precession because Earth's internal structure is not known with sufficient detail. If Earth were homogeneous the term would equal its third eccentricity squared,[21]

e''^2 = \frac{\mathrm{a}^2 - \mathrm{c}^2}{\mathrm{a}^2 + \mathrm{c}^2}


Applicable parameters for J2000.0 rounded to seven significant digits (excluding leading 1) are:[22][23]

Sun Moon Earth
e = 0.016708634 e = 0.05554553 \epsilon\,\! = 23.43928°
i= 5.156690°

which yield

S/dt = 2.450183×10−12 /s
L/dt = 5.334529×10−12 /s



The solar equation is a good representation of precession due the Sun because Earth's orbit is close to an ellipse, being only slightly perturbed by the other planets. The lunar equation is not as good a representation of precession due to the Moon because its orbit is greatly distorted by the Sun.





The rate of precession is the derivative of that:

p = 5,028.796195 + 2.2108696×T + higher order terms.

The constant term of this speed (5,028.796195 arcseconds per century in above equation) corresponds to one full precession circle in 25,771.57534 years (one full circle of 360 degrees divided with 5,028.796195 arcseconds per century)[24] although some other sources put the value at 25771.4 years, leaving a small uncertainty.


p = A + BT + CT2 + …

is an approximation of

p = a + b sin (2πT/P), where P is the 410-century period.




p = 50.475838 − 26.368583T + 21.890862T2
p+ = 50.475838 − 27.000654T + 15.603265T2



See also[edit]


  6. ^ "A Complete Tour of the Astrological Ages". Robert Ohotto, Intuitive Astrologer. Retrieved 2013-12-17. 
  10. ^ Milbrath, S. "Just How Precise is Maya Astronomy?", Institute of Maya Studies newsletter, December 2007.[dead link]
  11. ^ Siddhānta-shiromani, Golādhyāya, section-VI, verses 17–19
  13. ^ Vāsanābhāshya commentary Siddhānta Shiromani (published by Chowkhamba)
  14. ^ cf. Suryasiddhanta, commentary by E. Burgess, ch.iii, verses 9-12.
  17. ^ Kaler, James B. (Reprint 2002). The ever-changing sky: a guide to the celestial sphere. Cambridge University Press. p. 152. ISBN 978-0521499187. 
  18. ^ The Columbia Electronic Encyclopedia, 6th ed., 2007
  25. ^ J. Laskar et al., "A long-term numerical solution for the insolation quantities of the Earth", Astronomy and Astrophysics 428 (2004) 261–285, pp.276 & 278.


  • A.L. Berger (1976), "Obliquity & precession for the last 5 million years", Astronomy & astrophysics 51, 127
  • N. Capitaine et al. (2003), "Expressions for IAU 2000 precession quantities" 685KB, Astronomy & Astrophysics 412, 567–586.
  • Dreyer, J. L. E.. A History of Astronomy from Thales to Kepler. 2nd ed. New York: Dover, 1953.
  • Explanatory supplement to the Astronomical ephemeris and the American ephemeris and nautical almanac
  • J.L. Hilton et al. (2006), "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic" (pdf, 174KB). Celestial Mechanics and Dynamical Astronomy (2006) 94: 351..367
  • J.H. Lieske et al. (1977), "Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants". Astronomy & Astrophysics 58, 1..16
  • Precession and the Obliquity of the Ecliptic has a comparison of values predicted by different theories
  • Pannekoek, A. A History of Astronomy. New York: Dover, 1961.
  • Parker, Richard A. "Egyptian Astronomy, Astrology, and Calendrical Reckoning." Dictionary of Scientific Biography 15:706–727.
  • Rice, Michael (1997), Egypt's Legacy: The archetypes of Western civilization, 3000–30 BC, London and New York.
  • Schütz, Michael: Hipparch und die Entdeckung der Präzession. Bemerkungen zu David Ulansey, Die Ursprünge des Mithraskultes, in: ejms = Electronic Journal of Mithraic Studies,
  • J.L. Simon et al. (1994), "Numerical expressions for precession formulae and mean elements for the Moon and the planets", Astronomy & Astrophysics 282, 663..683
  • Tomkins, Peter. Secrets of the Great Pyramid. With an appendix by Livio Catullo Stecchini. New York: Harper Colophon Books, 1971.
  • Toomer, G. J. "Hipparchus." Dictionary of Scientific Biography. Vol. 15:207–224. New York: Charles Scribner's Sons, 1978.
  • Toomer, G. J. Ptolemy's Almagest. London: Duckworth, 1984.
  • Ulansey, David. The Origins of the Mithraic Mysteries: Cosmology and Salvation in the Ancient World. New York: Oxford University Press, 1989.
  • W.R. Ward (1982), "Comments on the long-term stability of the earth's obliquity", Icarus 50, 444

External links[edit]