The term Great Year has a variety of related meanings. It is defined by NASA as "The period of one complete cycle of the equinoxes around the ecliptic, about 25,800 years […] also known as [a] Platonic Year." One complete cycle of the equinoxes here means one complete cycle of axial precession; this precession was known to Plato, who defined the "perfect year" as the return of the celestial bodies (planets) and the diurnal rotation of the fixed stars (circle of the Same) to their original positions. Cicero followed Plato in defining the Great Year as a combination of solar, lunar and planetary cycles  (61 XX) Nicholas Campion writes of "periods of History, analogous to the solar year, known as 'Great Years' " 
Plato's description of the perfect year is found in his dialogue Timaeus
And so people are all but ignorant of the fact that time really is the wanderings of these bodies, bewilderingly numerous as they are and astonishingly variegated. It is none the less possible, however, to discern that the perfect number of time brings to completion the perfect year at that moment when the relative speeds of all eight periods have been completed together and, measured by the circle of the Same that moves uniformly, have achieved their consummation."
The 'Great Year' as defined by the historian Josephus is 600 years in length. (Book 1, Chapter 3, Paragraph 9)
In De Natura Deorum, Cicero wrote
On the diverse motions of the planets the mathematicians have based what they call the Great Year," which is completed when the sun, moon and five planets having all finished their courses have returned to the same positions relative to one another. The length of this period is hotly debated, but it must necessarily be a fixed and definite time." 
"The difficulty with the term "great year" lies in its ambiguity. Almost any period can be found sometime or somewhere honored with this name." 
Macrobius in his commentary on Cicero's Somnium Scipiones states that 'the philosophers' reckon the Great Year as 15,000 years. (p. 97) Censorinus wrote that Aristarchus of Samos reckoned a Great Year of 2484 years: it has been argued that this is a miscopying of 2434, which represents 45 Exeligmos cycles. (p. 96)  (p. 6)
The Platonic Year in origin would seem to have no connection with this concept (as the precession of the equinox was unknown to Europe in Plato's time). and two centuries after Plato, Hipparchus is credited with discovering the period of equinox precession, and the term "Great Year" eventually came to be applied to the period of that precession caused by the slow gyration of the Earth's axis.
Some time around the middle of the second century BC, the astronomer Hipparchus discovered that the fixed stars as a whole gradually shifted their position in relation to the annually determined locations of the Sun at the equinoxes and solstices... Otto Neugebauer argued that Hipparchus in fact believed that this [36,000 years] was the maximum figure and that he also computed the true rate of one complete precession cycle at just under 26,000 years...
It is argued that the confusion originates with the astronomer Ptolemy, who "adopted the larger, erroneous, figure, with the result that henceforth the two versions of the Great Year — the Platonic Great Year, defined by the planets, and the precessional, defined by the stars — were to be increasingly confused." Ptolemy has been accused of committing scientific fraud by making up observations that would give the figure of 36,000 years even though the data available to him were good enough to get very near the true figure of 26,000.
God afforded them a longer time of life on account of their virtue, and the good use they made of it in astronomical and geometrical discoveries, which would not have afforded the time of foretelling [the periods of the stars] unless they had lived six hundred years; for the great year is completed in that interval.
Isaac Newton determined the cause of precession and established the rate of precession at 1 degree per 72 years, very close to the true value, thus demonstrating the magnitude of the error in the value of 1 degree per century. (letter 17)
Walter Cruttenden wrote of the Great Year
Some people called it the Yuga cycle, others called it the Grand cycle and others the Perfect Year...But the most common name found in use from ancient Europe to ancient China, was simply the Great Year".
- "Aerospace Science and Technonlogy Dictionary G Section". Hq.nasa.gov. 1989-10-18. Retrieved 2014-03-02.
- "Full text of "De natura deorum; Academica; with an English translation by H. Rackham"". Archive.org. Retrieved 2014-03-02.
- Nicholas Campion, "The Great Year: Astrology, Millenarianism and History in the Western Tradition" (Arkana/Penguin Books, 1994), p. 6. Cite error: Invalid
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- Plato, Timaeus 39d, in John M. Cooper (ed.), "Plato: Complete Works" (Hackett Publishing Company, 1997), p. 1243
- God afforded them a longer time of life on account of their virtue, and the good use they made of it in astronomical and geometrical discoveries, which would not have afforded the time of foretelling [the periods of the stars] unless they had lived six hundred years; for the great year is completed in that interval.
- Neugebauer O., (1975)A History of Ancient mathematical astronomy, Birkhäuser, p.618
- Stars, Mind & Fate: Essays in Ancient and Mediaeval Cosmology by J. D. North. Books.google.co.uk. Retrieved 2014-03-02.
- William Harris Stahl, "Macrobius: Commentary on the Dream of Scipio" (Columbia University Press, 1952), p. 21
- "Aerospace Science and Technonlogy Dictionary G Section". Hq.nasa.gov. 1989-10-18. Retrieved 2015-08-23.
- R.R.Newton, "The Authenticity of Ptolemy's star data" ()
- Josephus, Jewish Antiquities, Loeb, p.1, note a,
- "Internet History Sourcebooks". Fordham.edu. Retrieved 2014-03-02.
- Walter Cruttenden, "Lost Star of Myth and Time" (St. Lynn's Press, 2006), p.xix–xx.
Boris Cristoff proved that duration in his book "El destino de la humanidad" (Barcelona, editorial Martínez Roca, 1981; colección "Fontana Fantástica").
Callatay G. de, Annus Platonicus, a study of worldcycles in Greek Latin and Arabian sources, Publication de l'Institut Orientaliste de Louvain #47, Louvain, 1996
Nicholas Campion, "The Great Year" (book)
Walter Cruttenden, "The Great Year" (documentary film)-->