The origin of the theory of trepidation comes from the Small Commentary to the Handy Tables written by Theon of Alexandria in the 4th century CE. In precession, the equinoxes appear to move slowly through the ecliptic, completing a revolution in approximately 25,800 years (according to modern astronomers). Theon states that certain (unnamed) ancient astrologers believed that the precession, rather than being a steady unending motion, instead reverses direction every 640 years. The equinoxes, in this theory, move through the ecliptic at the rate of 1 degree in 80 years over a span of 8 degrees, after which they suddenly reverse direction and travel back over the same 8 degrees. Theon describes but did not endorse this theory.
A more sophisticated version of this theory was adopted in the 9th century to explain a variation which Islamic astronomers incorrectly believed was affecting the rate of precession. This version of trepidation is described in De motu octavae sphaerae (On the Motion of the Eighth Sphere), a Latin translation of a lost Arabic original. The book is attributed to the Arab astronomer by Thābit ibn Qurra, but this model has also been attributed to Ibn al-Adami and to Thabit's grandson, Ibrahim ibn Sinan. In this trepidation model, the oscillation is added to the equinoxes as they precess. The oscillation occurred over a period of 7000 years, added to the eighth (or ninth) sphere of the Ptolemaic system. "Thabit's" trepidation model was used in the Alfonsine Tables, which assigned a period of 49,000 years to precession. This version of trepidation dominated Latin astronomy in the later Middle Ages.
Islamic astronomers described other models of trepidation. In the West, an alternative to De motu octavae sphaerae was part of the theory of the motion of the Earth published by Nicolaus Copernicus in De revolutionibus orbium coelestium (1543). Copernicus' version of trepidation combined the oscillation of the equinoxes (now known to be a spurious motion) with a change in the obliquity of the ecliptic (axial tilt), acknowledged today as an authentic motion of the Earth's axis.
- a fully quoted translation is found in Jones A., Ancient Rejection and Adoption of Ptolemy’s Frame of Reference for Longitudes in Ptolemy in Perspective, (ed) A. Jones, Spinger, 2010, p.11
- James Evans, (1998), The History and Practice of Ancient Astronomy, page 276
- Jamil Ragep, F.; Bolt, Marvin (2007). "Ādamī: Abū ʿAlī al‐Ḥusayn ibn Muḥammad al‐Ādamī". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. p. 12. ISBN 9780387310220. (PDF version)
- This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.
- Otto Neugebauer, "Thabit ben Qurra 'On the Solar Year' and 'On the Motion of the Eighth Sphere'," Proceedings of the American Philosophical Society 106 (1962): 264–299.
- F. Jamil Ragep, "Al-Battani, Cosmology, and the Early History of Trepidation in Islam," in From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, Barcelona 1996.
- N. M. Swerdlow and O. Neugebauer, Mathematical Astronomy in Copernicus's De Revolutionibus, (Studies in the History of Mathematics and Physical Sciences 10), Springer-Verlag 1984.
- Jerzy Dobrzycki, "Theory of Precession in Medieval Astronomy" (1965), in Selected Papers on Medieval and Renaissance Astronomy (Studia Copernicana XLIII), ISBN 9788386062034, Institute for the History of Science, Polish Academy of Sciences, Copernicus Center for Interdisciplinary Studies, 2010: 15-60.
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