Trepidation (from Lat. ''trepidus'', "trepidatious"), in now-obsolete medieval theories of

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, refers to hypothetical

oscillation Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

in the

precession of the equinoxes In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's Rotation around a fixed axis, rotational axis. In the absence of precession, the astronomical body's orbit would show ...

. The theory was popular from the 9th to the 16th centuries. The origin of the theory of trepidation comes from the ''Small Commentary to the Handy Tables'' written by

Theon of Alexandria Theon of Alexandria (; ; ) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathema ...

in the 4th century CE. In

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...

, the equinoxes appear to move slowly through the

ecliptic The ecliptic or ecliptic plane is the orbital plane of Earth's orbit, Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making. Fr ...

, 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 does 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.James Evans, (1998), ''The History and Practice of Ancient Astronomy'', p. 276. 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 Arabs (, , ; , , ) are an ethnic group mainly inhabiting the Arab world in West Asia and North Africa. A significant Arab diaspora is present in various parts of the world. Arabs have been in the Fertile Crescent for thousands of years ...

astronomer

Thābit ibn Qurra Thābit ibn Qurra (full name: , , ; 826 or 836 – February 19, 901), was a scholar known for his work in mathematics, medicine, astronomy, and translation. He lived in Baghdad in the second half of the ninth century during the time of the Abba ...

, but this model has also been attributed to Ibn al-Adami and to Thabit's grandson,

Ibrahim ibn Sinan Ibrahim ibn Sinan (Arabic: ''Ibrāhīm ibn Sinān ibn Thābit ibn Qurra'', ; born 295296 AH/ in Baghdad, died: 334-335 AH/946 in Baghdad, aged 38) was a mathematician and astronomer who belonged to a family of scholars originally from Harran in n ...

. 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 In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...

. "Thabit's" trepidation model was used in the ''

Alfonsine Tables The ''Alfonsine Tables'' (, ), sometimes spelled ''Alphonsine Tables'', provided data for computing the position of the Sun, Moon and planets relative to the fixed stars. The tables were named after Alfonso X of Castile, who sponsored their cr ...

'', 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 Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a Renaissance polymath who formulated a mathematical model, model of Celestial spheres#Renaissance, the universe that placed heliocentrism, the Sun rather than Earth at its cen ...

in ''

De revolutionibus orbium coelestium ''De revolutionibus orbium coelestium'' (English translation: ''On the Revolutions of the Heavenly Spheres'') is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543) of the Polish Renaissance. The book ...

'' (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 In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbita ...

), acknowledged today as an authentic motion of the Earth's axis. Trepidation was a feature of Hindu astronomy and was used to compute ayanamsha for converting sidereal to tropical longitudes. The third chapter of the Suryasiddhanta, verses 9-10, provides the method for computing it, which E. Burgess interprets as 27 degree trepidation in either direction over a full period of 7200 years, at an annual rate of 54 seconds.Chapter 3, verse 9-10, ''Surya-Siddhanta: A Text Book of Hindu Astronomy'' by Ebenezer Burgess. This is nearly the same as the Arab period of about 7000 years. The zero date according to the Suryasiddhanta was 499 AD, after which trepidation is forward in the same direction as modern equinoctial precession. For the period before 1301 BCE, Suryasiddhantic trepidation would be opposite in sign to equinoctial precession. For the period 1301 BCE to 2299 AD, equinoctial precession and Suryasiddhantic precession would have the same direction and sign, only differing in magnitude. Brahma Siddhanta, Soma Siddhanta and Narada Purana describe exactly the same theory and magnitude of trepidation as in Suryasiddhanta, and some other Puranas also provide concise references to precession, esp Vayu purana and Matsya Purana.

Notes

References

* *

Otto Neugebauer Otto Eduard Neugebauer (May 26, 1899 – February 19, 1990) was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences as they were practiced in an ...

, "Thabit ben Qurra 'On the Solar Year' and 'On the Motion of the Eighth Sphere'," ''Proceedings of the American Philosophical Society'' 106 (1962): 264–29
JSTOR link
* 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.
''Surya-Siddhanta: A Text Book of Hindu Astronomy'' by Ebenezer Burgess, ed. Phanindralal Gangooly
(1989/1997) with a 45-page commentary by P.C. Sengupta (1935).

Notes

References

Further reading