Trepidation

Last updated

Trepidation (from Lat. trepidus, "trepidatious"), in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries.

Contents

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. [1] 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. [2] 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 Thābit ibn Qurra, but this model has also been attributed to Ibn al-Adami and to Thabit's grandson, Ibrahim ibn Sinan. [3] 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.

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. [4] 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

  1. 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, Springer, 2010, p. 11.
  2. James Evans, (1998), The History and Practice of Ancient Astronomy, page 276
  3. Jamil Ragep, F.; Bolt, Marvin (2007). "Ādamī: Abū ʿAlī al‐Ḥusayn ibn Muḥammad al‐Ādamī". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. p. 12. ISBN   9780387310220. (PDF version)
  4. chapter 3, verse 9-10, Surya-Siddhanta: A Text Book of Hindu Astronomy by Ebenezer Burgess.

Related Research Articles

Ecliptic Apparent path of the Sun on the celestial sphere

The ecliptic is the plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

Zodiac Area of the sky divided into twelve signs

The zodiac is an area of the sky that extends approximately 8° north or south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are also within the belt of the zodiac.

Ecliptic coordinate system

The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

Axial precession Gravity-induced, slow, and continuous change in the orientation of an astronomical bodys rotational axis

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 can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. 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.

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.

Al-Ṣābiʾ Thābit ibn Qurrah al-Ḥarrānī was a Syrian Arab mathematician, physician, astronomer, and translator who lived in Baghdad in the second half of the ninth century during the time of the Abbasid Caliphate.

Heliocentrism Astronomical model where the Earth and planets revolve around the Sun

Heliocentrism is the astronomical model in which the Earth and planets revolve around the Sun at the center of the Universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center. The notion that the Earth revolves around the Sun had been proposed as early as the 3rd century BC by Aristarchus of Samos, but at least in the medieval world, Aristarchus' heliocentrism attracted little attention—possibly because of the loss of scientific works of the Hellenistic period.

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 mathematician.

Nicolaus Copernicus 15th–16th-century Polish mathematician and astronomer

Nicolaus Copernicus was a Polish Renaissance-era mathematician, astronomer, and Catholic canon who formulated a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier.

Celestial spheres elements of some cosmological models

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like jewels set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.

Al-Battani

Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī was a Syrian Arab astronomer, and mathematician. He introduced a number of trigonometric relations, and his Kitāb az-Zīj was frequently quoted by many medieval astronomers, including Copernicus. Often called the "Ptolemy of the Arabs", al-Battani is perhaps the greatest and best known astronomer of the medieval Islamic world.

Great Year Length of time

The term Great Year has two major meanings. It is defined by scientific astronomy as "The period of one complete cycle of the equinoxes around the ecliptic, or about 25,800 years". A more precise figure of 25,772 years is currently accepted. The position of the Earth's axis in the northern night sky currently almost aligns with the star Polaris, the North Star. This is a passing coincidence and has not been so in the past and will not be so again until a Great Year has passed.

Astronomy in the medieval Islamic world

Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age, and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.

Tusi couple

The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a 2-cusped hypocycloid.

<i>Commentariolus</i> Work by Copernicus

The Commentariolus is Nicolaus Copernicus's brief outline of an early version of his revolutionary heliocentric theory of the universe. After further long development of his theory, Copernicus published the mature version in 1543 in his landmark work, De revolutionibus orbium coelestium.

Islamic cosmology is the cosmology of Islamic societies. It is mainly derived from the Qur'an, Hadith, Sunnah, and current Islamic as well as other pre-Islamic sources. The Qur'an itself mentions seven heavens.

Copernican heliocentrism Concept that the Earth rotates around the Sun

Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths, modified by epicycles, and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe. Copernican heliocentrism is often regarded as the launching point to modern astronomy and the Scientific Revolution.

In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. Although there are two intersections of the ecliptic with the celestial equator, by convention, the equinox associated with the Sun's ascending node is used as the origin of celestial coordinate systems and referred to simply as "the equinox". In contrast to the common usage of spring/vernal and autumnal equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

A tropical year is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. This differs from the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars by about 20 minutes because of the precession of the equinoxes.

Ibn al‐Ādamī, was a 10th-century Islamic astronomer who wrote an influential work of zij based on Indian sources. The book, now lost, uses the Indian methods found in the Sindhind. The 11th-century historian Sa'id al-Andalusi informs us that the theory of trepidation that became known to Europe and was ascribed to Thabit ibn Qurra can be found instead in the Zij of Ibn al-Adami, who himself may have known of this theory from Thabit's grandon, Ibrahim ibn Sinan. Ibn al-Adami is also the source for the story of how Indian astronomy reached the court of Caliph al-Mansur in the early 770s in Baghdad.

References

Further reading