Trepidation
Encyclopedia
According to a medieval theory of astronomy
, trepidation is oscillation
in the precession of the equinoxes
. 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
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 the attribution has been contested in modern times. 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.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, trepidation is oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
in the precession of the equinoxes
Precession of the equinoxes
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, like a wobbling top, traces out a pair of cones joined...
. 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
Theon was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and Ptolemy's Handy Tables, as well as writing various commentaries...
in the 4th century CE. In precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
, the equinoxes appear to move slowly through the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
, 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
Arab
Arab people, also known as Arabs , are a panethnicity primarily living in the Arab world, which is located in Western Asia and North Africa. They are identified as such on one or more of genealogical, linguistic, or cultural grounds, with tribal affiliations, and intra-tribal relationships playing...
astronomer by Thābit ibn Qurra
Thabit ibn Qurra
' was a mathematician, physician, astronomer and translator of the Islamic Golden Age.Ibn Qurra made important discoveries in algebra, geometry and astronomy...
, but the attribution has been contested in modern times. 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
Alfonsine tables
The Alfonsine tables provided data for computing the position of the Sun, Moon and planets relative to the fixed stars....
, 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
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
in De revolutionibus orbium coelestium
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus...
(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
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...
), acknowledged today as an authentic motion of the Earth's axis.