An equatorium (plural, equatoria) is an astronomical calculating instrument. It can be used for finding the positions of the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width ...

, Sun, and

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...

s without arithmetic operations, using a geometrical model to represent the position of a given

celestial body An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...

History

Planetary equatoria were probably made by ancient Greeks, although no findings nor descriptions have been preserved from that period. In his comment on Ptolemy's ''Handy Tables'', 4th century mathematician

Theon of Alexandria Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's ''Elements'' and wrote commentaries on works ...

introduced some diagrams to geometrically compute the position of the planets based on Ptolemy's epicyclical theory. The first description of the construction of a solar (as opposed to planetary) equatorium is contained in

Proclus Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophe ...

's fifth-century work ''Hypotyposis'', where he gives instructions on how to construct one in wood or bronze. The earliest surviving descriptions of planetary equatoria are the Latin translations of Arab works contained in the ''

Libros del saber de astronomia Libros is a municipality located in the province of Teruel, Aragon, Spain. According to the 2004 census (INE INE, Ine or ine may refer to: Institutions * Institut für Nukleare Entsorgung, a German nuclear research center * Instituto Nacional ...

'' (''Books of the knowledge of astronomy''), a Castilian compilation of astronomical works collected under the patronage of

Alfonso X of Castile Alfonso X (also known as the Wise, es, el Sabio; 23 November 1221 – 4 April 1284) was King of Castile, León and Kingdom of Galicia, Galicia from 30 May 1252 until his death in 1284. During the April 1257 Imperial election, election of 1257, ...

in the thirteenth century: an early eleventh century text by Ibn al‐Samḥ and a 1080/1081 treatise by al-Zarqālī. The ''Theorica Planetarum'' (c. 1261–1264) by Campanus of Novara is the earliest extant description of the construction of an equatorium in

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power ...

Europe. Campanus' instrument resembled an astrolabe, with several interchangeable plates within a mater. The best manuscripts of Campanus' treatise contain paper and parchment equatoria with moveable parts.

Variations

The history of the equatorium does not just end after the 11th century, but it inspired a more diverse invention called “The Albion”. The Albion is an astronomical instrument invented by Richard of Wallingford at the beginning of the 14th century. It has various functional uses such as that of the equatorium for planetary and conjunction computations. It can calculate when eclipses will occur. The Albion is made up of 18 different scales which makes it extremely complex in comparison to the equatorium. The history of this instrument is still disputed to this day, as the only Albion from the past is both unnamed and unmarked.

Astrolabe compared with equatorium

The roots of the equatorium lie in the

astrolabe An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستاره‌یاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate incli ...

. The history of the astrolabe dates back to roughly 220 BC in the works of

Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equ ...

. The difference between the two instruments is that the astrolabe measures the time and position of the sun and stars at a specific location in time. In contrast, the equatorium is used to calculate the past or future positions of the planets and celestial bodies according to the planetary theory of Ptolemy.

Uses

The equatorium can further be specialized depending on the

epicycle In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (, meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, S ...

. There are three possible epicycles that can be adjusted to serve for planetary positions in three groups: the moon, the stars, and the sun. The sun was considered a planet in the Ptolemaic system, hence why the equatorium could be used to determine its position. Through the use of Ptolemy's model, astronomers were able to make a single instrument with various capabilities that catered to the belief that the solar system had the earth at the center. In fact, specialized equatoriums had astrological aspects of medicine, as the orientation of planets gave insight to zodiac signs which helped some doctors cater medical treatments to patients. At least 15 minutes was needed to calculate the planetary position with the use of a table for each celestial body. A horoscope of that era would have required the positions of seven astronomical objects, requiring nearly two hours of manual calculation time.

History

Variations

Astrolabe compared with equatorium

Uses

See also

References

Further reading