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An equatorium (plural, equatoria) is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without calculation, using a geometrical model to represent the position of a given celestial body.
The earliest extant record of a solar equatorium, that is, one to find the position of the sun, is found in Proclus's fifth-century work Hypostasis, where he gives instructions on how to construct one in wood or bronze. Although planetary equatoria were also probably made by the ancient Greeks, the first surviving description of one is from the Libros del saber de astronomia (Books of the knowledge of astronomy), a Castilian compilation of astronomical works collected under the patronage of Alfonso X of Castile in the thirteenth century, which includes translations of two eleventh century Arabic texts on equatoria by Ibn al‐Samḥ and al-Zarqālī. Theorica Planetarum (c. 1261-1264) by Campanus of Novara describes the construction of an equatorium, the earliest known description in Latin Europe.
Richard of Wallingford (1292–1336) is known to have built a sophisticated equatorium named Albion in 1326. It could calculate lunar, solar and planetary longitudes. Unlike most equatoria, the Albion could also predict eclipses. The device is described in a manuscript and in drawings by the Abbot. It consisted of several rotating disks, showing the courses of the sun, moon and stars. These disks were operated manually. It was not a clockwork mechanism.
History and Inventor
The inventor of the Equatorium, Al-Zarqali, was an Arab Muslim instrument maker, mathematician, and leading astronomer at the time. Al-Zarqali based the equatorium off the Universal Astrolabe, yet made it more accurate and specialized. He was the first to show clearly the motion of the solar apogee, when the sun is furthest from earth, is 12.0 seconds per year (the actual value is 11.8 seconds per year). Al-Zarqali also corrected Ptolemy’s work, calculating that the length of the Mediterranean Sea was at 42°, while Ptolemy said it was 62°. His work was even quoted multiple times in Nicolaus Copernicus's “De Revolutionibus Orbium Celestium” where he discussed the revolution of the celestial orbs. Even though Al-Zaqali’s work was based on the belief that the earth was at the center of the universe, many of his primary concepts still apply to the modern world of astronomy.
The model of Ptolemy that was used by Al-Zarqali to create the equatorium put the earth at the center of the universe. The Equatorium was based on the notion that the stars were on a large sphere, where the earth is right in the middle of it held in place by air. Ptolemy theorized that all of the stars moved around the earth every single day, and the motion of the sun, moon, and planets surrounded it. He believed that each planet moved on a small sphere or circle, called an epicycle, that moved on a larger sphere or circle, called a “deferent” which contains the earth at the center. The epicycle and deferent are the basis of what the equatorium was built on.
How to Make it
To make an equatorium, one needs sheet wood or paper. One also needs black and white string and some nails or clips. In order to cut and etch, a saw and a pen will be needed. Begin by cutting the wood or paper into two circles. The sizing can be varied as long as later calculations are done to scale down the rest of the instrument. The traditional equatorium had a diameter of 6 feet, but an equatorium does not have to be that large. Cut two semi-circles within one of the circles. Leave a rim at least one inch wide around the outside and a half inch through the center. This circle is the epicycle. Next, make a label for the epicycle. It functions as a pointer, is fixed to the center of the epicycle and rotates. It is fixed to the center using a nail or clip, so that it may be rotated, and is not completely straight, but has a kink in the middle. The other circle is the face of the equatorium. The traditional equatorium was marked to divide the twelve zodiac signs: 360 degrees of the circles and 21,600 minutes on both the face and epicycle. Since the marks will have to extremely close together, modern equatoriums are sometimes divided only by degrees and the zodiacs. Then the face is marked with the rotation of the sun, moon, and planets. For the planets, since they move in retrograde, medieval astronomers marked them using two circles, the deferent and the epicycle. Because of the beliefs about the movement of earth and the celestial bodies, the earth, the center of the deferent, and the center of the epicycle’s movement (also known as the equant point) all lie in a straight line. The center of the deferent is in-between the other two. For each planet, the equant point needs to be marked as well as the center of deferent between that and the face. Also, astronomers need a table of mean motus and mean arguments to accompany the equatorium.
How to Use it
To use an equatorium, start by finding the planet's position on the epicycle. This is called the mean argument. The epicycle is used to describe planetary orbits in the Ptolemaic system; it is the top portion of the equatorium with the degree and distance marks. The epicycle moves around the base piece called the deferent, which determines the location of planets. Then we calculate the position of the center of the epicycle based on the mean motus and mean argument. To determine both values, consult a source such as the Toledan Tables, which provides calculations for the positions of the planets in the sky at various latitudes on Earth. After looking up the two values on the table, lay a colored thread from the center (common center deferent) to the edge of the equatorium going straight to the mean motus. Using another color string, lay it parallel to the string placed before, with one end at the equant point which is slightly north of the center of the equatorium. The equant point is known as the second center of the equatorium and varies based on the size of the instrument. The next step is to place the epicycle on the deferent centre (outer edge of the base circle) of the planet whose location one would calculate. After taking the label (ruler like piece), turn it counterclockwise to the number of degrees listed as the mean argument. Now, take the initial string and line it up with the planet’s mark on the label. Finally, wherever the initial thread crosses the edge of the label is the planet’s actual location.
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 vs. Equatorium
In the early 1000 CE (11th Century), the Equatorium was invented by Abū Ishāq Ibrāhīm Al-Zarqālī. To understand where the roots of the Equatorium began, look back to what inspired it: the Astrolabe. The history of the Astrolabe dates back to roughly 220 BC and was invented by Hipparchus. 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. There are also specialized astrolabes for land and for boats. The Astrolabe works by adjusting the moveable components (labels) to a specific date and time. Afterward, line up the astrolabe with the horizon by holding it up and setting one end of the label to where one end is at eye level and the opposite end is pointed towards whichever celestial structure you want to view. In contrast, the equatorium is a rarer astronomical instrument. It is used to calculate the past or future positions of the planets and celestial bodies according to the planetary theory of Ptolemy. What is similar about these tools is that they are both calculating devices that simplify and efficiently make geometrical calculations.
Uses and Other Facts
The equatorium can further be specialized depending on the epicycle. 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 equatorium’s had astrological aspects of medicine, as the orientation of planets gave insight to zodiac signs which helped some doctors cater medical treatments to patients.
A fact that can be discovered when learning about the equatorium was that at least 15 minutes was needed to calculate the planetary position with the use of a table for each celestial body. Since during this time, horoscopes were very popular, to create one there would be needs of at least seven celestial body positions needed. This then would make it difficult to create a horoscope in less than two house.
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