Sunday, October 11, 2015

Moon: Eudoxus

Crater Eudoxus with satellite features and crater Lamèch
(detail of LRO - WAC global moon mosaic; Mercator projection)
Image NASA via Wikimedia
Eudoxus Crater
Eudoxus is a prominent lunar impact crater that lies to the east of the northern tip of the Montes Caucasus range. It is located to the south of the prominent crater Aristoteles in the northern regions of the visible Moon. To the south is the ruined formation of Alexander, and the small crater Lamèch lies to the southwest.

The rim of Eudoxus has a series of terraces on the interior wall, and slightly worn ramparts about the exterior. It lacks a single central peak, but has a cluster of low hills about the midpoint of the floor. The remainder of the interior floor is relatively level. Eudoxus has a ray system, and is consequently mapped as part of the Copernican System.

Eudoxus of Cnidus
Eudoxus of Cnidus (Greek: Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios; 408–355 BC) was a Greek astronomer, mathematician, scholar and student of Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy.

Theodosius of Bithynia's important work, Sphaerics, may be based on a work of Eudoxus.

In ancient Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus' astronomical texts whose names have survived include:
  • Disappearances of the Sun, possibly on eclipses
  • Oktaeteris (Ὀκταετηρίς), on an eight-year lunisolar cycle of the calendar
  • Phaenomena (Φαινόμενα) and Entropon (Ἔντροπον), on spherical astronomy, probably based on observations made by Eudoxus in Egypt and Cnidus
  • On Speeds, on planetary motions
We are fairly well informed about the contents of Phaenomena, for Eudoxus' prose text was the basis for a poem of the same name by Aratus. Hipparchus quoted from the text of Eudoxus in his commentary on Aratus.

Callippus, a Greek astronomer of the 4th century, added seven spheres to Eudoxus' original 27 (in addition to the planetary spheres, Eudoxus included a sphere for the fixed stars). Aristotle described both systems, but insisted on adding "unrolling" spheres between each set of spheres to cancel the motions of the outer set. Aristotle was concerned about the physical nature of the system; without unrollers, the outer motions would be transferred to the inner planets.

A major flaw in the Eudoxan system is its inability to explain changes in the brightness of planets as seen from Earth. Because the spheres are concentric, planets will always remain at the same distance from Earth. This problem was pointed out in Antiquity by Autolycus of Pitane. Astronomers responded by introducing the deferent and epicycle, which caused a planet to vary its distance. 
However, Eudoxus' importance to Greek astronomy is considerable, as he was the first to attempt a mathematical explanation of the planets.

Excerpts from Wiki texts have been incorporated into the blog as kinds of abstracts for reader's convenience. By clicking the links much more can be learned about these subjects.

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