**Eudoxan Astronomy**

In classical Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. This tradition began with the Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music). The study of number comprising the four arts was later called the *quadrivium*.

Although he was not a creative mathematician, Plato (427–347 BCE) included the *quadrivium* as the basis for philosophical education in the *Republic*. He encouraged a younger mathematician, Eudoxus of Cnidus (c. 410 BCE–c. 347 BCE), to develop a system of Greek astronomy. According to a modern historian of science, David Lindberg:

*In their work we find (1) a shift from stellar to planetary concerns, (2) the creation of a geometrical model, the "two-sphere model," for the representation of stellar and planetary phenomena, and (3) the establishment of criteria governing theories designed to account for planetary observations*. (Lindberg 1992, p. 90)

The **two-sphere model** is a geocentric model. It divides the cosmos into two regions:

- A spherical Earth, central and motionless (the sublunary sphere).
- A spherical heavenly realm centered on the Earth, which may contain multiple rotating spheres made of aether.

Plato's main books on cosmology are the *Timaeus* and the *Republic*. In them he described the two-sphere model and said there were eight circles or spheres carrying the seven planets and the fixed stars. He put the celestial objects in the following order, beginning with the one closest to Earth:

- Moon
- Mercury
- Venus
- Sun
- Mars
- Jupiter
- Saturn
- Fixed stars

According to the "Myth of Er" in the *Republic*, the cosmos is the Spindle of Necessity, attended by Sirens and spun by the three daughters of the Goddess Necessity known collectively as the Moirai or Fates.

According to a story reported by Simplicius of Cilicia (6th century CE), Plato posed a question for the Greek mathematicians of his day: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" (quoted in Lloyd 1970, p. 84). Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century.

Eudoxus rose to the challenge by assigning to each planet a set of concentric spheres. By tilting the axes of the spheres, and by assigning each a different period of revolution, he was able to approximate the celestial "appearances." Thus, he was the first to attempt a mathematical description of the motions of the planets. A general idea of the content of *On Speeds*, his book on the planets, can be gleaned from Aristotle's *Metaphysics* XII, 8, and a commentary by Simplicius on *De caelo*, another work by Aristotle. Since all his own works are lost, our knowledge of Eudoxus is obtained from secondary sources. Aratus's poem on astronomy is based on a work of Eudoxus, and possibly also Theodosius of Bithynia's *Sphaerics*. They give us an indication of his work in spherical astronomy as well as planetary motions.

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.

Read more about this topic: Greek Astronomy

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“It is noticed, that the consideration of the great periods and spaces of *astronomy* induces a dignity of mind, and an indifference to death.”

—Ralph Waldo Emerson (1803–1882)