Eudoxus of Cnidus is perhaps the first of the great ancient Greek astronomers and mathematicians. Although he studied
a variety of disciplines including medicine, law, philosophy and mathematics, he is best known for his contributions
to mathematics (geometry and number theory) and astronomy. He is also believed to have been the first to construct
and operate his own personal observatory (in Cnidus) and is considered the father of both observational astronomy and
Eudoxus is perhaps best known or recognized for his ingenious attempts to describe the motion of the sun, moon and five observeable planets of the time (Mercury, Venus, Mars, Jupiter and Saturn). His model based on a set of 27 homeocentric (or concentric) spheres to describe the rise and setting of the planets as well as planetary retrograde motion is considered an ingenious hypothesis and mathematical model which stood the test of time until the 17th century and the work of Kepler.
To summarize, the homeocentric sphere system proposed by Eudoxus incorporated one sphere inside the other with the innermost central sphere being earth and, thus, his system was geocentric. On the outermost sphere which purposely rotated from east to west, Eudoxus placed the stars and all of the other non-planetary celestial objects which rose and set on a daily basis from east to west respectively. The sun's motion was described by three spheres as was the case for the moon. In contrast, each of the five observeable planets of the time had their motion described by four spheres. Each sphere has its own axis of rotation as well as rotational speed.
Using this system of homeocentric spheres, Eudoxus was able to describe the motion of all celestial objects as they appeared from earth. For example, for the moon, one of the three spheres described the daily motion from east to west; the second of the three spheres and its rotation from west to east described the monthly motion across the sky and consequently the lunar phases; and the third sphere accounted for the movement of the moon above and below the ecliptic with a period of 18.5 years so as to account for the Saros cycle. A similar approach was adopted for planets with the exception that an extra sphere was incorporated in order to explain planetary retrograde motion (two of the spheres rotated with the same angular velocity but in opposite directions and observation of the planet's motion relative to a third sphere would produce motion similar to a figure eight, labelled as hippopede ("ιπποπέδη"), and which allows and accounts for retrograde motion; the final fourth sphere accounted for stellar motion).
Although Eudoxus is best known for his geocentric homeocentric sphere system, he is also recognized for systematically having recorded the location of the stars in the sky and mapped the constellations; for developing the theory of planetary motion; was the first to measure the size of the moon and sun and their distance from earth; proposed a calendar system so as to account and be in synchrony with the moon and its phases; identified the stars which are and are not circumpolar; developed a star catalog; and defined the equator (0° N or S) as well as the Tropics of Cancer (23.5° N) and Capricorn (23.5° S).
Eudoxus has been honored by the naming of a 67-km wide lunar crater after him (see Rukl: 13). Lying on the northeastern quadrant of the moon with selenographic cooordinates (44.3° N, 16.3° E), this perfectly circular but steep formation has a height of 3.350 km and lies between Mare Serenitatis to the south and the impressive crater Aristoteles to the north. Crater Eudoxus is best viewed around first and third quarters (photo by the author available shortly).
For a thorough discussion on the life and ingenious work of Eudoxus of Cnidus, the reader is referred to: