Cleomedes (Greek: Κλεoμήδης) was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.
His birth and death dates are not known—historians have suggested that he wrote his work sometime between the mid-1st century BCE and 400 CE. The earlier estimates rely on the fact that Cleomedes refers extensively in his writing to the work of mathematician and astronomer Posidonius of Rhodes (135 BC-51 BCE), and yet seemingly not at all to the work of Ptolemy (85-165 CE). (Cleomedes also refers to Aristotle (384 - 322 BCE), Pytheas of Massalia (325 BCE), Aratus (310 - 240 BCE), Eratosthenes (276 - 195 BCE), and Hipparchus (190 - 120 BCE)) . These conclusions have been challenged on the grounds that Cleomedes' work was in relatively elementary astronomy, and that reference to Ptolemy would not necessarily be expected. The 20th century mathematician Otto Neugebauer, however, looked closely at the astronomical observations made by Cleomedes, and concluded that a date of 371 CE (±50 years) better explains what is found there. Neugebauer's estimate has been challenged on the grounds that Cleomedes makes observational errors with enough frequency that there is difficulty in deciding which observations to trust for the purpose of dating his work.
Cleomedes is a prominent lunar crater located in the northeast part of the visible Moon, to the north of Mare Crisium. It is surrounded by rough ground with multiple crater impacts. The irregular crater Tralles intrudes into the northwest rim. To the east is Delmotte. North of Cleomedes is a triple-crater formation with Burckhardt occupying the center.
The outer wall of Cleomedes is heavily worn and eroded, especially along the southern part of the wall. Cleomedes C lies across the south-southwest rim. The crater floor is nearly flat, with a small central peak to the north of the midpoint, forming a linear ridge toward the north-northeast. There are several notable craterlets on the floor, including a pair of overlapping craters just inside the northwest rim.
A rille named Rima Cleomedes crosses the northern floor, running southeast from the northwest rim. This rille branches in a fork after crossing the crater mid-line. Smaller clefts lie in the southeast part of the floor.