Callippus was taught by Ptolemarchus (a friend of Eudoxus) and at the age of 40 he left Cyzicus in Asia Minor to study with Aristotle in Athens.

Callippus took the idea of concentric sphere proposed by Eudoxus and added a total of seven more spheres. Each sphere was for one of the visible planets (Mercury, Venus, Mars, Jupiter and Saturn) as well a sphere for the sun and the moon, both considered a planet. This took the total number of Eudoxus’ spheres to 34.

His calculations of the length of each season were incredibly accurate. He measured spring as 94 days, summer as 92, autumn as 89 and winter as 92. This proved to be off by between .08 and .4 days!

This precision in measuring the seasons allowed him to improve on the Metonic calendar. He took the 19 year cycle of that calendar and extended it to 76 years (4*19). By skipping one day every 76 years, he gave a year of 365.25 days, called a Callippic year.

His only written work, "On the System of Planets", has been lost forever.

There are two craters, Callippus and Rima Callippus, named in his sake on the moon.

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Callippus.html