Ptolemy developed several mathematical models to describe the
motions of the sun, the moon, the planets and the stars. The book
that describes these models is called "The Almagest" or "Ptolemy's
Almagest". The models all assume:
1. The earth is stationary.
2. All objects travel with uniform speed on a perfectly circular
orbit.
However, a model that placed the earth in the centre of the
orbits of all other objects would not work because it does not
account for various anomalies, including the varying length of
seasons, the irregularity of eclipses of the moons and the
retrograde motion of the planets. Ptolemy used two mathematical
devices to deal with the anomalies: eccentricity (an offset from
the centre of a circle) and epicycles - circular orbits whose
centre (or eccentric) itself traveled in a uniform circular
orbit.
Much of the material in The Almagest was already known to Greek
astronomers. Ptolemy's contribution was to consolidate all known
results, make large improvements to the models, and to write it all
down in a way that became a standard for the way to present the
results of scientific enquiry.
His book was the standard text book for astronomers until his
models were ultimately improved by Copernicus, Kepler and
Newton.
Ptolemy also wrote a treatise on Astrology, based on his deep
knowledge of the motions of the heavenly bodies. This work is
called The Tetrabiblos.