The document describes several ancient geocentric models of the universe: - The Pythagorean model placed Earth stationary at the center with celestial bodies orbiting in perfect circular motion. Plato and Eudoxus later expanded on this model using concentric spheres to explain planetary retrograde motion. - Aristotle's model also used concentric spheres driven by an outer Prime Mover, and divided the universe into terrestrial and celestial realms separated by the moon's orbit. He provided evidence Earth was spherical. - Ptolemy further refined the geocentric model by introducing the idea of epicycles, where planets orbit along smaller circles that move along a larger circular deferent, better explaining planetary variations. His model survived over

1. GEOCENTRIC MODEL
Alfredo Meneses III

2. THE PYTHAGOREAN
MODEL

3. THE PYTHAGOREAN MODEL
• In his model, Earth is at rest at the center of the universe and
everything rotates around it.

4. Plato’s “Saving the Appearances”
• Plato adopted the Pythagorean
view of the motion of the
heavenly bodies as combinations
of circular motion about the earth.
• He assumed that all motions in
the universe are perfectly circular
and all heavenly bodies are
ethereal or perfect.

5. Plato’s “Saving the Appearances”
• Most of the time, planets move from west to east as predicted.
• But occasionally, they backtrack for a while; that is, they move
westward before resuming their eastward motion or called
retrograde motion.

6. EUDOXUS’ MODEL

7. EUDOXUS’ MODEL
• Eudoxus was the first
to “save the
appearances” that
Plato referred to,
using a series of 27
concentric spheres on
which the sun, the
moon and the planets
moved in perfect
circular motion.

8. EUDOXUS’ MODEL
• The breakdown of the 27 spheres is as follows: one sphere for
fixed stars, three spheres for the sun, three spheres for the
moon, and four spheres each of the five known planets at the
time – Mercury, Venus, Mars, Saturn, and Jupiter.

9. ARISTOTLE’S MODEL

10. ARISTOTLE’S MODEL
• Aristotelian model also used the 27
celestial spheres of Euxodus.
• In addition, Aristotle used 27 “buffering”
spheres between the celestial spheres of
Eudoxus and an outermost sphere that
was the domain of what he called the
Prime Mover.
• Prime Mover rotated this outermost sphere
with constant angular speed, causing the
other spheres to rotate as well.

11. ARISTOTLE’S MODEL
• ~Aristotle divided the universe into two
realms-the terrestrial and the celestial-with
the orbit of the moon as the boundary.

12. ARISTOTLE’S MODEL
• Earth is a sphere, he based this
proposition on several observations.
• First, it is only at the surface of a sphere
that all objects fall straight down.
• Second, the view of the constellations
changes as one travels from north to
south.
• Lastly the shadow of Earth on the Moon
during a lunar eclipse was round.

13. PTOLEMY’S MODEL

14. PTOLEMY’S MODEL
• The Greek mathematician Apollonius,
known in his time as the “The
GreatGeometer,” introduced the idea of an
epicycle to explain planetary motion.
Apollonius

15. PTOLEMY’S MODEL
• An epicycle is a circle on which a planet
moves.
• The center of this small circle in turn
moves around Earth along a bigger circular
path called the deferent.
• To account for the variation in the speed of
the sun during its annual motion.

16. PTOLEMY’S MODEL
• Greek astronomer Hipparchus refined this
model by considering that Earth was off-
center or eccentric in the deferent where
the sun moved.

17. PTOLEMY’S MODEL
• Around 140 AD, Ptolemy devised a more
complex epicyclic model.
• He defined a point on the other side of the
deferent’s center and called it the equant.
• The equant and the center of the Earth are
equidistant from the center of the deferent.

18. PTOLEMY’S MODEL
• Ptolemy’s model of the universe survived
for more than 14 centuries.
• The Greeks not only knew that the Earth
was round.
• They also knew the circumference of Earth
to be 25 000 miles.
• Eratosthenes measured it in 235 BCE using
trigonometry and the knowledge of the
angle of elevation of the sun at noon in
Alexandria and Syene (now Aswan, Egypt).