The document discusses the astronomical contributions of Eudoxus, a Greek astronomer from the 4th century BCE. Eudoxus developed the first mathematical model to explain the motions of the sun, moon, and planets. His model assigned multiple spheres to each celestial object, with the inner spheres rotating at different rates and angles than the outer spheres. This system could reproduce the observed retrograde motion of planets and was an important early step in developing mathematical astronomy.

1. EUDOXUSBiography
Life and Works
Contribution to Mathematics
Contribution to Astronomy
Contribution to Geometry in Relation to Astronomy

2. EUDOXUSContribution to Astronomy

3. Our principal source of
his astronomy were :
 Aristotle -3rd BCE
 Aratus -3rd BCE
 Hipparchus-2nd BCE
 Simplicius-6TH CE

8. 5 BASIC PRINCIPLES

9. 5 BASIC PRINCIPLES

11. In most modern reconstructions of the
Eudoxan model, the Moon is assigned three
spheres:

12. In most modern reconstructions of the
Eudoxan model, the Moon is assigned three
spheres:

13. In most modern reconstructions of the
Eudoxan model, the Moon is assigned three
spheres:

14. The Sun is also assigned
THREE SPHERES.

15. The five visible planets
(Venus, Mercury, Mars, Jupiter, and Saturn)
are assigned FOUR SPHERES each:

16. The five visible planets
(Venus, Mercury, Mars, Jupiter, and Saturn)
are assigned FOUR SPHERES each:

17. The five visible planets
(Venus, Mercury, Mars, Jupiter, and Saturn) are assigned
FOUR SPHERES each:

18. HOMOCENTRIC SPHERE FOR THE MOON

19. • The outer sphere rotates in one day as the
sphere of the stars and with axis perpendicular to
the zodiac circle. One period is 24 hours.
• The next middle sphere rotates on an circle at
an angle to the plane of zodiac circle, and from east
to west.
• The inner sphere rotates about an axis inclined to the
axis of the second at an angle equal to the highest latitude
attained by the moon, and from west to east.

20. IMPORTANCE OF
EUDOXAN SYSTEM
• He was the first to attempt a
mathematical explanation of the
planets.

21. IMPORTANCE OF
EUDOXAN SYSTEM
• The first person to devise a model that
could explain the retrograde motion of the
planets in the sky.

22. a planet is attached to a
particular spot on a
sphere.
Earth would be at the
center of the sphere
and the sphere would
rotate around the Earth.
As the sphere rotates, it
would carry the planet
around in a circle at
whatever latitude we
had attached the planet
on to the sphere.

23. imagine attaching that
sphere to a second sphere,
also centered on the earth.
If the two axes are parallel,
then the resulting motion of
the planet with respect to
the earth is simply the sum
of the rotations of the two
axes.
If the two axes are rotating
with opposite rates, then the
planet would appear to be
motionless, from the point
of view of the earth. (This is
shown in the image to the
right.)

24. Now imagine what happens
when we take the second
axis of rotation and we tilt it
with respect to the first.
We will also keep the
rotation rates of the two axes
equal and opposite. (This is
really the heart of the
model.) Because the rotation
rates are the same speed, but
the opposite direction, the
planet would almost stay in
the same place; because the
axes are not parallel, the
planet would actually
wobble a little bit left and
right and also up and down.

25. . The net effect would be
the planet making a
figure eight loop. (The
mathematical name for
the resulting curve is a
"hippopede.")
To make the planet
actually go around the
earth, and also create the
retrograde motion, we
take the two spheres
creating the hippopede
and have them rotate
about a third sphere.