Legacy of Aristotle

1. Legacy of Aristotle • Earth at the center of the universe • Unmoving • Unchanging • Corruptible • All other objects moving in uniform, circular motion about the Earth • Except the stars which were fixed

2. Problem • Given these constraints • Some planets (for example, Venus) do show a simple movement • Other planets (for example, Mars, Jupiter) do not move uniformly across the sky • How can we explain non-uniform motion given the constraints of Aristotle?

3. Solutions • Combine several circular motions • Nested spheres • Circular motion centered about a moving point (epicycle) • Or, reorder the structure of the universe (heliocentric) • Historically, epicycles were used

4. Simple version of an epicycle Motion of planet in opposite sense to the movement of the epicycle

5. First version • Viewed from the Earth, object would appear to move at a non-constant velocity • Would explain the solar anomaly • But, cannot explain the motion of the superior planets – retrograde motion • Need a different version of the epicycle • Motion around deferent same as motion of the epicycle.

6. A the bottom, planet is moving left, epicycle is moving right – here we have retrograde motion Second version: motion in the same sense as the epicycle moves.

7. Important observations: • Width of the retrograde motion (see above) • Spacing of the ret. Motions • Planet brightest at retrograde

9. Epicycles • Web site • http://csep10.phys.utk.edu/astr161/ • lect/retrograde/aristotle.html • Are reasonable mechanism to explain retrograde motion • Did it work? – Mars was the great test

10. Inferior planets • Mercury and Venus • Show a simple oscillation back and forth about the Sun • A simple epicycle does the job

11. Side view of the Sun as seen from Earth with an inferior planet oscillating about the Sun.

12. Epicycle description of the motion of an inferior planet. Not a unique solution (see later).

13. Superior planet motion. Observed retrograde motions of Mars from AD 109 on Note the uneven spacing and the variable widths

14. Problem with Mars • Epicycle description gives retrograde events evenly distributed around the zodiac • Epicycle description gives retrograde events of equal width. • Not the observation!

15. Departure from the model • Move the Earth from the center of the deferent • Moving in one direction changes the apparent spacing of the events • Moving in the other direction changes the apparent width of the retrograde events.

16. Moving the Earth off center changes the apparent spacing of the retrograde events

17. Moving the Earth off center changes the apparent width of the retrograde events.

18. Here the offset allows the correct spacing. But not the width. Here the width of the predicted events is good. But not the spacing. The two cannot be accomplished together.

19. But the problem still remains • It is impossible to solve both width and spacing by moving the Earth is the same direction • So we need another degree of freedom to solve the problem

20. Ptolemy • 2nd C AD • Claudius Ptolemeus, Alexandria • Mathematics • Trigonometry • Calculated table of sine values • Astronomy • Accurate catalog of stars (best ever)

21. Final solution • Not only move the Earth off center, but - • Create a fictitious point on the opposite side of the center from the Earth (called the equant). • From the equant, the epicycle appears to move uniformly. This means non-uniform motion. • Huge break with Aristotle.

22. Ptolemy’s description of retrograde motion.

23. Apparent motion of an epicycle as seen from Earth displaced from the center of the epicycle.

24. The placement of the equant and the Earth on opposite sides of the center of the deferent give an excellent match between calculated and observed retrograde motions for Mars.

25. Still had problems • One was the size of the Moon as seen from Earth • The second was the actual placement of the inferior planets (structure of the universe).

26. But there remained some other problems. For example, the size of the Moon would vary greatly due to its epicycle.

27. Three different descriptions of the inferior planets Traditional view.

28. Planets move about the Sun

29. Or lie beyond the Sun

30. Ptolemy • Also was interested in the size of the universe. • He reasoned that the planets could not get closer together because of their epicycle motion • This would give a minimum estimate of the solar system (a very modern idea).

31. Each color represents the forbidden zone for other planets. The size of the epicycles gives the minimum size of the solar system.

32. Ptolemy’s estimate • Ptolemy got about 19,865 earth radii • This is about 75 million miles! • Not very accurate but it did establish that the solar system is larger than our comprehension allows. • A tremendous change in the view of the universe