1. HELIOCENTRIC MODEL Copernicus 16 th century Maybe things orbit the sun instead of the earth? 1473-1543 AD

2. Retrograde motion easy to explain without resorting to further embellishments! (like with epicycles)

3. Copernicus could also explain a lot about the differences observed in planetary movement! (Once again without any fancy embellishments!) Superior and Inferior planets

4. Superior planets (orbits bigger than earth’s) opposition conjunction

5. Inferior planets (orbits smaller than earth’s) never in opposition, but two kinds of conjunction (inferior)(superior)

6. Inferior planets (orbits smaller than earth’s) never have elongations larger than a certain value greatest EASTERN elongation: ‘evening star’ greatest WESTERN elongation: ‘morning star’

7. Orbital periods of the planets As seen from earth the planet repeats itself somehow. Synodic: Sidereal: Actual amount of time the planet takes to orbit the sun, in reference to the stars. How did Copernicus do it?

8. (inferior) Start

9. (inferior) Start

10. (inferior) Start

11. (inferior) Start

12. (inferior) Start

13. (inferior) Start

14. (inferior) Start (inferior again)

15. (inferior) Start (inferior again) S synodic period P sidereal period Angle 

16. (Earth)(Inferior planet)

17. 1546-1601 AD Tycho Brahe:

18. Hven (now Ven)

19. Uraniborg "The Castle of Urania"

20. NS Giant quadrant Mounted on N-S axis, for measuring the altitude of stars. Uraniborg

22. A Tycho quadrant

23. Stjerneborg "castle of the stars". (Instruments underground)

25. 1571-1630 AD Johannes Kepler: analyzed like crazy

26. Tycho Brahe: measured like crazy Johannes Kepler Kepler’s Laws ! 1546-1601 AD 1571-1630 AD

27. a (Semi-major axis) b (Semi-minor axis) K.L. #1 Planetary orbits are not circles, but ellipses! Eccentricity e a is also average distance from either foci e = 0 to 1

28. average distance from sun = semi-major axis Sun at one of the foci

29. Ellipses with differing eccentricities (but same a)

30. Planeta (AU)eb/a Mercury0.3870.2060.9786 Venus0.7230.0071.0000 Earth1.0000.0170.9999 Mars1.5240.0930.9957 Jupiter5.2030.0480.9988 Saturn9.5540.0530.9986 Uranus19.1940.0430.9991 Neptune30.0660.0100.9999 Eccentricity of the planets?

31. K.L. #2 The sun-planet line sweeps out equal areas in equal times! [Angular momentum] slowest fastest

32. slowest fastest perihelion aphelion Sun

33. K.L. #3 For a planet orbiting the sun … ! a : orbit semi-major axis in AU P : Orbital period in years

35. NOTE: Two orbits with the same a have the same period! (and vice-versa)

36. Two descriptive models, which is “right”? HELIOCENTRIC MODEL GEOCENTRIC MODEL

37. Galileo Galilei 1564-1642 found supporting evidence for the heliocentric model Telescope!

38. According to Aristotelian principles the Moon was above the sub-lunary sphere and in the heavens, hence should be perfect.

39. SUNSPOTS Even the sun isn’t perfectSun rotates

40. Moons of Jupiter (solar system analog)

41. Galilean satellites (Io, Europa, Ganymede and Callisto)

42. Phases of Venus