Kepler
- Clearly neither Ptolemaic nor Copernican system worked
- planets executing perfectly circular orbits at constant velocity
- Tycho himself believed in a geo-centric universe
- but his measurements belied this
Kepler inherited Tycho’s data and tried to make sense out of it.
- Used Copernican model and started with spheres
- Failure! orbits are not circles
- used trigonometry to determine orbit shapes
- Venus -- measure max elongation blackboard
- b = sin(?) x c
- b = Venus-Sun distance, c = Earth-Sun distance, 1 AU
- repeat each synodic period to map orbit shape
- Serendipitously, Mars’ orbit is especially non-circular
- Clearly shown by Tycho’s accurate data