Kepler’s empirical Laws
- Kepler III : P2 = a3
- Kepler found mathematical relationship between size of orbit
- a = semi-major axis of ellipse, in AU’s
- if ellipse is a circle, a is the radius
- And the period P of the orbit in years
- sidereal period
- measured with respect to fixed stars
- earth a=1; P=1. Jupiter a=5; P = a1.5 = a * sqroot(a) = 11
- check 53 = 125 ; 112 = 121 -- close enough here
- Newton proved this too
With these laws, Kepler could predict all the planetary positions with great accuracy
- Triumph of the Copernican system
- Laws totally empirical -- didn’t say why planets moved so
- Newton figured this out -- Chap. 5