Cosmology and Kepler's Laws

• Early western cosmology earth-centered.

• Ptolemy (140 A.D.) ``explained'' planets (which failed this model) with ``epicycles''. Church embraced this model as consistent with Genesis.

• Copernicus (1543 A.D.) solar-centered model.

• Tycho Brahe accumulated data and Johannes Kepler fit that data to specific orbits and deduced laws:

Kepler's Laws

1. All planets move in elliptical orbits with the sun at one focus (see next section).
2. A line joining any planet to the sun sweeps out equal areas in equal times ($dA/dt$ = constant).
3. The square of the period of any planet is proportional to the cube of the planet's mean distance from the sun ($T^2 = CR^3$). Note that the semimajor or semiminor axis of the ellipse will serve as well as the mean, with different contants of proportionality.