Astronomia Nova - Kepler's Laws

Kepler's Laws

The Astronomia nova records the discovery of the first two of the three principles known today as Kepler's laws of planetary motion, which are:

1. That the planets move in elliptical orbits with the sun at one focus.
2. That the speed of the planet changes at each moment such that the time between two positions is always proportional to the area swept out on the orbit between these positions.

Kepler discovered the "second law" before the first. He notices, as recorded in Chapter 32 of the Astronomia nova that the speed of the planet varies inversely based upon its distance from the Sun, and therefore he could measure changes in position of the planet by adding up all the distance measures, or looking at the area along an orbital arc.

However, Kepler's "area-time principle" did not facilitate easy calculation of planetary positions. Kepler could divide up the orbit into an arbitrary number of parts, compute the planet's position for each one of these, and then refer all questions to a table, but he could not determine the position of the planet at each and every individual moment because the speed of the planet was always changing. This paradox, referred to as the "Kepler problem," prompted the development of calculus.