Astronomical calculations
Kepler introduced the idea of elliptical orbits and increased the accuracy of prediction of planetary positions by a large factor. He based his calculations – essentially a curve fitting process – on the observations of Tycho Brahe, the first observational astronomer to produce continuous nightly observation records.
I’ve parked an old site of mine that contains low precision formulas and procedures for calculating the positions of the planets at http://bodmas.org/kepler/ for now. I’ll be bringing this all together into a PDF based handout over the next few months.