Why are planetary orbits elliptical? We've considered this as an example of how to understand frame of reference, but Newton supposedly solved this problem mathematically in Principia Mathematica:
Effect and Cause
When Empirical Isn’t
We (that's me and the Holy spirit) were asked: if Newton's law of universal gravitation is an empirical formula, how is the accepted mass of the sun (1.9^E30 kg) not empirical?