I have a very simple question. How Kepler knew that orbits are elliptical, say I was living in his time. How would Kepler explain that the orbits are elliptical (since none of his 3 laws explain why orbits are elliptical; I assume he must have had other reasons to believe why orbits are elliptical)? Also calculus was not invented, so how did he do that? How did he know that the distance to Sun was changing, and the velocity of the planet was changing to compensate for that? Was it solely because of the observational data provided by Tycho Brahe?
An ellipse was the only thing which fitted the data (without adding the circles within circles special fixes needed for Ptolemy's epicycles)
I suppose his (Kepler's) genius was in trying different mathematical shapes to fit the data rather than arguing from Divine Insight or Ancient Greek authority that orbits must be some special shape because that is what God would do.
ps. You don't need calculus to calculate any of this - it just makes it easier. Newton worked out his gravitational law with calculus but then proved it with the same geometrical tools available to Kepler.