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Suppose 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 had not yet been invented. So, how did he do that? How did he know that the distance to the Sun was changing, and that the velocity of the planet was changing to compensate for that? Was it solely because of the observational data provided by Tycho Brahe?

Can someone provide the details of his thinking on this?

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