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?

  • $\begingroup$ Short answer about Tycho Brahe: yes! That was the best data there was, and Kepler's conclusions were totally based on that data. Circular paths didn't work, therefore, try something else until it works. $\endgroup$
    – Bill N
    Nov 1 '17 at 17:24
  • $\begingroup$ @BillN Well that would have taken a lot of time, I heard 30 years? $\endgroup$
    – FlightMuj
    Nov 1 '17 at 17:32
  • $\begingroup$ On a side note I noticed the word genius in your title. Although Kepler’s first two laws are brilliant observations his third law was truly a genius. It’s hard to imagine just dreaming that one up. astro.physics.uiowa.edu/ITU/glossary/keplers-third-law $\endgroup$ Nov 1 '17 at 18:03
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    $\begingroup$ It's worth remembering that Kepler died twelve years before Newton was born. The question to consider is whether Newton could have formulated his gravitational laws without Kepler's work. $\endgroup$
    – StephenG
    Nov 1 '17 at 18:53
  • $\begingroup$ Cross-posted. Please only ask a question on one site, so that the answers are in one place. $\endgroup$ Nov 2 '17 at 16:52

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.

  • $\begingroup$ There is a hsitory of science site hsm.stackexchange.com which probably has more experts $\endgroup$ Nov 1 '17 at 17:18
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    $\begingroup$ Yes, the departure from circular orbits, along with placing the Sun at a focus rather than at the geometrical center is what made the data fit an ellipse. Interestingly, Galileo didn't like the circular orbits because he believed they weren't natural. To him, only circular and straight line motion was natural without outside interference (force). This was before Newton was born. see Malcolm Longair's Theoretical concepts in Physics. $\endgroup$
    – Bill N
    Nov 1 '17 at 17:21
  • $\begingroup$ @BillN interesting that most of Kepler's life was trying to model the solar system as interlocking platonic solids because that was perfect. I always pictured him as the first of the moderns, data first rather than theology $\endgroup$ Nov 1 '17 at 17:39
  • $\begingroup$ So chronologically he spent a lot of time trying to fit the data and then finally after the struggle he got the right shape: "elliptical orbits" (which was his first law) and THEN developed his rest of the two laws, right? $\endgroup$
    – FlightMuj
    Nov 1 '17 at 17:42
  • $\begingroup$ @FlightMuj the other 2 laws are pretty much a property of ellipses. $\endgroup$ Nov 1 '17 at 18:13

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