How did Kepler devise his three laws?

Question

I found it amazing how Newton figured out his theory of gravitation $(GMm/r^2)$ using Kepler's laws. The next logical question was how Kepler deduced his laws. This leads you to a rabbit hole of incorrect astronomical models. Aristotle, Ptolemy and Copernicus all developed incorrect models. It was, however, impossible for Kepler to find his laws without these models. In fact, Kepler produced a few erroneous theories of Mars's orbit around the Sun himself before narrowing upon the shape of an ellipse.

I've come to realize that the study of Physics is incomplete without understanding the history behind its development. So, now, I'm interested in understanding the ancient models of the heavens. What were these models? What mathematics went behind them? What experimental data justified them? Additionally, I am most interested in the work of Kepler and how he built his three laws using the data that were available to him.

In essence, I'm looking for a "history of science" book. Unfortunately, most such books are biographies of scientists as they hardly get down to the real mathematics and reasoning that went behind the models and theories. So, now, I'm not sure of the resources that would help me in this path (for context, I'm a freshman in University). Are there any books that would help me in this learning journey? Any guidance would be greatly appreciated. Thank you.

Answer 1

Q: "How did Kepler devise his three laws?"

Of Kepler's laws (not so called by Kepler himself), the first two appeared in 1609 (in 'Astronomia Nova Aitiologetos, seu Physica Coelestis', often 'Astronomia Nova' for short) and the third in 1619 (in 'Harmonices Mundi').

The four books in English about these that I would suggest in the first place, for their rich historical and explanatory content, also refreshingly close to the primary evidence (and presented without flinching from offering mathematical background where needed), are:

James Voelkel, "The Composition of Kepler's Astronomia Nova" (Princeton, 2001);

B Stephenson, "Kepler's Physical Astronomy" (Princeton, 1987),

Johannes Kepler, New Astronomy (1609), translated by William H. Donahue (Cambridge University Press, 1992) (with notes),

and "The Harmony of the World", (translation of Harmonices Mundi, 1619), translated with introduction and notes by E J Aiton, A M Duncan & J V Field, published by the American Philosphical Society, 1997 : see also (https://books.google.com/books?id=rEkLAAAAIAAJ).

One of the ways in which post-Keplerian treatments of Kepler's work can sometimes be rather misleading, is that they often ignore, or nearly ignore, parts of Kepler's treatment that some physicists and historians have considered important enough to deserve to be named as a law as well. Some have called this Kepler's "zero'th law" : see for example

H C Plummer (Cambridge, 1918) "An introductory treatise on dynamical astronomy", see also (https://archive.org/details/introductorytrea00plumiala) or (https://catalog.hathitrust.org/Record/001476484).

The question also mentions suggestions that "Newton figured out his theory of gravitation using Kepler's laws". This suggestion, though often made, implies a rather mixed-up summary of the historical evidence, which does show Newton relying on Kepler's third law, but not the others. So it may be useful also to suggest a few good sources to dip into about Newton's work:

I Bernard Cohen's 'Guide to Newton's Principia' published in the same volume with his (1999) English translation of the work,

and about its early history:

A R and M B Hall, "Unpublished Scientific Papers of Isaac Newton", (Cambridge, 1962 and 1978)

J Herivel, "Background to Newton's Principia", (Oxford, 1965)

and both of these give original papers with English translations where needed.

Other useful sources include

Curtis A Wilson, "From Kepler's Laws, So-called, to Universal Gravitation. Empirical Factors", in Archives for the History of Exact Sciences, vol.6 (1970), 89-170, and

S Westfall, 1971, "Force in Newton's Physics", (which covers the work of a number of Newton;s predecessors and can also usefully be compared with Bruce Stephenson's book cited above).