# When did physics texts start to teach Kepler's $3/2$'s power law as a result of Newton's $1/r^2$ law of gravitation, rather than the other way around?

In modern physics textbooks, we teach Newton's laws of motion, then Newton's law of Universal Gravitation, and then Kepler's laws of planetary motion. Specifically, from the $1/r^2$ form of the gravitational force, and some other parts of Newton's laws, we can derive Kepler's 3rd law, that the period of motion of a planet is proportional to the $3/2$ power of its distance from the sun.

But historically, Kepler developed his laws before Newton wrote the Principia. Newton formulated his laws in the Principia, then (also in the Principia) derived the specific $1/r^2$ form of his gravitational law from the $3/2$ power form of Kepler's 3rd law.

My question is: when did physics texts and/or courses switch from the historical order of these two laws to the more recent (and possibly more pedagogical)? Was there a reason given at the time? The historical order was more inductive in its reasoning, while the modern presentation is more deductive in its reasoning.

One possibility I can think of is that we derive the $1/r^2$ form of Coulomb's law using Gauss's law and the fact that (macroscopic) space is 3-dimensional. That derivation carries over word-for-word to gravity. That becomes a very logical reason to say gravity should have the $1/r^2$ form once you know vector calculus. That might be a fruitful time period to look at.

• The first text to have derived Kepler's law from Newton's law is surely Principia itself. Do you have any evidence that texts after that kept teaching Kepler's law before Newton's? From a modern perspective that would seem rather strange, but I don't know much about physics pedagogy in the 17th and 18th centuries so I can't rule it out. Oct 29, 2014 at 3:30
• No. Principia takes Kepler's laws as given, then derives the 1/r^2 from of gravity from them. It does not derive Kepler's law from Newton's. I don't have any evidence about what happened after the publication of Principia; that's what I'm asking. Oct 29, 2014 at 3:39
• Yes, it seems you're correct about that. Principia also seems to not be the earliest work to contain this derivation, as De motu corporum in gyrum predates it by 3 years. I don't know when the philosophical switch happened as to which is fundamental. Oct 29, 2014 at 4:13
• Very interesting question!!
– Danu
Oct 29, 2014 at 8:11
• @LoganMaingi I can't see why you would find strange that some deduce a general law from an observation. Until Cavendish's experiment of 1798 I can't see any reason for not treating Newton's law as a result of Kepler's law. Nov 1, 2014 at 12:32