Peter Moylan wrote: > Yusuf B Gursey wrote: >> On Feb 26, 11:13 am, R H Draney <dadoc...@spamcop.net> wrote: >>> Peter T. Daniels filted: >>> >>> >>> >>>> On Feb 25, 1:29=A0pm, Adam Funk <a24...@ducksburg.com> wrote: >>>>> "archaeoastronomy" >>>> No, that's speculation about the alignments of Stonehenge or the Nasca >>>> figures or whatever. >>>> Which is different from the sort of _recorded_ observations made from >>>> at least the early first millennium BCE in Mesopotamia (and from some >>>> point in China) down to the time of Tycho Brahe, on the basis of >>>> nothing but whose naked-eye observations, Kepler worked out the theory >>>> of elliptical planetary orbits. >>> Impressive, true, but I once got my hands on a book on celestial mechanics >>> that derived the fact of elliptical orbits (and the "equal areas in equal >>> times" principle) starting with nothing but the fact that gravity is in >>> inverse-square proportion to distance....r >> >> but Kepler didn't know that. it took Newton to figure it out. > > In fact Newton did it the other way around. He started with Kepler's > results about the shape of the orbits, and deduced from that that the > force acting on the planets must obey an inverse-square law. > > Once I tried to follow the same line of reasoning, and got nowhere. > Showing that an inverse-square law leads to elliptical orbits is a > simple undergraduate exercise these days, although it would have been > harder in Newton's day. Showing that elliptical orbits leads to an > inverse-square law is a problem of fiendish difficulty. > > I imagine that Newton started with a variety of guesses (constant force; > force varying inversely with distance; etc.) and tried each one until he > found one that gave a match with Kepler's results.
If he imagined gravity as force lines emanating from an object A into infinity, then another object B would be struck by a number of such force lines depending on its distance from the object A. The relationship between distance A to B, and gravity attraction is similar to the relationship between diameter and surface areas of the spheres of various diameters.
I would be surprised if the inverse-square-of-the-distance law wasn't the first one he thought of. It seems to be so obvious.
> In some other problem domains, e.g. radiant energy, > conservation-of-energy arguments lead directly to an inverse-square law. > In the case of gravity, anything other than an inverse-square law would > lead to planets that either fell into the sun or flew off into the outer > void. It's not clear to me, though, that Newton had enough information > to be able to guess that inverse-square was the most obvious candidate. > These days it's standard practice to publish only the final tidied-up > version of theoretical results, omitting any insight into the reasoning > that led to the results. I think that's also what Newton did.