Reading the Master: Newton and the Birth of Celestial Mechanics

Summary

One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.

— Freeman J. Dyson

In January of 1684, the young astronomer Edmund Halley travelled from Islington up to London for a meeting of the Royal Society. Later, perhaps over tea and chocolate at a nearby coffee house, he chatted casually about natural philosophy and other topics with Sir Christopher Wren and Robert Hooke. Talk soon turned to celestial motions, and Halley later reconstructed the conversation [22 p. 26]:

I having from the consideration of the sesquialter proportion of Kepler concluded that the centripetall force [to the Sun] decreased in the proportion of the squares of the distances reciprocally, came one Wednesday to town, where I met with S^r Christ. Wren and M^r Hook, and falling in discourse about it, M^r Hook affirmed that upon that principle all the Laws of the celestiall motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts; and S^r Christopher to encourage the Inquiry said that he would give M^r Hook or me 2 months time to bring him a convincing demonstration thereof, and besides the honour, he of us that did it, should have from him a present of a book of 40 shillings. M^r Hook then said that he would conceale [his] for some time that other triing and failing, might know how to value it, when he should make it publick.