Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

Gravity Theory: The Tenuous Link

Newton's original manuscript for TMM is dated February 1700, which is the month Newton was confirmed as Master of the Mint in London. It was published in David Gregory's (1702) Astronomia Physicae. In the 18th century, it was reprinted four times in Latin and 13 times in English (Cohen, 1975, p.8). Enigmatically, the manuscript contains no allusion to a theory of gravity. In 1975, Bernard Cohen posed the challenge: Cohen offered no comment upon either the accuracy of the theory - whether it was an improvement upon those available - or, to what extent if any it was based upon a theory of gravitation. Craig Waff commented in his review of Cohen's book upon the historical irony, that the brief 1702 essay "Theory of the Moon's Motion" was 'probably the most obscure of Newton's publications', and yet it 'appeared in print during the early eighteenth century more times than anything else which left the hand of Newton.' Waff made a claim which I have confirmed: Of TMM's composition, Bernard Cohen wrote: I rather doubt whether resolution of a three-body problem appeared in that 1702 thesis. It was only years after abandoning such an endeavour that Newton produced instead a recipe for finding lunar celestial longitude. His calculations on lunar theory (at Cambridge University Library) are in Latin for the Principia calculations, while those for TMM tended to be in English - his reasoning on the more practical side of the problem took place in English.

I agreed with Dr Waff, that these notes showed:

The Principia of 1687 did well account for the lunar inequality known as the Variation, by modelling it on a yearly-revolving elliptical orbit with Earth at its centre. The French astronomer D'Alembert remarked that this derivation of the Variation from gravity theory was done 'avec beaucoup de clart' et precision' - whereas, in contrast, he doubted whether Newton's derivation of the 'annual equation' was sound: Bernard Cohen commented on these three-body problems: 'He [Newton] was really successful only in accounting for the variation and the nodal motion.' (1980, p.276)

A problem with these three-body problems is that scholars expounding them never mention the two or thee-hundred percent error in lunar mass that was embedded in these weighty computations (See Lunar Mass Error page). For a computation in celestial mechanics, this should be at least be mentioned. In 1713 the bulk of TMM was incorporated into a scholium of the Principia. It was still a recipe for finding longitude, but it was also averred that each of its steps had been derived from gravity theory: a dual-track policy, so to speak.

In the Third Edition of 1726, the former goal was abandoned, by dropping the crucial paragraph stating that lunar longitude could thereby be found, so that the text became solely a tract about gravity theory. As the only version of the Principia translated into English, it gave no clue that one of its scholia contained the remains of a recipe for finding longitude. (See Return of the Epicycles, and The Forgetting of TMM)


The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998