"If so, her motion must be influenced by it; perhaps she is retained in her orbit thereby. However, though the power of gravity is not sensibly weakened in the little change of distance, at which we can place ourselves from the centre of the earth, yet it is very possible that, so high as the moon, this power may differ much in strength from what it is here. To make an estimate what might be the degree of this diminution, he considered with himself that, if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried round the sun by the like power. And, by comparing the periods of the several planets with their distances from the sun, he found that if any power like gravity held them in their courses, its strength must decrease in the duplicate proportion of the increase of distance. This he concluded by supposing them to move in perfect circles concentrical to the sun, from which the orbits of the greatest part of them do not much differ. Supposing therefore the power of gravity, when extended to the moon, to decrease in the same manner, he computed whether that force would be sufficient to keep the moon in her orbit. In this computation, being absent from books, he took the common estimate, in use among geographers and our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the earth. But as this is a very faulty supposition, each degree containing about 691/2 of our miles, his computation did not answer expectation; whence he concluded, that some other cause must at least join with the action of the power of gravity on the moon. On this account he laid aside, for that time, any farther thoughts upon this matter."
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Republished in: Stephen Peter Rigaud (1838) Historical Essay on the First Publication of Sir Newton's Principia. p. 50-51
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Henry Pemberton
Henry Pemberton (1694 – 9 March 1771) was an English physician and man of letters. He became Gresham Professor of Physic, and edited the third edition of Isaac Newton's Principia Mathematica.
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