Hooke, Newton, and the Trials of Historical Examination

Abstract

Nauenberg replies: Ofer Gal writes that he discovered, to his surprise, that “a closed curve orbit created by force had simply been inconceivable” to Isaac Newton before Newton finally learned about the idea from Robert Hooke. But ample historical evidence indicates that Gal’s opinion is incorrect. For example, in a cryptic remark written in his notebook 15 years before his 1679 correspondence with Hooke, Newton stated that “if the body moved in an Ellipsis, then the force in each point … may be found.” 1 1. J. Herivel, The Background to Newton’s Principia, Clarendon Press, Oxford, England (1965), p. 130. In another manuscript, composed before his appointment as the Lucasian chair in mathematics in 1669 at Cambridge University, Newton found that “the force of gravity [at Earth’s surface] is 4000 times and more greater than the endeavor of the Moon to recede from the Earth.” 2 2. Ref. 1, p. 196. The discrepancy between Newton’s figure and the correct value of approximately 3600 (according to the inverse square law) resulted from the erroneous estimate that he used for Earth’s radius.Apparently, Newton did not discover his error until shortly before starting to write the Principia. By applying Kepler’s third law—that for the “primary planets the cubes of their distances from the Sun are reciprocally as the square of the number of revolutions in a given time”—Newton had found that his apparently failed assumption that Earth’s gravitational force satisfies the inverse square law did apply to the gravitational force of the Sun. He wrote that “the endeavours [of the planets] of receding from the Sun will be reciprocally as the squares of the distances from the Sun.” 3 3. Ref. 1, p. 197. By insisting that Newton did not develop a “sophisticated mathematical theory of orbital motion” before 1684, Gal indicates that he cannot understand the subtle mathematical results about orbital dynamics that Newton had exposed in his 13 December 1679 letter to Hooke. Acknowledging those results, however, would invalidate Gal’s arguments of what Newton learned about orbital dynamics from his correspondence with Hooke.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. Herivel, The Background to Newton’s Principia, Clarendon Press, Oxford, England (1965), p. 130. Google Scholar2. Ref. 1, p. 196. Google Scholar3. Ref. 1, p. 197. Google Scholar© 2004 American Institute of Physics.