Principia Mathematica Philosophiae Naturalis

Author: Isaac Newton

Law of Gravitation

Issac Newton

Hitherto we have explained the phaenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes use to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always in the duplicate proportion of the distances. Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun decreases accurately in the duplicate proportion of the distances as far as the orb of Saturn, as evidently appears from the quiescence of the aphelions of the planets; nay, and even to the remotest aphelions of the comets, if those aphelions are also quiescent. But hitherto I have not been able to discover the cause of those properties of gravity from phaenomena, and I frame no hypotheses; for whatever is not deduced from the phaenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phaenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.

Trans by Motte


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Chicago: Isaac Newton, "Law of Gravitation," Principia Mathematica Philosophiae Naturalis in A Source Book in Physics, ed. William Francis Magie (Cambridge, MA: Harvard University Press, 1963), 92–93. Original Sources, accessed December 6, 2022,

MLA: Newton, Isaac. "Law of Gravitation." Principia Mathematica Philosophiae Naturalis, in A Source Book in Physics, edited by William Francis Magie, Cambridge, MA, Harvard University Press, 1963, pp. 92–93. Original Sources. 6 Dec. 2022.

Harvard: Newton, I, 'Law of Gravitation' in Principia Mathematica Philosophiae Naturalis. cited in 1963, A Source Book in Physics, ed. , Harvard University Press, Cambridge, MA, pp.92–93. Original Sources, retrieved 6 December 2022, from