---
title: "Isaac Newton"
chunk: 7/17
source: "https://en.wikipedia.org/wiki/Isaac_Newton"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:07:12.165802+00:00"
instance: "kb-cron"
---

=== Philosophiæ Naturalis Principia Mathematica ===

Newton had been developing his theory of gravitation as far back as 1665. In 1679, he returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler's laws of planetary motion. Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed. After his exchanges with Robert Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. He shared his results with Edmond Halley and the Royal Society in De motu corporum in gyrum, a tract written on about nine sheets which was copied into the Royal Society's Register Book in December 1684. As part of this work, Newton also coined the term centripetal force. This tract contained the nucleus that Newton would develop and expand to form the Principia.
The Philosophiæ Naturalis Principia Mathematica was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the three universal laws of motion. Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics. They contributed to numerous advances during the Industrial Revolution and were not improved upon for more than 200 years. Many of these advances still underpin non-relativistic technologies today. Newton used the Latin word gravitas (weight) for the effect that would become known as gravity, and formulated the law of universal gravitation. His work achieved the first great unification in physics. He solved the two-body problem, and introduced the three-body problem.
In the same work, Newton presented a calculus-like method of geometrical analysis using 'first and last ratios', gave the first analytical determination (based on Boyle's law) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the Moon, provided a theory for the determination of the orbits of comets, and much more. Newton's biographer David Brewster reported that the complexity of applying his theory of gravity to the motion of the moon was so great it affected Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692–93, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According to Brewster, Halley also told John Conduitt that when pressed to complete his analysis Newton "always replied that it made his head ache, and kept him awake so often, that he would think of it no more". [Emphasis in original] He provided the first calculation of the age of Earth by experiment, and also described a precursor to the modern wind tunnel.
Newton identified two "principal cases of attraction"—the inverse-square law and a central force proportional to distance—showing that both yield stable conic-section orbits and that spherically symmetric bodies behave as if their mass were concentrated at a point; in modern terms, this linear force law is mathematically equivalent to the force associated with the cosmological constant.
Through Book II of the Principia, Newton was an important pioneer of fluid mechanics, and later analysis has shown that of its 53 propositions almost all are correct, with only two or three open to question. Propositions 1–18 of the book are the first comprehensive treatment of motion under resistance proportional to velocity or its square, leading the scholar Richard S. Westfall to remark that 'almost without precedent, Newton created the scientific treatment of motion under conditions of resistance, that is, of motion as it is found in the world'. Proposition 15 showed that under an atmosphere whose density falls inversely with distance, a circular-orbiting body subject to drag will trace an equiangular spiral—a result later independently derived by Morduchow and Volpe (1973). In Section IX of Book II, he  formulated the linear relation between viscous resistance and velocity gradient that now defines a Newtonian fluid, despite his experiments giving little direct insight into viscosity. Newton also discussed the circular motion of fluids and was the first to analyse Couette flow, initially in Proposition 51 for a single rotating cylinder and extended in Corollary 2 to the flow between two concentric cylinders. Further, he was the first to analyse the resistance of axisymmetric bodies moving through a rarefied medium. 
In Principia, Newton provided the first quantitative estimate of the solar mass, with later editions incorporating more accurate measurements, bringing his Sun-to-Earth mass ratio calculation close to the modern value. He further determined the masses and densities of Jupiter and Saturn, putting all four celestial bodies (Sun, Earth, Jupiter, and Saturn) on the same comparative scale. This achievement by Newton has been called "a supreme expression of the doctrine that one set of physical concepts and principles applies to all bodies on earth, the earth itself, and bodies anywhere throughout the universe".
Newton made clear his heliocentric view of the Solar System—developed in a somewhat modern way because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System. For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line". (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.)
Newton was criticised for introducing "occult agencies" into science because of his postulate of an invisible force able to act over vast distances. Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomenon implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomenon. (Here he used what became his famous expression "Hypotheses non fingo".)
With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier.