Isaac Newton And The Newtonian Synthesis

Newton studied at Cambridge University and was appointed professor of mathematics there in 1669. In 1687 his greatest work was published, the Mathematical Principles of Mathematical Philosophy, a work that is commonly known as the Principia from the first word of its Latin title. The Principia was the crowning achievement of the revolution in cosmology and physics that began one and a half centuries earlier with Copernicus. It contained the "Newtonian synthesis," a mathematical dynamics of forces acting on bodies that unified the inertial physics of Galileo and the heliocentric astronomy of Copernicus and Kepler. Kepler's ideal of a celestial physics was finally realized in the theory of universal gravitation presented in the Principia.

The chain of events leading to the publication of the Principia was a visit by astronomer Edmund Halley (1656—1742) to Cambridge in 1684. Halley asked Newton what would be the magnitude of the force exerted by the Sun on the planets, given that the planets revolved about the Sun in elliptical orbits. Newton immediately replied that such a force would vary inversely as the square of the distance to the planet. At Halley's encouragement he began to compose a systematic mathematical analysis of the action of a central force (a force that originates in a point) upon one or more particles. The resulting tract would become the core of book one of the Principia.

In the third book of the Principia, titled "System of the World," Newton took the mathematical theory from the first book and applied it to the solar system. The planets were considered as a system of point masses acting on each other by the force of gravity. The fundamental law that all bodies satisfy was the universal law of gravitation: every two bodies attract each other by a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. Although Newton did not think that gravitation was an intrinsic property of matter, he also did not attempt to speculate about the underlying physical process by which it acts. He would "feign no hypotheses" (Jammer 1969, 98) concerning the nature of gravity but simply investigate its action according to the inverse-square law.

Some of Newton's contemporaries objected to the idea of action at a distance across empty space and sought a mechanical explanation of gravity in terms of particles of matter interacting by contact or collision. Proponents of this point of view tended to be followers of Descartes. The fluid-dynamical concept of a vortex was used to model the motion of a planet about the Sun. The solar system was filled with a very fine fluid that rotated rather like a whirlpool about the Sun, propelling the planets in their orbits. The Cartesian mathematical physicist Christiaan Huygens (1629-1695) further elaborated the vortex mechanism in an attempt to explain the action of gravity near the surface of the Earth.

Newton believed that a fluid-dynamical explanation of planetary motion was untenable, a fact he attempted to document in his study of the motion of bodies in a resisting fluid in book two of the Principia. During the eighteenth century, there was considerable interest in the vortex theory of planetary motion, but it was eventually abandoned. It proved difficult to derive mathematical laws that described the vortex action, and some of the main predictions of the theory were found to be false. By 1750 Newton's theory of universal gravitation based on the inverse-square law had triumphed throughout European scientific circles.

Gravity is fundamental to cosmology because it acts between any two bodies anywhere in the universe. Among the different fundamental forces of physics, gravity is the only one that acts over the great distances of interest in cosmology. Newton wrote that gravity "must proceed from a cause that penetrates to the very centres of the Sun and planets, without suffering the least diminution of its force ... and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances" (Koyré 1957, 228). A theory of gravitation underpins any attempt to describe the universe as a whole and therefore is basic to all attempts to produce a scientific cosmology.

With the consolidation and acceptance of Newton's theory the main unresolved problem was to show that the solar system as governed by the inverse-square law of gravitation was in fact a stable dynamical system. It was known from a comparison of ancient and modern observations that no disturbance increasing indefinitely with time had occurred in this system. During the eighteenth century, researchers developed methods of increasing mathematical sophistication to analyze the gravitational interactions of systems of three and more bodies. By the 1790s Simon Laplace (1749-1827) was able to apply this theory to the three-body system consisting of the Sun, Jupiter, and Saturn and proved that there were no perturbations of the system that increased with time over the long term.

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