The highly influential English polymath Isaac Newton[1] (1642–1727) synthesized the new mathematical conceptions into an even simpler and more general theory—his laws of motion (or mechanics) and gravitation. Newton moved astronomy from descriptive model science to causal model science.
Newton’s first law was effectively a restatement of the principle of Galileo’s inertia.[2] His second law described how the motion of an object changes when force is applied. He explained that a given force will accelerate a lighter object more rapidly than a heavy object. He also stated that for an object of given mass, a larger applied force will cause greater acceleration. He combined these concepts into a simple equation, , meaning that the force on an object is equal to its mass multiplied by its acceleration. Newton applied this law to the concept of gravitation, a force of attraction between two objects which increases as their mass increases but decreases with the square of the distance between them. He showed that his second law could describe the motion of an apple falling from a tree, and just as successfully explain the motion of planets around the sun, and the moon around the earth. Newton even provided an explanation for tidal motion by invoking the gravitational effects of the sun and the moon on the seas.
Newton’s third law is usually summarized as “for every action there is an equal and opposite reaction”, from which is derived the well-known principle of the conservation of momentum.
Newton’s three laws were the foundation of a simple mathematical system with extraordinary explanatory power. Although Newton never explained what gravity was or why it occurred, his laws of motion and gravitation explained how it behaved. These laws were based on Euclidean geometry. They described motion as occurring in a three-dimensional Euclidean space within a medium called time.[3] At this point in history, it was almost universally held that both Newton’s laws of motion and gravity, and Euclidean geometry, were literally true.[4]
Newton also independently discovered the mathematical technique of infinitesimal calculus. This used the concept of infinitesimally small distances along a curved graph line to calculate the slope accurately at any point. Developing this method further, Newton was able to calculate the area of a segment between a graph line and the horizontal coordinate axis. These were powerful analytic techniques that marked the beginning of the use of infinity in modern mathematics.
[1] Despite Newton’s distinguished place in scientific history, his private papers have revealed that he was intensely interested in alchemy—his life’s main work. Physics and mathematics were merely his sideline pursuits. John Maynard Keynes famously described Newton as “the last of the magicians” (Kean, 2011). Indeed, Newton’s gravity is sometimes described as “action at a distance”—a concept in which one object affects another while widely separated by empty space. Prominent physicists found this aspect of Newton’s theory unconvincing and bordering on irrational, because it was historically associated more with concepts from “magic” or the occult (French, 2005) than objective science. It is important to note that by our definition, Newton was a non-Christian, because he denied the doctrines of the Trinity (Snobelen, 1999) and the incarnation (Dulles, 2005).
[2] Feynman, Leighton, & Sands, 2010, p. 9~1.
[3] Ibid., p. 2~3.
[4] Even as late as 1906, J.L.E. Dreyer wrote: “From Thales to Kepler philosophers had searched for the true planetary system; Kepler had completed the search; Isaac Newton was to prove that the system found by him not only agreed with observation, but that no other system was possible” (Dreyer, 1953, p. 424).