Cosmos - Carl Sagan [39]
Students both of Kepler and of Newton never knew what they were missing.
Newton discovered the law of inertia, the tendency of a moving object to continue moving in a straight line unless something influences it and moves it out of its path. The Moon, it seemed to Newton, would fly off in a straight line, tangential to its orbit, unless there were some other force constantly diverting the path into a near circle, pulling it in the direction of the Earth. This force Newton called gravity, and believed that it acted at a distance. There is nothing physically connecting the Earth and the Moon. And yet the Earth is constantly pulling the Moon toward us. Using Kepler’s third law, Newton mathematically deduced the nature of the gravitational force.* He showed that the same force that pulls an apple down to Earth keeps the Moon in its orbit and accounts for the revolutions of the then recently discovered moons of Jupiter in their orbits about that distant planet.
Things had been falling down since the beginning of time. That the Moon went around the Earth had been believed for all of human history. Newton was the first person ever to figure out that these two phenomena were due to the same force. This is the meaning of the word “universal” as applied to Newtonian gravitation. The same law of gravity applies everywhere in the universe.
It is a law of the inverse square. The force declines inversely as the square of distance. If two objects are moved twice as far away, the gravity now pulling them together is only one-quarter as strong. If they are over ten times farther away, the gravity is ten squared, 102 = 100 times smaller. Clearly, the force must in some sense be inverse—that is, declining with distance. If the force were direct, increasing with distance, then the strongest force would work on the most distant objects, and I suppose all the matter in the universe would find itself careering together into a single cosmic lump. No, gravity must decrease with distance, which is why a comet or a planet moves slowly when far from the Sun and faster when close to the Sun—the gravity it feels is weaker the farther from the Sun it is.
All three of Kepler’s laws of planetary motion can be derived from Newtonian principles. Kepler’s laws were empirical, based upon the painstaking observations of Tycho Brahe. Newton’s laws were theoretical, rather simple mathematical abstractions from which all of Tycho’s measurements could ultimately be derived. From these laws, Newton wrote with undisguised pride in the Principia, “I now demonstrate the frame of the System of the World.”
Later in his life, Newton presided over the Royal Society, a fellowship of scientists, and was Master of the Mint, where he devoted his energies to the suppression of counterfeit coinage. His natural moodiness and reclusivity grew; he resolved to abandon those scientific endeavors that brought him into quarrelsome disputes with other scientists, chiefly on issues of priority; and there were those who spread tales that he had experienced the seventeenth-century equivalent of a “nervous breakdown.” However, Newton continued his lifelong experiments on the border between alchemy and chemistry, and some recent evidence suggests that what he was suffering from was not so much a psychogenic ailment as heavy metal poisoning, induced by systematic ingestion of small quantities of arsenic and mercury. It was a common practice for chemists of the time to use the sense of taste as an analytic tool.
Nevertheless his prodigious intellectual powers persisted unabated. In 1696, the Swiss mathematician Johann Bernoulli challenged his colleagues to solve an unresolved issue called the brachistochrone problem, specifying the curve connecting two points displaced from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time. Bernoulli originally specified a deadline of six