One law for heaven and earth

Asking Kepler why

Newton’s second giant was Kepler. His three laws predicted the planets beautifully, but they only described what happens. A planet moves in an ellipse and sweeps out equal areas in equal times. But why? Physicists love nothing more than asking why. Newton answered.

In 1665–66, while plague closed Cambridge, the young Newton, then about twenty-three, went home to his family’s farm at Woolsthorpe. There he began three great projects: the calculus, experiments splitting light with a prism, and the first ideas of universal gravitation. They laid the foundations of modern mathematics, optics, and mechanics.

But he didn’t finish the work on gravity for years. Two other people pushed him. In 1679 Robert Hooke, the Royal Society’s curator of experiments, suggested in a letter that a planet’s orbit could be understood as two motions combined: a straight-line motion of its own, and a pull toward the sun. Then in 1684 the astronomer Edmond Halley, later famous for his comet, visited Newton in Cambridge. What curve would a planet follow, he asked, if the sun attracted it with a force that weakens with the square of the distance? An ellipse, Newton replied. He had calculated it. Halley urged him to write it all up, and paid for the printing himself. The result was the Principia.

Falling around the earth

Put Galileo’s inertia together with Hooke’s hint, and orbits make sense. By inertia, a planet on its own would fly off in a straight line. It curves around the sun because a force keeps pulling it inward. The force doesn’t push it along its path. It only bends the path, adding a fall toward the sun to the planet’s straight-line motion.

Newton imagined a cannon on top of a very high mountain, firing horizontally. A slow shot falls to the ground nearby. A faster one lands farther away. Fire fast enough, and the ball falls toward the earth exactly as fast as the curved surface drops away beneath it. It keeps falling and never lands. That is an orbit.

There is a reason mechanics succeeded first in astronomy. Galileo had struggled with friction and air, polishing his balls and tracks to reduce them. Space has neither. The heavens were a perfect laboratory, where the only thing acting on a planet is gravity.

Three laws and one force

The Principia opens with three laws of motion. Here is the first, in the 1729 English translation:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

Isaac Newton, Principia, Law I

That is Galileo’s inertia, and it overturns Aristotle: rest and motion are equals. The second law says that a force changes an object’s motion in proportion to its strength and in its own direction, which is exactly what bends a planet into an ellipse. The third says that every action has an equal and opposite reaction.

To these Newton added one force, universal gravitation. Every body attracts every other body, with a force proportional to their masses and inversely proportional to the square of the distance between them. There is something almost uncanny about the discovery. Gravity between everyday objects is far too weak to notice. You can’t see or feel the pull between two people in a room. Newton found it by reasoning, and it worked everywhere.

The apple and the Moon

Here is the famous test. An apple dropped near the ground falls about 4.9 meters in its first second. The Moon is about 60 times farther from the earth’s center than the apple is. If gravity weakens with the square of the distance, the Moon should fall toward the earth 60 × 60 = 3,600 times more slowly. It should drop just 1.4 millimeters in a second while it moves along its orbit. It does. The force that drops the apple is the force that holds the Moon.

This was another revolution in how people saw the world. Galileo’s telescope had shown that the heavens look like the earth. Newton showed that they obey the same laws, with the same constant, even the same numbers. The heavens were no longer a separate realm of perfection. In this reading, the stars would keep turning even without gods, as long as the law held. The poet Alexander Pope wrote an epitaph for Newton:

Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light.

Alexander Pope, epitaph intended for Newton, 1730

Over the next three hundred years, this course argues, science on this new track achieved more than in the previous two or three thousand.

Laplace’s demon

The result was a mechanical view of the universe, best captured by a famous thought experiment. The French mathematician Pierre-Simon Laplace, a devoted follower of Newton, wrote in 1814:

An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, … for such an intellect nothing would be uncertain, and the future, just like the past, would be present before its eyes.

Pierre-Simon Laplace, A Philosophical Essay on Probabilities, 1814

Later writers called this all-knowing intellect “Laplace’s demon.” Only a demon could handle that much calculation. Humans have limits; the demon has none. Know where everything is and what forces act on it, and the future and the past unroll like a machine running forward or backward on its track.

Consider how much this changed. The world no longer needed gods to run it; a set of laws was enough. Stars turn, apples fall, and carts roll by the same rules. Things relate to one another simply, through forces that change their motion. The old cosmos, where every element had its natural place and purpose, was gone. In this reading, the picture of independent bodies, each moving by the same laws, also suited an age of intellectual liberation and individual independence.