THE LAWS OF PLANETS

For fifteen hundred years, astronomers believed the heavens ran on perfect circles. Ptolemy, writing in the second century, built an elaborate machine of circles-on-circles — epicycles — to make his predictions line up with reality. Copernicus, in 1543, put the sun in the middle instead of the Earth. He kept the circles.

Then Johannes Kepler, working from the astonishingly careful observations of Tycho Brahe, gave up on circles altogether. He tried everything else he could think of. After eight years of calculation, he landed on the truth.

Orbits are ellipses.

An ellipse is a stretched circle with two special points inside it, called foci. What makes an ellipse an ellipse is that if you pick any point on the curve and draw lines to each focus, the two lengths always add to the same number.

The number a is the semi-major axis — the long radius. The number e is the eccentricity — how "squished" the ellipse is, from zero (perfect circle) to almost one (nearly flat). Every planet's orbit is one of these shapes, with the sun sitting at one of the two foci.

Kepler noticed something else: planets don't move at constant speed. They move faster when they're closer to the sun, and slower when they're far away.

But the area swept by the line from the sun to the planet, per unit of time — that stays the same.

Watch it happen.

The wedges look wildly different. Some are long and thin, some are fat and round. And yet the readout below says they're all the same area, to three decimal places.

That is Kepler's second law. It doesn't look like it should be true. It is.

For every planet orbiting the sun, there is a single number that comes out the same.

In plain English: the square of the orbital period, divided by the cube of the semi-major axis, is the same for every body orbiting the same star. Kepler called this the "harmony of the worlds."

Look at the rightmost column. Mercury, Earth, Mars, Jupiter — four worlds with nothing in common except that they orbit the same star — and the ratio T² / a³ lines up to three decimal places. That's not curve-fitting. That's a law of nature, hiding in plain sight for every astronomer who ever looked up.

Kepler described the laws. He never explained them. That job was left to Isaac Newton, who realized — eighty years later — that if you assume a single force pulling the planet toward the sun, with magnitude proportional to one over the distance squared, you get every one of Kepler's three laws for free.

The further the planet is from the sun, the weaker the pull — but it weakens fast, as the square of the distance. When the planet swings close, the force balloons. When it drifts far, the force barely tugs.

The arrow shows how hard gravity pulls. Watch it grow as the planet dives toward perihelion, and shrink as it coasts out to aphelion.

Every artificial satellite in orbit around Earth obeys Kepler's laws. Every rocket we've ever sent to another planet used them to plan its trajectory. When Le Verrier predicted the existence of Neptune in 1846, based on perturbations in the orbit of Uranus, he used Kepler. When we find exoplanets today by watching stars wobble, we're using Kepler. When LIGO detects gravitational waves from merging black holes, the orbital decay is Kepler's laws, generalized to Einstein's gravity.

Three sentences from a half-blind mystic in 1609. Still running the universe.