Kepler’s Laws of Nature

Kepler’s Laws of Nature

In an elliptical orbit the Sun is not at the center but is offset, at the focus of the ellipse. When a given planet is at its nearest to the Sun, it speeds up. When it is at its farthest, it slows down. Such motion is why we describe the planets as forever falling toward, but never reaching, the Sun. Johannes Kepler’s first law of planetary motion is simply this: A planet moves in an ellipse with the Sun at one focus.

In uniform circular motion, an equal angle of fraction of the arc of a circle is covered in equal times. So, for example, it takes twice as long to go two-thirds of the way around a circle as it does to go one-third of the way around. Kepler found something different for elliptical orbits: As the planet moves along its orbit, it sweeps out a little wedge-shaped area within the ellipse. When it is close to the Sun, in a given period of time it traces out a large arc in its orbit, but the area represented by that arc is not very large because the planet is then near the Sun. When the planet is far from the Sun, it covers a much smaller arc in the same period of time, but that arc corresponds to a bigger area because the Sun is now more distant. Kepler found that these two areas were precisely the same no matter how elliptical the orbit: the long skinny area, corresponding to the planet far from the Sun, and the shorter, squatter area, when the planet is close to the Sun, are exactly equal. This was Kepler’s second law of planetary motion: Planets sweep out equal areas in equal times.

Green Sea. Photo by Elena

Many years later, Kepler came upon his third and last law of planetary motion, a law that relates the motion of various planets to one another, that lays out correctly the clockwork of the solar system. He described it in a book called The Harmonies of the World.

Kepler’s first two laws may seem a little remote and abstract: planets move in ellipses, and sweep out equal areas in equal times. Well, so what? Circular motion is easier to grasp. We might have a tendency to dismiss these laws as mere mathematical tinkering, something removed from everyday life. But these are the laws our planet obeys as we ourselves, glued by gravity to the surface of the Earth, hurtle through interplanetary space. We move in accord with laws of nature that Kepler first discovered. When we send spacecraft to the planets, when we observe double stars, when we examine the motion of distant galaxies, we find that throughout the Universe Kepler’s laws are obeyed.

Not given to quiet understatement, Kepler assessed his discoveries in these words: With this symphony of voices man can play through the eternity of time in less than an hour, and can taste in small measure the delight of God, the Supreme Artist… I yield freely to the sacred frenzy… the die is cast, and I am writing a book – to be read either now or by posterity, it matters not. It can wait a century for a reader, as God Himself has waited 6,000 years for a witness.

With this symphony of voices man can play through the eternity. Image: Animated Moving Flashing Colors by © Elena