Kepler’s Hypothesis

12 June 2013

One of the common misconceptions presented in science is that it occurs in revolutionary steps. For example, the idea that Copernicus developed the heliocentric (sun-centered) model of the solar system, then Kepler showed that planets moved in ellipses and introduced Kepler’s laws, then Newton introduced the law of gravity that proved Kepler’s laws to be true. Each revolutionary idea replacing the previous one. But the real history is not quite so clean. Take for instance the development of Kepler’s laws.

Kepler’s first two rules, that the orbit of a planet is an ellipse, and that a line drawn from the Sun to a planet sweeps out area at a constant rate were proposed in 1609. While these rules allowed for a more accurate description of observed planetary motion, they weren’t perfect. For one thing, the planets don’t actually move in exact ellipses, nor is Kepler’s “constant area” rule exact. We now know the reason for this is due to the gravitational interactions between planets, which cause planets to speed up and slow down slightly as their positions align.

Another reason was due to the limitation of planetary measurements at the time. While is is true that planetary orbits have a generally elliptical shape, most of the orbits are nearly circular. Earth’s orbit, for example, differs by only 0.014% from a perfect circle. In the 1600s, only the orbits of Mercury (2%) and Mars (0.4%) were known to be non-circular. The orbits of Mercury and Mars were accepted to be oval in shape, but whether they were true ellipses was still a matter of debate.

An illustration of Kepler's third law.Gusbelluwiki, via Wikipedia
An illustration of Kepler’s third law.

In 1619 Kepler added a third rule, relating the square of a planet’s orbital period to the cube of its semi-major axis (a measure of its distance from the Sun). But by the late 1600s there were several proposed models for planetary motion that were similarly accurate to Kepler’s model. Kepler’s first two rules were favored by many astronomers, largely due to Kepler’s prediction of Mercury’s 1631 transit of the Sun. But there were two major difficulties with Kepler’s approach.

The first difficulty concerned the elliptical nature of planetary orbits. Kepler proposed that all planet have elliptical orbits. Observationally this was far from proven. While it was generally agreed that ellipses were an accurate approximation of the oval orbits of Mercury and Mars, it wasn’t clear that they were true ellipses (they aren’t). As for the other planets, their orbits appeared circular.

The second difficulty had to deal with the orbit of the Moon. Kepler’s model was that of a fundamental relationship between planetary motion. In 1643 it was found that the four known moons of Jupiter (now known as the Galilean moons) followed Kepler’s rules. This would imply that the orbit of the Moon should likewise follow them. But the Moon’s motion doesn’t obey Kepler’s rules with nearly the accuracy of planetary motion. Some of the other proposed models made more accurate lunar predictions. This is understandable because they were based off lunar observations, whereas Kepler based his model largely off the motion of Mars.

The upshot of all this is that Kepler’s laws were not universally accepted before Newton began his work on universal gravity in the late 1600s. It was only after Newton showed the rules to be exact for two (and only two) bodies moving under mutual gravitational attraction that Kepler’s model was preferred over the alternatives. They weren’t referred to as laws until Voltaire’s Elements of Newton’s Philosophy was published in 1738.

Then again, Kepler’s laws aren’t really laws in the way that we commonly think. The planets don’t orbit the Sun in perfect ellipses, a line traced from the Sun to a planet doesn’t trace out area at a constant rate, and the square of an orbital period is not exactly proportional to the cube of its semi-major axis. These rules are a good summary of the overall motion of the planets, and they are even a decent approximation of their motion. But they aren’t exact, and at no point did astronomers think they were exact.

That idea of “exactness” in physics didn’t become popular until Newton’s ideas rose to prominence. But that’s a story for another time.