In 1609, Johannes Kepler published Astronomia Nova, a book containing ten years of his efforts
to understand the orbit of the planet Mars. He was using state-of-the-art astronomical
observations from his mentor and employer, Tycho Brahe, who was famous for generating
an enormous amount of high-quality data, and he needed to find the best explanation for
the motions of Mars - a very tricky problem!
There were three models of the solar system out there at the time, but none of them worked
very well for Mars. First, the Ptolemaic system put the Earth at the center, with the Sun
and planets orbiting it in perfect circles. There was also Copernicus’s heliocentric
model, which set the Earth among the planets, revolving around the Sun. And finally, Tycho
had his own system to propose, which combined aspects of both: he put the Earth at the center
with the Sun and moon orbiting it, but let the other planets orbit the Sun.
All three systems relied upon circular orbits, because the circle was accepted as an ideal
shape. Copernicus, Tycho, and Galileo all believed that planets should travel along
circular paths, but the data just didn’t fit.
Instead, Kepler found that another shape, the ellipse, works a lot better. An ellipse
is sort of like a flattened circle, and it has some special properties. You can draw
one by taking a loose string...
...attaching both ends to the paper, and using a pencil to keep the string taught while moving
all the way around the perimeter... The result is an ellipse! The length of the string never
changed, meaning that the sum of the distances between each endpoint, or focus, and any point
on the ellipse is constant.
In Astronomia Nova, Kepler states that Mars travels in an elliptical orbit around the
Sun, which is at one of the foci of the orbit. Later on, he expanded this first law to include
all of the planets and demonstrated that this shape fit the available observations.
The further apart the two foci are, the longer and skinnier the ellipse, and this “skinniness”
parameter is called “eccentricity.” Comets can have very eccentric orbits, coming in
quite close to the Sun before traveling back to the outer reaches of the solar system.
On the other hand, In a perfect circle, the two foci would lie right on top of each other
right at the center. The orbits of the planets in our solar system are not very eccentric
at all. They’re really very close to circular, which is partly why perfectly round orbits
seemed like a natural thing to expect in the first place.
It wasn’t easy to abandon a central idea like that, but with his first law of planetary
motion, Kepler rejected circular orbits and showed that an ellipse could better explain
the observed motions of Mars. Generalized to all planets, it states that the orbit of
a planet follows an ellipse with the Sun at one focus.