For as long as we've been able to crane our necks up at the stars, we've wondered about how to precisely explain how those bright twinkly lights move - some of them being the planets. We've come a long way from geocentricism, all the way to Kepler's Laws, universal laws defining any orbit.
Attempting to understand how the planets move has been an obsession of astronomers since people first began to look up at the stars. Indeed, the Greek philosopher, Thales, is said to have fallen into a well once because he was too busy looking up examining stars. They are a natural target of curiosity, so you can hardly blame him: hundreds of thousands of bright pricks of light, moving across the sky with the time of night and the season—and some made patterns that just didn't make sense to astronomers, loop-to-loops and spirals in the sky. Eventually, Kepler came along and figured it all out, but he built upon centuries of work by countless other astronomers, just to figure out the basic structure of our solar system.
Pre-Kepler: Epicycles And Geocentricism
All those odd years ago, a theory called geocentrism existed, that the Earth is the center of the universe and that everything, including the sun, orbits it. This stemmed from the general human feeling that, of course, our species must be the center of it all; this was later expressed in statements in the Bible, which for centuries was taken as scientific truth.
Of course, the scientists had difficult reconciling canon with what they were observing. Over-elaborate models for planetary motion included some movements that today are most likely to be found on a roller coaster.
Eventually, with much resistance by the religious institutions of the day, heliocentricism was overtaken by geocentricism through the work of astronomers like Copernicus and Galileo. Though this theory simplified models of planetary motion considerably, it still didn't explain a critical kink: a short backwards movement in the orbit of every planet - called retrograde motion, the usual forward motion being known as prograde. This was explained through an older Greek theory that called for epicyclic movement of the planets, or a short circle within the greater circle within the orbit like a loop-to-loop.
This was later to be unraveled to really just be another consequence of our perspective from here on Earth: since we are not, actually, at the center of the universe, nor even our solar system, we are observing the movement of the planets from a skewed angle.
However, serious problems still existed with the theories of planetary motion. Everything was assumed to move in circles, a belief that stemmed from the thought that celestial motion must be perfect, and thus in the clean smooth lines of a perfect circle.
It never really occurred to anyone that all those little discrepancies between observation and theory that they were still finding—planets moving too quickly here, or too slowly there—might be due to non-circular motion. Until Kepler, that is.
Deriving The Laws
Kepler did not have a computer to help him out. Let's get that perfectly straight from the get go. Imagine doing this all by hand. Calculations made trivial by the modern convenience of the computer took hundreds or even thousands of hours for him to complete by hand with nothing but pen, paper, and his brain.
Nor did he derive his theories from preexisting notions. He took thousands of data points, observations of all the known planets, taken from himself and from astronomers such as Tycho Brahe, and just crunched the numbers. His laws are empirically derived, found to fit exactly what the data says is true.
Kepler's Laws work not just for planetary motion, but for any object orbiting another, from moons orbiting their own planets to asteroids and comets. With a little geometric wizardry, one can even derive the laws for binary star orbits. The relative masses of the two objects, their distance between each other, none of it matters, as long as they are orbiting each other—ultimate generality, something all scientists yearn for when they attempt to explain things.
Indeed, later astronomers found that they perfectly agreed with even more general physical laws. Deriving Kepler's laws from Newton's own laws and basic geometry, in fact, is a staple assignment of many introductory level college physics courses. The enormity of his accomplishment, the originality and veracity of his claim, is one that must be admired.
Without further ado, Kepler's Laws on the next page: