beccastareyes

Tara had to ask a very hard quesiton -- even a top five list would be easier.
I would have to say that Kepler's Laws are the greatest achievement of astronomy, as those are the first truly mathematical model of the heavens from a non-Earth POV. It took astronomy from 'the observations and calculations you make to do the astrology that the ruler pays you to do' to real-live science.
For reference, Kepler's Laws are:

1) The planets trace out an ellipse (a type of oval) with the sun as one focus. Most of the planets are pretty much in circular orbits -- Mercury and Pluto have rather squashed ones, and Mars's isn't perfect either.
2) The 'year' squared of a planet is proportional to the distance form the sun cubed.
3) Planets move faster when they are closer to the sun. Kepler said that planets would sweep out equal arcs in equal time (so if you made a triangle of a planet's position, it's position in 30 (or whatever) days and the sun, it would always be the same area).

Kepler's laws actually fixed up Copernicus's model -- Copernicus couldn't quite get things to work out, and Kepler's ellipses and variable speeds fixed things beatifully. It also told us the relative distances to the planets -- once we found the Earth-Sun distance, we knew how big the Solar System was.
Now, Newton took these laws and ran with them and, with some stuff from Galileo, came up with his four laws, which was a Big Deal. And, later on these laws were used to discover Neptune and make us wonder what the heck is making our Galaxy act so weird (see: dark matter)

So, yeah, yay Kepler!