The first and oldest of the experiments in the Top Eleven is actually a two-fer: Galileo Galilei is nominated both for the discovery of the moons of Jupiter, and for his experiments on the motion of falling objects.
Who: Galileo Galilei (1564-1642), the great Italian physicist, astronomer, and general Renaissance man.
When: He’s known to have made the first observations of the moons of Jupiter around 1610. The dates of the experiments on accelerated objects are fuzzier, but around the same time.
What: Shortly after obtaining a telescope (after its invention by Dutch astronomers), Galileo began observing just about everything there was to observe. He discovered the mountains of the Moon and the phases of Venus, made early measurements of sunspots, determined that the Milky Way was made of stars, and may or may not have spotted Neptune without realizing the significance.
The most significant of his astronomical discoveries was the observation of the four largest moons of Jupiter. Using his telescope, he notices a set of small bright objects associated with Jupiter, and observed that they moved in and out of view. He correctly attributed this to their orbiting the planet, and occasionally moving behind it. This turned out to be a discovery that would cause a great deal of trouble for a great many people.
As for the motion of objects, the legend of Galileo dropping balls of different masses off the Leaning Tower of Pisa is almost certainly not true, and anyway, he wouldn’t've had the timing accuracy to do much with actual falling objects. He did, however, realize that similar information could be gained by rolling objects of different masses down ramps. This slows their motion down to a level that could be accurately timed with the technology of the 1600′s, and allowed him to observe that the distance moved by an accelerating object in a given time scales as the time squared.
Why It’s Important: The discovery of the moons of Jupiter turned out to be a huge point in support of the heliocentric model of the Solar System, that is, the idea that the Sun is stationary and the planets revolve around it. This directly contradicts the accepted model of the time, that held (on the basis of Scripture and Aristotle) that the Earth was stationary, with the Sun, Moon, stars, and planets revolving around it.
If Jupiter had its own set of moons, then that was a major blow to the theory that the Earth was unique. If Jupiter can have satellites, there’s no reason why other bodies can’t orbit the Sun, and thus the heliocentric model gains some credence. This got him into a world of trouble with the Church, which had a great deal invested in the geocentric model at the time.
The experiments on the motion of objects were less splashy, but are arguably some of the very first experiments recognizable as science in the modern sense. He set out to measure a physical phenomenon, devised an experiment that would let him do what he wanted, and came up with a mathematical relationship to describe the results.
His results and his experimental approach would lead in time to the work of Isaac Newton (famously born in the year of Galileo’s death), whose Principia Mathematica was deemed the Greatest Physics Paper by the folks at Cosmic Variance.
Reasons to Vote for Him:: More or less the first modern scientist, put a thumb in the eye of the Catholic Church, inspired a pretty good Indigo Girls song.
Reasons to Vote Against Him: Cited by every crackpot with a Theory of Everything and a persecution complex, inspired an Indigo Girls song.