This presentation will touch upon the laws developed near the end of this story. Not laws that are written down and should subsequently be obeyed, but in science, laws are back-engineered--things that are observed to always happen a certain way must be obeying certain laws.
Kepler and Newton are the lawgivers of astronomy. We'll see that the characters of their laws are quite different, even though they both concern themselves with the motions of planets. You should be able to differentiate between Kepler's three laws and Newton's three laws, but most importantly understand the distinct difference between describing how things happen, and explaining why things happen.
First, Kepler's laws describe how planets move, which we will also demonstrate with an online simulation.
Which planet has the most nearly circular orbit? For this planet, where is the sun located with respect to the center?
Which planet has the most elliptical orbit? For this planet, where is the sun located with respect to the center?
To illustrate Kepler's second law, we observe how a planet moves along a circular orbit, and compare it to how it would move along an elliptical orbit. Here the length of the arrow shows how fast (or slow) the planet moves along its orbit. Also note the amount of time a planet "sweeps" out each of the colored areas is always the same (despite moving faster or slower along different parts of the orbit).
Are there colored sections that contain more area than others? Which section(s) contain the most area? The least area? Or do they all contain the same amount of area? (If you had an elliptical pie, would this be a fair way to cut the slices?)
In contrast to Kepler's laws, which are merely a set of rules that planets seem to follow, Newton's laws explain why planets move the way they do.
Newton's second law is much more interesting--exerting a force (such as gravity) on an object (such as a planet) will change its motion. The more force you exert, then the object's motion will change more. This is a cause-and-effect statement, and surprisingly it is the very first such statement in the history of science. This is also the key to understanding why planets move the way that they do--they are forced to orbit the sun because of the sun's gravitational force.