The final law, Kepler's third law, is one of the most useful relations in astronomy. It states that the period of time it takes a planet to orbit the sun, squared (that's period*period), is proportional to its distance from the sun, cubed (distance*distance*distance). Or, as astronomers would say: P^2=a^3, where P is period and a is semi-major axis (i.e. distance). The graph above shows the period and orbital distance of some planets in our solar system. The line going through all the points corresponds to the spot where P^2=a^3. The fact that all the planets fall on this line means that Kepler's third law is correct, and that we can predict the orbital time if we know the orbital distance, or vice versa. This relationship can be applied to most objects orbiting a larger object in space. Astronomers use it to estimate the period of exoplanets orbiting stars, and stars orbiting galaxy centers.
And there you have it! Kepler's three laws of planetary motion!
Image Credit: Kevin Brown, Reflections on Relativity
