This is a picture of the (elliptical) orbit of a planet around the sun. The sun is at point A, point P is where the planet is closest to the sun during its orbit, and point Q is where the planet is farthest from the sun during its orbit. Kepler made the following amazing discovery: if a is the average of the closest and farthest distances of the planet from the sun and t is the time it takes the planet to make one full orbit around the sun then the quotient does not depend on the planet. In what follows, we measure t in years and a in astronomical units where one astronomical unit is the average of the closest and farthest distances from the earth to the sun. These units are helpful since we have t=1 and a=1 for the earth, allowing us to find the quotient