the aphelion). A circle is also an ellipse and the orbits of most planets are far more nearly circularthan the diagram would suggest. However, they are not circles nonetheless; they are ellipses with non-zero eccentricity. The third law means that if Y is the length of a planet's year, and if A is the length of the semimajor axis of the planet's orbit, then the quantity Y2/A3 is the same for every planet (and comet, and other satellites) in the solar system. Thus, if a planet's orbit is known, the length of it's year can be immediately calculated, and vice versa. Kepler's laws were derived strictly from careful observation and had no theoretical basis. However, about 30 years after Kepler died, the English mathematician/physicist Sir Isaac Newton derived his inverse square law of gravity, which says that the force acting on two gravitating bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Kepler's laws may be derived from this theoretical principle using calculus....
