Call this factor k . Explain what the major axis of an ellipse is. Explain what the semimajor axis is. See figure 1.29 on page 46 . We will use those two terms, semimajor axis and average distance, interchangeably.
P is the time to go around the Sun.
But the point of Kepler's third law is that it is the same k for all the planets. They weren't perfectly equal, this does indicate some minor flaws in Kepler's law. But the distances weren't known well enough in Kepler's time for him to have computed with this much accuracy. We'll explain the slight inaccuracy later. Kepler's law is accurate enough for our purposes and we will use it to solve problems.