Kepler's Third Law: Square of Planet's Orbital Period is Proportional to the Cube of its Major Axis

In this video, I derive Kepler's 3rd Law of planetary motion and obtain a formula for a planet's period of orbit around the Sun in terms of the length of its major axis. Using the results of Laws 1 and 2, and using the formula for a horizontally shifted ellipse in Cartesian coordinates, as well as its area, I show that the square of the period is proportional to the cube of the major axis. This proportionality is independent of the planet as it is just in terms of the gravitational constant and mass of the Sun.

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