Why does the area swept by a planet in a given period of time remain constant even as the planet speeds up and slows down

The planet speeds up when it's closer to the sun, and sweeps out a short fat triangle every hour. It moves slower when it's farther from the sun, and sweeps out a long skinny triangle every hour. The triangles have equal areas.

The only way I know to explain WHY this happens is:. That's how gravity works.

By the time you finish a couple of semesters of college Physics, you'll be able to take Newton's laws of gravity and motion, add some geometry and some calculus, stir well, and show why the planets must follow Kepler's laws.