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By Lawrence

5 minutes

Equal Areas, Equal Times

The gold ellipse shows the path. It can't tell you when a ball will reach any point on it. Let's put a clock on it.

Kepler's area rule

A ball on an ellipse doesn't move at a steady speed. It races past the planet and crawls at the far end. Kepler found the rule. Draw a line from the planet to the ball, and that line sweeps out equal areas in equal times.

The speed-12 ellipse with twelve dots at equal times. A green wedge near the planet is short and wide. A pink wedge at the far end is long and thin. Both cover the same area and the same time.

Near the planet the line is short, so the ball has to cover a lot of ground to sweep its share. Far away the line is long, so a little movement does it.

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