Kepler's Second Law
Equal areas in equal times
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Kepler's Second Law captures how an orbiting body speeds up and slows down. A line drawn from the central body to the orbiter sweeps out equal areas in equal times. Since the body is close near periapsis, it must move fast there to sweep the same area; far away at apoapsis it drifts slowly.
This is really the conservation of angular momentum in disguise. Comets show it dramatically: they whip around the Sun in days near periapsis, then crawl through the outer solar system for decades before returning.
Check yourself
Where in its elliptical orbit does a planet move fastest?
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