Equal-areas empirically derives from angular momentum conservation, which requires net force to be centripetal; tangential forces increase or decrease angular momentum systematically.

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Centripetal(physics/mechanics): A force that pulls something toward the center of a circular path, like gravity keeping a planet orbiting the sun.
angular momentum conservation(the physical law that explains why equal-areas happens): A principle stating that the rotational motion of an object stays constant unless something pushes on it—like how a spinning ice skater keeps spinning at the same rate if nothing interferes.
empirically derives(describing how equal-areas is discovered through actual observation): Comes from or is proven by observing and measuring real-world evidence, rather than just thinking about it theoretically.
net force(the combined effect of all forces being applied): The total push or pull on an object after adding up all the forces acting on it from different directions.

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