Which physical conservation law necessitates the variation in planetary speed between perihelion and aphelion?
Answer
Conservation of angular momentum.
The variation in orbital speed exhibited by planets traveling along an ellipse is directly enforced by the principle of conservation of angular momentum. Angular momentum must remain constant throughout the planet's movement, as the gravitational force exerted by the Sun acts centrally and therefore produces no torque on the orbiting body. When the planet is close to the Sun (perihelion), its radius vector is small, so its tangential velocity must increase substantially to keep the angular momentum product constant. Conversely, at aphelion, when the radius vector is large, the velocity decreases.
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