Kepler's second law — equal areas

Statement

The radius vector from Sun to planet sweeps equal areas in equal times — so the planet moves faster at perihelion and slower at aphelion.

Why is it true?

This is angular-momentum conservation for orbital motion. A central force produces zero torque around the Sun, so L = m·r²ω is conserved — small r means large ω.

It is why northern summer is longer than northern winter (Earth is farthest from the Sun in July, moving slower).

Applications

Estimating flight times in space missions, comet and asteroid orbit models, n-body simulations.

Topics that use this theorem

Related theorems

Step-by-step proofs