According to Kepler's second law of planetary motion, the radius vector joining planet to the sun sweeps out equal areas, in equal interval of time. i.e., ‌‌‌
∆A
∆t
=constant
According to figure, r be the position vector of the planet w.r.t sun and F be the gravitational force on the planet due to the sun. Then, torque exerted on the planet by this force about the sun is τ=r×F=0 [∵r and F are oppositely directed ] But ‌‌τ=‌
dL
dt
∴‌‌‌
dL
dt
=0⇒L= constant Angular momentum = constant Hence, Kepler's second law (law of areas) is equivalent to law of conservation of angular momentum.