86.3 Kepler's laws of planetary motion Define orbital angular momentum L=r×p dd Then (r×p)=0 dt dt The orbital angular momentum of a particle (or planet) under the influence of a central force is conserved 86.3 Keplers laws of planetary motion We can prove that the conservation of the angular momentum is equivalent to the Kepler’ s law of area (rd6)rdA=r×dF da i rxdr 1 dr =-r r×p L13 §6.3 Kepler’s laws of planetary motion Define orbital angular momentum: L r p r r r = × The orbital angular momentum of a particle (or planet) under the influence of a central force is conserved. ( ) 0 d d d d = r × p = t t L r r r Then §6.3 Kepler’s laws of planetary motion dθ dA rdθ r r We can prove that the conservation of the angular momentum is equivalent to the Kepler’s law of area. A r r A r r r r r d 2 1 ( d ) d 2 1 d = θ = × m L r v t r r t r r t A 2 2 1 d d 2 1 d d 2 1 d d r r r r r r r r = × = = × × =