CBSE 11TH PHYSICS - Online Test

The law of areas can be understood as the consequence of conservation of angular momentum which is valid for any central for A central force is such that the force on the planet is along the vector joining the sun and the planet. Let the sun be at the origin and let the position and momentum of the planet be denoted by r and p  respectively. Then the area swept out by the planet of mass m in the time interval Δt is given by ΔA = ½  (r × vΔt).

Hence ΔA/Δt    =½ (r × p)/m, (since  v=p/m)    

                 =    L / (2 m) 

where v is the velocity,  where v is the velocity,  L is the angular
momentum equal to   ( r  ×  p  ).  For a central force, which is directed along r, L is a constant