Let the speed of the planet at the perihelion P be V_pand the sun-planet distance SP be r_p Relates (r_p,V_P )to the corresponding quantities at the aphelion (r_(A),V_A)Will the planet take equal times to tranverse BAC and CPB ?

Let the speed of the planet at the perihelion P be V_pand the sun-plan

1.	Let the speed of the planet at the perihelion P be V_pand the sun-planet distance SP be r_p Relates (r_p,V_P )to the corresponding quantities at the aphelion (r_(A),V_A)Will the planet take equal times to tranverse BAC and CPB ?
Answer» Solution : According to LAW of CONSERVATION of angular MOMENTUM. Angular momentum of the planet at P = Angular momentum of the planet at A `implies mV_pr_(p) = mV_(A)r_(A) " (or) " V_p/V_A=r_(p)/r_(p)` Since `r_A gt r_p` so `V_p gt V_A` Here area SBAC is greater than the area SCPB. According to Kepler.s second law, as areal velocity of the planet , is constant around the sun. i.e. equal areas areas are swept on equal times, hence the planet will take longer time to traverse BAC then CPB.