Let the speed of the planet at the perihelion P be V_pand the sun-planet distance SP be r_p .Relate (r_p, V_p)to the corresponding quantities at the aphelion (r_A,V_A) . Will the planet take equal times to transverse 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 .Relate (r_p, V_p)to the corresponding quantities at the aphelion (r_A,V_A) . Will the planet take equal times to transverse 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 ` rArr =mV_p r_p = m V_A r_A "or " V_P/V_A = r_A/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 the areal VELOCITY of the planet is constant around the sun, i.e equal areas are swept on equal TIMES, the planet will TAKE longer time to traverse BAC than CPB.