Let the speed of the planet at the perihelion P be V_P and the sun-planet distance SP be r_p .Relates (r_p,V_P) to the corresponding quantities at 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_P and the sun-pla

1.	Let the speed of the planet at the perihelion P be V_P and the sun-planet distance SP be r_p .Relates (r_p,V_P) to the corresponding quantities at 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 `rArr mV_P r_P=mV_A r_A` (or) `V_P/V_A=r_A/r_P` Since `r_A gt r_P` or `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, HENCE the planet will take longer time to traverse BAC than CPB.