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 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_(P) and the sun-p

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 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 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)` so `V_(P) gt V_(A)` Here area SBAC is greater than the area SCPB. According to Kepler.s second law, as the arcal velocity of the planet is contant AROUND the sun , i.e. equal areas are swept on equal times, hence the planet will take longer TIME to traverse BAC than CPB.