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Let the speed of the planet at the perhe...

Let the speed of the planet at the perhelion Pin Fig. 8.1 (a) be `v_(p)` and the sun-planat distance SP be `r_(p)`. Relate `(r_(p')v_(p))` to the corresponding quantities at the aphelion `(r_(A).v_(A))` will the planat take equal times to traverse BAC and CPB?

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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.
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