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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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`:'` angular momentum `L=m_(P)r_(P)v_(P)=m_(P)r_(A)v_(A)`
`:. v_(P)/v_(A)=r_(A)/r_(P)` since `r_(A) gt r_(P), v_(P) gt v_(A)`.
The area SBAC bounded by the ellipse and the radius vectors SB and SC is larger than SBPC in Fig. From Kepler's second law, equal areas are swept in equal time intervals. Hence the planet will take a longer time to traverse BAC than CPB.
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