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Let the speed of the planet at the perih...

Let the speed of the planet at the perihelion `P` in figure be `v_(P)` and the Sun planet distance `SP` be `r_(P)`. Relater `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`?

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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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