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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`?

Text Solution

Verified by Experts

The magnitude of angular momentum at P is `L_(p)=m_(p)r_(p)v_(p)`
Similarly magnitude of angular momentum at A is `L_(A)= m_(A)r_(A)v_(A)`
From conservation of angular momentum
`m_(p)r_(p)v_(p)= m_(A)r_(A)v_(A)`
`(v_p)/(v_A)= (r_A)/(r_p)`
`r_(A) gt r_(p) :. v_(p) gt v_(A)`
area bound by SB and SC `(SBAC gt SBPC)`
By 2nd law equal areas are swept in equal intervals of time. Time taken to transverse `BAC gt ` time taken to transverse CPB.
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