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A planet is revolving around the S in the elliptical path with semi-major and semi-minor axes as a and b respectively. If time taken by the planet for one complete revolution is T, then time taken by planet to move from point A to B as shown in figure will be

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$T / 4$

$T /8$

$T /6$

$2 T / 9$

answer is B.

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Detailed Solution

Since we know that the time taken by a planet in an orbit is directly proportional to the area swiped:

Time taken by planet from A to B will be:

$t_{A \to B} = (\frac{T}{π a b}) (\frac{π a b}{4} - \frac{1}{2} (a e) b)$

$( where eccentricity e = \frac{π}{4})$

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