A planet is revolving around the sun in an elliptical orbit having eccentricity e ( = 4 π ) . If the time period of revolution is 16 months then find the time taken by the planet in going from A to

Question

A planet is revolving around the sun in an elliptical orbit having eccentricity e ( = 4 π ​ ) . If the time period of revolution is 16 months then find the time taken by the planet in going from A to B in months.

TestHub · Accepted Answer

Areal velocity is constant, so time is proportional to area swept

$t = \frac{T}{πab} (\frac{πab}{4} + \frac{1}{2} ab e) = T (\frac{1}{4} + \frac{e}{2 π})$

With $T = 16$ months and $e = \frac{π}{4}$ : $t = 16 (\frac{1}{4} + \frac{1}{8}) = 16 \times \frac{3}{8}$

$t = 6$ months

Answer: 6.00

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