Question

A planet is revolving around the sun in an elliptical orbit having eccentricity $e\left(= \frac{\pi }{4}\right)$ . 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.

Answer 1

$t=\frac{T}{\pi a b}\left(\frac{\pi a b}{4} + \frac{1}{2} a b e\right)$
$t=T\left(\frac{1}{4} + \frac{e}{2 \pi }\right)$
$t=18\left(\frac{1}{4} + \frac{1}{8}\right)$
$t=6$ months