A planet revolves around the sun in elliptical orbit of eccentricity 'e'. If 'T' is the time period of the planet then the time spent by the planet between the end of the minor axis and close to the sun is

Options

A. `(T pi)/(2e)`
B. `T((2e)/(pi)-1)`
C. `(Te)/(2pi)`
D. `T((1)/(4)-( e)/(2pi))`

Answer

D

Explanation

(d)
As a real velocity of a planet around the sun is constant. Therefore, the desired time is
`t_(AB)=(("area ABS")/(" area of ellipse"))xx " time period"`
If a= semi-major axis and b=semi- minor axis of ellipse, then , area of ellipse =` pi ab`
Area ABS`=(1)/(4)`(area of ellipse)- Area of triangle ASO
`(1)/(4)xxpi ab -(1)/(2)(ea)xx(b)`
`:. t_(AB)=([(pi(ab))/(4)-(1)/(2) eab])/(pi ab ) xxT- T((1)/(4)-(e)/(2pi))`