A planet of mass m moves in an elliptical orbit around sun with sun at its Focus. (e=eccentricity of ellipse). Then `T_(ACB)//T_(BDA)` is `[T_(ACB)` is time taken to travel from A to C B & `T_(BDA)` is time taken to travel from B to D to A]

Options

A. `(pi+2e)//(pi-2e)`
B. `1`
C. `(pi+e)//(pi-e)`
D. `pi//(pi-1)`

Answer

A

Explanation

`because(dA)/(dt)={"Kepler's 2nd law"]`
`therefore(T_(1))/(T_(2))=(A_(1))/(A_(2))=((piab)/(2)+(1)/(2)xx2bxxae)/((piab)/(2)-(1)/(2)xx2bxxae)`
or `(T_(1))/(T_(2))=((pi+2e))/((pi-2e))`