The figure represents an elliptical orbit of a planet around sun. The planet takes time `T_(1)` to travel from `A` to `B` and it takes time `T_(2)` to travel from `C` to `D`. If the area `CSD` is double that of area `ASB`, then

Options

A. `t_(1)gtt_(2)`
B. `t_(1)=4t_(2)`
C. `t_(1)=2t_(2)`
D. `t_(1)=t_(2)`

Answer

C

Explanation

Applying Kepler's law of area of planetary motion. The line joining the sun to the planet sweeps out equal areas in equl time interval i.e. areal velocity is constant.
`(dA)/(dt)`=constant or `(A_(1))/(t_(1))=(A_(2))/(t_(2))implies t_(1)=(A_(1))/(A_(2))t_(2)`
Given `A_(1)=2A_(2)`
`:. t_(1)=2t_(2)`