The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded are SAB. If `t_1` is the time for the planet to move from C to D and `t_2` is the time to move from A to B then ......

Options

A. `t_1 =4t_2`
B. `t_1 =2t_2`
C. `t_1 =t_2`
D. `t_1 gt t_2`

Answer

B

Explanation

`implies` According to Kepler.s law, the areal velocity of the planet around the sun is constant .
`:. ("Area "(A_1)" of SCD")/("time"t_1) =("Area "(A_2)" of SAB")/("time "t_2)`
`:. (A_1)/t_1=A_2/t_2`
`:.t_1 = t_2 (A_1)/(A_2) " but " A_1 = 2A_2`
`:. t_1 =t_2 (2A_2)/A_2`
`:. t_1 = 2t_2`