Two planets of equal mass orbit a much massive star (figure). Planet `m_(1)` moves in circular orbit of radius `1 xx 10^(8) km` with period `2 yr`. Planet `m_(2)` moves in an elliptical orbit with closest distance `r_(1) = 1 xx 10^(8) km` and farthest distance `r_(2) = 1.8 xx 10^(8) km`, as shown.

(a) Using the fact that the mean radius of an elliptical orbit is the length of the semi-major axis, find the period of `m_(2)'s` orbit.
(b) Which planet has the greater speed at point `P`? Which has the greater total energy?
(c ) Compare the speed of planet `m_(2)` at `P` with that at `A`.

Options

A. `5.29xx10^(20) kg`
B. `1.49xx10^(25) kg`
C. `1.49xx10^(29) kg`
D. `1.49xx10^(30) Kg`

Answer

C

Explanation

`T=(2pir^(3//2))/(sqrt(GM)) :. M=(4pi^(2)(r^(3)))/(GT^(2))`
`=((4)(3.14)^(2)(10^(11))^(3))/((6.67xx10^(-11))(2xx365xx24xx3600)^(2))`
`=1.49xx10^(29) kg`