A comet is in highly elliptical orbit around the Sun. The period of the comet's orbit is `90` days. Some statements are given regarding the collision between the comet and the earth. Mark the correct statement. [Mass of the Sun `= 2 xx 10^(30) kg`, mean distance between the earth and the Sun `= 1.5 xx 10^(11)m`.]

Options

A. Collision is there.
B. Collision is not possible
C. Collision may or may not be there
D. Enough information is not given

Answer

B

Explanation

Using Kepler's third law, the semi major axis of the comet's orbit is given by
`T^(4)=(4pi^(2))/(GM_(s))xxa^(3)`
`a=[(T^(2)xxGM_(s))/(4pi^(2))]^(1/3)`
`=[((90xx24xx3600)xx6.67xx10^(-11)xx2xx10^(30))/(4pi^(2))]^(1/3)`
`=5.89xx10^(10m)`
So the major axis of the comet's orbit would be `2a=1.178xx10^(11)m`
As `2alt` mean distance between the earth and the Sun, so the collision is not possible.