Consider a comet moving in a parabolic orbit in the plane of Earth's orbit. If the distance of closest approach of the comet to the Sun is βrE, where rE is the radius of Earth's (assumed) circular orbit and where β<1, show that the time the comet spends within the orbit of Earth is given by
2(1−β)⋅(1+2β)/3π×1 year
If the comet approaches the Sun to the distance of the perihelion of Mercury, how many days is it within Earth's orbit?