There is a finite probability of an asteroid colliding with the earth in a cataclysmic event. Such collisions are known to have occurred over the history of the earth, and some responsible scientific and technical organizations, including the American Institute of Aeronautics and Astronautics (AIAA), have studied what measures could be taken if such an event were to threaten the earth in the foreseeable future. Consider the head-on collision of an asteroid with the earth. Assume the asteroid's velocity (in a reference frame fixed on the sun) is equal to nine-tenths of the escape velocity from the sun. In the same reference frame, the velocity of the earth around the sun is 29.77 km/s. Calculate the velocity, relative to the earth, at which the asteroid would enter the earth's atmosphere. Assume the earth is moving in a circular orbit about the sun, with a radius of 147 x 109 m. Note: This problem represents a worst-case scenario where there is a head-on collision between the earth traveling in one direction and the asteroid traveling in the opposite direction.
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