Assumptions

You may assume that the Sun is located at the origin (0,0) and does not move. You may also assume that all objects move in a two-dimensional plane. You may assume that the positions of the other planetary objects in the solar system will not affect the motion of the Earth, its moon or the asteroid on the timescale of this problem. You can assume that the asteroid will hit Earth or its moon if it's center of gravity passes within 20,000 km of Earth's or the moon's center of gravity, respectively.