After seeing an old movie, you become concerned about a large asteroid that could be gravitationally attracted to Earth from very far away. You realize that long ago such an asteroid's speed relative to Earth's might have been very small, and thus you are able to calculate the relative speed it has at any separation distance from Earth. In order to get a baseline, you assume that the only object exerting a gravitational force on the asteroid is Earth, and you ignore the speed of Earth in its path around the Sun. What worries you is that observers might not sight the asteroid until it passes the imaginary line defining the Moon's orbit around Earth, and how little time that would give humanity to react.