1. The problem statement, all variables and given/known data The gravitational pull of the earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the earth's surface this force is equal to the object's normal weight mg, where g = 9.8m/s^2, and at large distances, the force is zero. If a 20,000-kg asteroid falls to earth from a very great distance away, what will be its minimum speed as it strikes the earth's surface, and how much kinetic energy will it impart to our planet? You can ignore the effects of the earth's atmosphere 2. Relevant equations K=(1/2)(mv2) g=~1/r^2, where r is the distance from the center of earth to the asteroid W=∫Fxdx 3. The attempt at a solution I've seen a solution where the equation for potential energy (U) is involved, but it seems I'm supposed to solve this using calculus. I'm not quite sure where to start. I'm trying to use the integral of the work formula, but I'm not sure how to relate it to this problem where the gravity is involved. Thank you.