In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained undetected until three days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth-about a third of the distance to the Moon.

(a) Find the speed of the asteroid at closest approach, assuming its speed at infinite distance to be zero and considering only its interaction with the Earth.

(b) Observations indicate the asteroid to have a diameter of about 0.730 km. Estimate the kinetic energy of the asteroid at closest approach, assuming it has an average density of 3.33 g / cm3. (For comparison, a 1-megaton nuclear weapon releases about 4.2 × 1015 J of energy.)