When the lunar excursion module (LEM) was set adrift after returning two of the Apollo astronauts to the command module, which was orbiting the moon at an altitude of 140 km, its speed was reduced to let it crash on the moon’s surface. Determine (a) the smallest amount by which the speed of the LEM should have been reduced to make sure that it would crash on the moon’s surface, (b) the amount by which its speed should have been reduced to cause it to hit the moon’s surface at a 45° angle. (Hint: Point A is at the apogee of the elliptic crash trajectory. Recall also that the mass of the moon is 0.0123 times the mass of the earth.)
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