A lunar excursion module (LEM) was used in the Apollo moon-landing missions to save fuel by making it unnecessary to launch the entire Apollo spacecraft from the moon’s surface on its return trip to earth. Check the effectiveness of this approach by computing the energy per kilogram required for a spacecraft to escape the moon’s gravitational field if the spacecraft starts from

(a) The moon’s surface,

(b) A circular orbit 80 km above the moon’s surface. Neglect the effect of the earth’s gravitational field. (The radius of the moon is 1740 km and its mass is 0.0123 times the mass of the earth.)