During the Apollo lunar explorations of the late 1960s and early 1970s, the main

Question

During the Apollo lunar explorations of the late 1960s and early 1970s, the main section of the spaceship remained in orbit about the Moon with one astronaut in it while the other two astronauts descended to the surface in the landing module. Assume the mass of this section is 5300kg.

Part A
If the main section orbited about 52mi above the lunar surface, determine the gravitational potential energy.(In Joules)

Part B
Determine the total energy. (In Joules)

Part C
Determine the energy needed to "escape" the Moon for the main section of the lunar exploration mission in orbit. (In Joules)

Explanation / Answer

Mass of moon = 7.36 x 10^22 kg Radius of moon = 1737400 metres Distance of section from moon = 1737400 + 52 x 1609 = 1821068 metres GPE = -GMm/r = 6.673 x 10^-11 x 5300 x 7.36 x 10^22 / 1821068 = -1.43 x 10^10 J Total energy = GPE + KE Gravitational force = GMm/r^2 = 1.43x10^10/1821068 = 7853N MV^2/r = 7853N V^2 = 7853/5300*1821068 =2698113 KE = 0.5 MV^2 = 2698113 x 5300 x 0.5 = 7.15 x 10^ 9 Total energy = -1.43 x 10^ 10 + 7.15 x 10^9 = -7.15 x 10^ 9 Energy needed to escape = GPE = 1.43 x 10 ^ 10 Additional energy required = 7.15 x 10^9

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