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 5400kg .

a)If the main section orbited about 50mi above the lunar surface, determine the gravitational potential energy.Express your answer using two significant figures.

b)Determine the total energy.Express your answer using two significant figures.
c)Determine the energy needed to "escape" the Moon for the main section of the lunar exploration mission in orbit.Express your answer using two significant figures.

Explanation / Answer

#a)

GPE = -GMm/r = -(6.67e-11*7.35e22*5400)/(1737400+(50*1609))

GPE = - 1.456*10^10 J

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#B)

KE = 0.5*m*Vo^2 = 0.5*m*G*M/r

TE = KE + GPE

TE = -GMm/2r = 7.28*10^9 J

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#c)

Ve = sqrt(2GM/r)

Ve = 2322.43 m/s

Ve = 2.3 km /s

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