A space shuttle, after delivering supplies to a lunar base, is preparing to retu

Question

A space shuttle, after delivering supplies to a lunar base, is preparing to return to Earth. The mass of the moon is M_moon = 7.35 times 10^22kg, and the radius of the moon is r_moon = 1.738 times 10^6m. At what minimum speed does the space shuttle have to travel after launch to escape the gravitational pull of the moon? How many Joules of potential energy does a 200 kg object-moon system have, if the object is 800 km above the surface of the moon? How fast would the space shuttle have to be travelling if it needed to place a satellite into a stable, circular orbit by just releasing it 800 km above the surface of the Moon? If the satellite has inertia 200kg, what is its angular momentum in this circular orbit? If the speed were not quite correct because of an error in the mass of the moon and the orbit started to decay just due to the pull of gravity, what would the angular momentum be when the satellite was at 200 km above the surface? Why? Calculate g_moon.

Explanation / Answer

a) Escape speed on the moon, Ve = sqrt(2*G*M_moon/R_moon)

= sqrt(2*6.67*10^-11*7.35*10^22/(1.738*10^6))

= 2375 m/s or 2.375 km/s

b) U = -G*M_mmon*m/(R_moon + h)

= -6.67*10^-11*7.35*10^22*200/(1.738*10^6 + 800*10^3)

= -3.86*10^8 J

c) orbital speed, vo = sqrt(G*M_moon/(R_mmon+h))

= sqrt(6.67*10^-11*7.35*10^22/(1.738*10^6 + 800*10^3))

= 1390 m/s or 1.39 km/s

d) Angular momenum = m*v*(Re+h)

= 200*1390*(1.738*10^6 + 800*10^3)

= 7.06*10^11 kg.m^2/s

e) g_moon = G*M_mmon/R_moon^2

= 6.67*10^-11*7.35*10^22/(1.738*10^6)^2

= 1.62 m/s^2

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