Question

In Apollo's lunar program, the command module, orbits the
Moon, while the lunar module lands on the Moon's surface. The
command module's orbit was circular and was 100 km above the Moon's
surface. The speed of the orbit was uniform and lasted 2.00
hours.

1) Determine the tangential velocity of the module in m/
s

2) Determine the centripetal acceleration of the module

Answer #1

1) The command module's orbit was 100km above the Moon's surface. So the radius of the circular orbit r = 100km = 100000m. Also the speed of the orbit was uniform and lasted 2 hours. So the time period T = 2 hours = 7200 seconds.

If is the angular velocity, then the tangential velocty is given by,

But we know that the angular velocity and time period is related as,

Therefore,

So the tangential velocity of the module is 87.27m/s.

2) The centripetal acceleration is given by,

So the centrripetal acceleration of the module is 0.076m/s2.

You Will need
Radius of the Moon = 1.74 x 106 m
Lunar Module Mass 5.56 x 103 kg
G = 6.67 x 10-11 Nm2 / kg2
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