The Moon has a mass of M = 7.3 · 1022 kg, a radius of R = 1.7 · 106 m and a rotation period of
T = 27.3 days. Scientists are planning to place a satellite around the Moon that always remains
above the same position (geostationary).
(a) Calculate the distance from the Moon’s surface to this satellite.
(b) Explain if such a Moon satellite is possible in reality.
1
Expert's answer
2019-05-13T11:22:47-0400
Gravitational force causes centripetal acceleration
F=R2GMm=mω2R
Using ω=T2π , we derive
R3GM=T24π2⇒R=34π2GMT2=8.82⋅107m=88200km
Such a sattelite is impossible in reality, because be couldnt ignore gravitation of Earth, bacause it is 384 400 km away.
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