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During an Apollo lunar landing mission, the command module continued to orbit the Moon at an...

During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 104 km. How long did it take to go around the Moon once?

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Answer #1

rm = 1737400 m

M = 7.36 * 1022kg, G = 6.673 * 10-11 Nm2/kg2

r = rm+ 104000 m = 1841400 m

v = sqrt(GM/r) = sqrt(6.673 * 10-11 * 7.36 * 1022 / 1841400)

= 1633 m/s

T = 2pi * r / v = 2pi * 1841400 / 1633

= 7085 s

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Answer #2

Force due to gravity =Centripetal force

Gm1m2/r2=m1V2/r

since

V=2pir/T

Gm2/r =4pi2r2/T2

T=sqrt[4pi2*r3/Gm2]

T=sqrt[4pi2*(1.738*106+104*103)3/(6.67*10-11)*(7.36*1022)]

T=7089.45 sec or 1.97 hour

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