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Grade 12th passMechanics

Kindly solve this.........
A moon rotates about its axis. In future scientists may wish to put a satellite into an orbit around the moon such that the satellite remains stationary above the one point on moon surface, the period of rotation of moon about its axis is 27.4 days, what is the radius of required orbit?(mass of moon=7.35 * 10^22kg)

Profile image of shy
8 Years agoGrade 12th pass
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1 Answer

Profile image of Eshan
8 Years ago
Dear student,

For satellite to be stationary with respect to moon, the time period of its revolution must be same as that of moon’s rotation.

\dfrac{mv^2}{R}=\dfrac{GMm}{R^2}\implies v=\sqrt{\dfrac{GM}{R}}

Hence time period of revolution=\dfrac{2\pi R}{v}=2\pi\sqrt{\dfrac{R^3}{GM}}=T

\implies R=(\dfrac{GMT^2}{4\pi ^2})^{1/3}

Put the values to get the answer.

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