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An artificial satelite of the moon revol...

An artificial satelite of the moon revolves in a circular orbit whose radius exceeds the radius of the moon `eta` times. The process of motion the satelite experiences a slight resistance due to cosmic dust. Assuming the resistance force to depend on the velocity of the satellite as `F=alphav^2`, where `alpha` is a constant, find how long the satellite will stay in orbit until it falls onto the moon's surface.

A

`1/alpha([sqrt(etaR)-sqrtR])/sqrt(GM)`

B

`1/alpha([sqrt(etaR)-sqrtR])/M`

C

`m/alpha([sqrt(etaR)-sqrtR])/sqrt(GM)`

D

`m/alpha([sqrt(etaR)-sqrtR])/sqrt(GM)`

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