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The percentage by which the moon should ...

The percentage by which the moon should move faster, so that it escapes from the gravitational field of the earth is:

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The gravitational force of attraciton by the earth provides the necessary centripetal force to the moon to revolve around it.
`:. (m v_(0)^(2))/(R ) = (GMm)/(R^(2))`
`rArr v_(0) = sqrt((GM)/(R )) = sqrt((gR^(2))/(R )) = sqrt(gR)`
This is the orbital velocity of moon.
Escape velocity, `v_(e) = sqrt(2gR)`
`:.` Percentage increase in velocity of the moon
`= (v_(e) - v_(0))/(v_(0)) xx 100 = (sqrt(2gR) - sqrt(gR))/(sqrt(gR)) xx 100`
`= (sqrt(2)-1)/(1) xx 100 = 41.4% ~= 42%`
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