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The value of escape speed from the surfa...

The value of escape speed from the surface of earth is

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No, the velocity of escape arises from the energy required to take it from the present condition to infinity. This is equal to the difference between energy on the surface of the earth and infinity. For particle at rest
`1/2mv_(e)^(2)=(GM)/R` (only potential energy)
`:.v_(e)=sqrt((2GM)/R)`
For a particle in circular motion.
`E` (energy) `=-(GM)/R+1/2mv^(2)`
But `(mv_(e)^(2))/R=-(GMm)/(R^(2))`
(from dynamics of circular motion)
`:. E=-1/2(GMm)/R`
`:. 1/2mv^(2)=1/2(GMm)/R`
or `v_(c)=sqrt((GM)/R`
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