A satellite of a mass `m` orbits the earth at a hight `h` above the surface of the earth. How much energy must be expended to rocket the satellite out of earth's gravitational influence? (where `M_(E)` and `R_(E)` be mass and radius of the earth respectively)

Options

A. `(GM_(E)m)/(4(R_(E)+h))`
B. `(GM_(E)m)/(2(R_(E)+h))`
C. `(GM_(E)m)/((R_(E)+h))`
D. `(2GM_(E)m)/((R_(E)+h))`

Answer

B

Explanation

Total energy of the orbiting satellite at a height `h` is
`E=-(GM_(E)m)/(2(R_(E)+h))`
The total energy of the satellite at infinity is zero.
`:.` Energy expended to rocket the satellite out of the earth's gravitational field is
`DeltaE=E_(oo)-E`
`=0-(-(GM_(E)m)/(2(R_(E)+h)))=(GM_(E)m)/(2(R_(E)+h))`