To project a body of mass $$m$$ from earths surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E$$, $$g =$$ acceleration due to gravity on the surface of earth):

To just reach infinity with zero final speed, total mechanical energy at infinity should be zero.

At Earth’s surface:

Potential energy is

$$U=-\frac{GMm}{R_E}$$

Required kinetic energy = escape energy so that

$$K+U=0$$

Thus

$$K=\frac{GMm}{R_E}$$

Now use

$$g=\frac{GM}{R_E^2}$$

$$GM=gR_E^2$$

Substitute:

$$K=\frac{(gR_E^2)m}{R_E}$$

$$K=mgR_E$$

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