The escape velocity from earth is given by
ve=2gRe.....(i)
The orbital velocity of a satellite revolving around earth is given by
v0=(Re+h)GMe
where, Me= mass of earth, Re= radius of earth, h= height of satellite from surface of earth.
By the relation GMe=gRe2
So, v0=(Re+h)gRe2.....(ii)
Dividing equation (i) by (ii), we get
v0ve=(Re)2(Re+h)
Given, v0=2ve
ve2ve=Re2(Re+h)
Squaring on both side, we get
4=Re2(Re+h)
or Re+h=2Re.
⟹ h=Re
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