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(1/2)Gm/R2=Gm/(R+h)2
Where:
G is the gravitational constant
m is the mass of the Earth
R is the Radius of the Earth
h is the height above the Earth where Gravity is 1/2 surface gravity
Canceling Gm from both sides gives:
1/2R2 = 1/(R+h)2
inverting to make things simpler:
2R2 = (R+h)2
taking the square root of both sides:
sqrt(2)R=R+h
(sqrt(2)-1)R=h
the sqrt(2)=1.4142135623730950488016887242097
(sqrt(2)-1) = 0.4142135623730950488016887242097
so h=0.4142 R
The required height is 0.41 times the radius of Earth.
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