How much height above the Earth's surface, a person's weight would be half.
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Since the radius of the Earth is 6378 km, that is our initial "r", if we are standing on the ground. That's our answer. At an altitude of 2642 km (approx. 1641 miles) above the Earth's surface, the gravitational acceleration will be 4.89m/s^2, which is half of 9.78 m/s^2 (the gravity at the surface).
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Explanation:
R = radius of earth
g = GM/R²
g' = GM/R'²
g/g' = R'²/R² = 2
R' = √2.R
height above the Earth's surface = R' - R = R(√2 - 1) ≈ 0.4R
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