At what height above the surface of the Earth does the force of gravity decrease by 10%?

At what height above the surface of the Earth does the force of gravity decrease by 10%? The radius of the Earth is 6400 km.

Р = m * g, m – body mass (constant value), g – gravitational acceleration.

The force of gravity (body weight) will decrease by 10% when g decreases by 0.9 times.

0.9g = G * M / (R + h) ², G – gravity. constant (G = 6.67 * 10-11 m³ / (kg * s²)), M is the mass of the Earth (M = 5.97 * 1024 kg), R is the radius of the Earth (R = 6371000 m), h is the height above surface of the Earth.

(R + h) ² = G * M / 0.9g.

h = sqrt (G * M / 0.9g) – R = sqrt (6.67 * 10-11 * 5.97 * 1024 / 0.5 * 9.8) – 6371000 = 348172 m ≈ 348 km.