At what height H from the surface of the Earth (R = 6400 km) Acceleration of gravity: Is 1% of g near the Earth.

The force of gravity acting on a body with mass m can be expressed in two ways:

F = GMz * m / R ^ 2, where Mz is the mass of the Earth.

F = mg, where g is the acceleration due to gravity.

On the surface of the Earth, this is the same force:

GMz * m / R ^ 2 = mg;

g = GM3 / R ^ 2 (1).

At some height H, the gravitational acceleration is 0.01g:

g / 100 = GMz / (R + H) ^ 2 (2).

Divide (1) by (2):

g / (g / 100) = (GM3 / R ^ 2) / (GM3 / (R + H) ^ 2);

100 = (R + H) ^ 2 / R ^ 2;

100R ^ 2 = R ^ 2 + 2HR + H ^ 2;

H ^ 2 + 2HR – 99R ^ 2 = 0;

H = (-2R + √ (4R ^ 2 + 4 * 99R ^ 2)) / 2 = -2R + R√ (4 + 396) = (-2R + 20R) / 2 = 9R = 9 * 6400 km = 57 600 km.

Answer: 57,600 km.