# At what distance from the surface of the Earth will the force of attraction of the spacecraft

**At what distance from the surface of the Earth will the force of attraction of the spacecraft to it become 100 times less than on the surface of the Earth?**

F1 = 100 * F2.

Rz = 6371 km.

H -?

According to the law of universal gravitation, the force of gravitational attraction is determined by the formula: F = G * m * M / R ^ 2, where G is the gravitational constant, m, M is the mass of interacting bodies, R is the distance between them.

The force of attraction of the spacecraft on the surface of the earth will be determined by the formula: F1 = G * m * M / Rz ^ 2, where Rz is the radius of the earth.

The gravitational force of the spacecraft at a height H above the earth’s surface will be determined by the formula: F2 = G * m * M / R ^ 2.

Where R is the distance from the center of the earth to the spacecraft.

R = Rz + H.

F1 / F2 = G * m * M / R3 ^ 2: G * m * M / R ^ 2 = R ^ 2 / R3 ^ 2.

R ^ 2 / R3 ^ 2 = 100.

R = √ (100 * Rz ^ 2) = 10 * Rz.

Rz + H = 10 * Rz.

H = 10 * Rz – Rz = 9 * Rz.

H = 9 * 6371 km = 57339 km.

Answer: at an altitude of H = 57339 km, the force of attraction of the spacecraft to the earth will be 100 times less.