At what distance from the Earth, measured in the radii of the Earth, will the force of gravity acting

At what distance from the Earth, measured in the radii of the Earth, will the force of gravity acting on a body decrease by 9 times in comparison with the force acting on the same body on the Earth’s surface?

Given:

m is body weight;

M is the mass of the Earth;

R is the radius of the Earth;

F1 is the force of gravity acting on a body near the surface of the Earth;

F2 = F1 / 9 is the force of gravity acting at some distance from the Earth’s surface.

It is required to determine R2 – the distance from the body to the surface of the earth.

At the surface of the Earth, the force of gravity is:

F1 = G * m * M / R ^ 2.

At which distance from the surface of the earth the force of gravity is:

F2 = G * m * M / R2 ^ 2.

Then:

F1 / F2 = G * m * M / R ^ 2 / (G * m * M / R2 ^ 2) = 9;

R2 ^ 2 / R ^ 2 = 9;

R2 / R = 3;

R2 = R * 3.

Answer: gravity will be 9 times less at a distance of 3 * R from the Earth’s surface.