How many times is the Earth’s gravity force of an artificial satellite greater

How many times is the Earth’s gravity force of an artificial satellite greater on the Earth’s surface than at a height of three Earth’s radii above its surface?

To calculate the ratio of the forces of attraction by the Earth of the specified satellite on the surface and a given height, we apply the formula: k = Fп / Fв = (G * mс * Mz / Rz ^ 2) / (G * mс * Mz / (hc + Rz) ^ 2) = (hc + R3) ^ 2 / R3 ^ 2.

Variables: hс – given satellite altitude (hс = 3Rз).

Let’s perform the calculation: k = (hc + Rz) ^ 2 / Rz ^ 2 = (3Rz + Rz) ^ 2 / Rz ^ 2 = 16Rz ^ 2 / Rz ^ 2 = 16 p.

Answer: The force of gravity of this satellite on the surface is 16 times greater.