Near the surface of the Earth (i.e., at a distance of radius (R) from its center), the body is affected by the force of universal

Near the surface of the Earth (i.e., at a distance of radius (R) from its center), the body is affected by the force of universal gravitation 36 N. What is the force of gravity acting on this body at a distance of 3R from the surface of the Earth?

We consider the Earth to be a material point, which is allowed for spherical bodies with a certain density distribution.
The force of attraction F at the Earth’s surface:
F = GmMz / R², where G is the gravitational constant, m is the mass of the body, Mz is the mass of the Earth.
The distance 3R from the surface of the Earth corresponds to the distance 3R + R = 4R between the centers of the body and the Earth:
The force of attraction F расстоянии at a distance of 4R:
F₁ = GmMz / (4R) ² = GmMz / 16R²;
F / F₁ = (GmMz / R²) / (GmMz / 16R²) = 16;
F₁ = F / 16 = 36 N / 16 = 2.25 N.
Answer: 2.25 N.



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