Suppose that the diameter of the Earth has become 2 times larger, but its mass remains the same. Under these conditions, the force acting from the Earth on a person who is on its surface will be …
Problem data: D2 (considered diameter of the Earth) = 2D1 (real diameter); Mz (mass of the Earth) = const.
1) Ratio of gravitational accelerations: n = g2 / g1 = (G * Mz / R2 ^ 2) / (G * Mz / R1 ^ 2) = R1 ^ 2 / R2 ^ 2 = (0.5D1) ^ 2 / ( 0.5D2) ^ 2 = D1 ^ 2 / D2 ^ 2 = D1 ^ 2 / (2D1) ^ 2 = D1 ^ 2 / 4D) ^ 2 = 1/4.
2) Change in the force of attraction: n = Ft2 / Ft1 = mh * g2 / (mh * g1) = g2 / g1 = 1/4.
Answer: The force acting from the side of the Earth will decrease by 4 times.
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