How many radii of the earth do you need to increase the distance between the body
| May 9, 2021 | education
How many radii of the earth do you need to increase the distance between the body and the earth so that the force of attraction between them decreases 9 times.
Data: F (the force of attraction of a body at the surface of the Earth) = 9F1 (the required value of the force of attraction between the body and the Earth).
The increase in the distance between the body and the Earth’s surface is determined from the ratio: F = F1 = G * m * M / R ^ 2 = 9G * m * M / (R + nR) ^ 2.
1 / R2 = 9 / (R + nR) ^ 2.
(R + nR) ^ 2 / R ^ 2 = 9.
(R + nR) / R = 3.
1 + n = 3 and n = 2.
Answer: The distance between the body and the surface of the Earth needs to be increased by 2 the radius of the Earth.
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