How and how many times should the distance between the bodies be changed in order

How and how many times should the distance between the bodies be changed in order for the gravitational force to quadruple?

In the first case, the force of gravitational attraction will be equal to:

F1 = G * m1 * m2 / R1 ^ 2.

In the second case, the force of gravitational attraction will be equal to:

F2 = G * m1 * m2 / R2 ^ 2.

According to the condition of the problem, the strength increased by 4 times, that is:

F2 / F1 = 4;

(G * m1 * m2 / R2 ^ 2) / (G * m1 * m2 / R1 ^ 2) = 4;

(G * m1 * m2 * R1 ^ 2) / (G * m1 * m2 * R2 ^ 2) = 4;

R1 ^ 2 / R2 ^ 2 = 4;

R1 / R2 = 2;

R2 = R1 / 2.

That is, the correct answer is: B) decrease by 2 times.



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