How will the force of mutual attraction of bodies change if the distance between the bodies is increased by 3 times?

Given:

F is the force of mutual attraction of bodies;

m1, m2 – body masses;

G – gravitational constant;

R1 = R is the distance between the bodies in the first case;

R2 = 3 * R is the distance between the bodies in the second case.

It is required to determine F2 / F1 – the change in the force of attraction of bodies with increasing distance to R2.

F2 / F1 = (G * m1 * m2 / R2 ^ 2) / (G * m1 * m2 / R1 ^ 2) =

= G * m1 * m2 * R1 ^ 2 / (G * m1 * m2 * R2 ^ 2) = R1 ^ 2 / R2 ^ 2 = R ^ 2 / (3 * R) ^ 2 = R ^ 2 / (9 * R ^ 2) = 1/9 times.

Answer: the force of attraction between bodies will decrease 9 times.