How will the force of universal gravity change if the mass of one of the interacting

How will the force of universal gravity change if the mass of one of the interacting bodies is increased by 3 times and the distance between the centers of the bodies is reduced by 3 times?

F = G * m1 * m2 / r², F – force of mutual attraction of bodies, G – gravity. constant, m1, m2 – mass interaction. bodies, R is the distance between the centers of bodies.

Before changes:

F1 = G * m1,1 * m2 / r1,1².

After increasing the mass of one of the bodies by 3 times and reducing the distance by 3 times:

F2 = G * m1,2 * m2 / r1,2², where m1,2 = 3m1, r1,2 = 1/3 r1.

F2 / F1 = (G * 3m1 * m2 / (1/3 r1) ²) / (G * m1 * m2 / r1²) = 3m1 * r1² / (m1 * 1/9 r1²) = 3 / 1/9 = 3 * 9 = 27.

Answer: The force of universal gravity will increase 27 times.



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