How will the force of universal gravity change if the mass of one of the interacting
September 1, 2021 | education
| 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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