How will the force of attraction between two bodies change if a) the distance between their centers is doubled

| August 4, 2021 | education

How will the force of attraction between two bodies change if a) the distance between their centers is doubled, b) the mass of each of the bodies is reduced by 3 times?

R1 = 2 * R.

m2 “= m2 / 3.

m1 “= m1 / 3.

F / F1 -?

F / F2 -?

According to the law of universal gravitation, the force F of attraction between bodies is determined by the formula: F = G * m1 * m2 / R ^ 2, where G is the gravitational constant, m1, m2 are the masses of interacting bodies, R is the distance between their centers.

F1 = G * m1 * m2 / R1 ^ 2 = G * m1 * m2 / (2 * R) ^ 2 = G * m1 * m2 / 4 * R ^ 2 = F / 4.

F2 = G * m1 “* m2” / R ^ 2 = G * m1 * m2 / 3 * 3 * R ^ 2 = G * m1 * m2 / 9 * R ^ 2 = F / 9.

Answer: with an increase in the distance by 2 times, the force will decrease by 4 times: F / F1 = 4. With a decrease in the mass of two bodies by 3 times, the force will decrease by 9 times: F / F2 = 9.



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