How will the force of mutual attraction between two bodies change if the distance between them has decreased 6 times?
| August 2, 2021 | education
The force of attraction of bodies to each other:
F = G * m1 * m2 / R², F is the force of mutual attraction of bodies, G is the gravitational constant, m1 is the mass of the first body, m2 is the mass of the second body, R is the distance between bodies.
The force of mutual attraction of bodies before changing the distance:
F1 = G * m1 * m2 / R1².
The force of mutual attraction of bodies before changing the distance:
F2 = G * m1 * m2 / R2², where R2 = 1/6 R1.
F2 / F1 = (G * m1 * m2 / R2²) / (G * m1 * m2 / R1²) = R1² / R2² = R1² / (1/6 R1) ² = 36.
Answer: It will increase 36 times.
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