Two objects gravitationally attract with a force of 22N. If the distance between the objects is quadrupled (x4), then the new force of attraction is...?

Question

Please explain how you found the answer and show work

Answer 1

Isaac Newton proposed the universal law of gravitation:

F₁ = F₂ = G (m₁ * m₂) / r²

Where F₁ and F₂ represent the force of gravity exerted by the two objects, G represents the universal gravitation constant, m₁ and m₂ are the masses of the two objects, and r is the distance between the two objects. The formula tells us that a decrease in the separation distance causes an increase in the force of gravity. The factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed. Since the distance between the objects has increased, the gravitational force that each exerts on the other will decrease by the inverse of that amount, squared.

So:

d = ↑ 4 units, so gravity ↓ (1/4)² = 1/16

We multiply that factor by the original gravitation force between the two objects of 22 N.

22 N x 1/16 = 1.375 N = 1.4 N (significant figures)