Final answer:
The question involves rearranging the gravitational force formula to solve for the distance, r, where r is set to equal 7 in relation to F, G, M₁, and M₂.
Step-by-step explanation:
Solving for the Distance between Two Objects in Gravitational Attraction
The formula for the gravitational force between two objects is given by F = GM₁M₂/r², where F is the gravitational force, G is the gravitational constant, M₁ and M₂ are the masses of the two objects, and r is the distance between the centers of the two objects. To solve for the distance r when the result is 7, we begin by rearranging the formula:
F = GM₁M₂/r² → F r² = GM₁M₂ → r² = GM₁M₂/F → r = √(GM₁M₂/F)
Then we set r = 7, resulting in an equation that allows us to solve for the positive value of r: 7 = √(GM₁M₂/F)
Substituting the aforementioned constants and values, the universal gravitational constant G is 6.674 × 10⁻¹¹ N·m²/kg², and the masses M₁ and M₂ are known quantities. Now the positive value of r, which equals 7, can be used to determine the necessary gravitational force F or vice versa.