Final answer:
The gravitational force between two objects can be calculated using Newton's law of universal gravitation. To find the distance at which the gravitational force becomes half, we can rearrange the equation and solve for the new separation distance. The distance should be kept at approximately 176.78 km.
Step-by-step explanation:
The gravitational force between two objects is given by Newton's law of universal gravitation: F = G ((M₁ * M₂)/(R²)), where F is the magnitude of the force, G is the gravitational constant (6.674 × 10-11 N·m² kg²), M₁ and M₂ are the masses of the two objects, and R is the separation between them.
To find the distance at which the gravitational force becomes half, we can set up the equation as follows:
1/2 * F = G ((M₁ * M₂)/(R'²)), where R' is the new separation distance.
By rearranging the equation and solving for R', we find:
R' = √((R² / 2)).
Using the given information, R = 2.5 * 10² km = 250 km. Plugging this value into the equation, we get:
R' = √((250² / 2)) = √(31,250) ≈ 176.78 km.
Therefore, the distance between the objects should be kept at approximately 176.78 km so that the gravitational force becomes half.