Question

in thinking about the uniform distribution of a gravitational field over a sphere, why does gravitational force have an inverse - square relationship with the distance between objects? (1 point)
because the surface area of a sphere is proportional to the square of its radius
because the volume of a sphere is proportional to its radius
because the volume of a sphere is proportional to the square of its radius
because the surface area of a sphere is proportional to its radius

Explanation:

The gravitational force spreads out uniformly over the surface of a sphere. The formula for the surface area of a sphere is \(A = 4\pi r^{2}\), which shows that the surface area is proportional to the square of the radius (\(r\)). As the gravitational force is distributed over this surface area, the force per unit area (intensity) decreases with the square of the distance (since the same amount of force is spread over a larger and larger surface area as the distance \(r\) increases). The volume of a sphere \(V=\frac{4}{3}\pi r^{3}\) is not relevant here as the gravitational field is a surface - related (flux - like) concept in the context of the inverse - square law.

Answer:

because the surface area of a sphere is proportional to the square of its radius