8. If the radius doubles, gravitational force would ___________________.  If the radius is cut by 1/2, the force would _________________________.

The gravitational force between two objects is given by the formula:

F = G * (m1 * m2) / r^2

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 (which is essentially the radius in this context).

1. If the radius doubles, the gravitational force would decrease by a factor of 4. This is because the radius is squared in the denominator of the formula, so if you double the radius, the denominator becomes 4 times larger, and therefore the overall force becomes 4 times smaller.

2. If the radius is cut by 1/2, the force would increase by a factor of 4. This is because if you halve the radius, the denominator of the formula becomes 4 times smaller, and therefore the overall force becomes 4 times larger.