How would the force of gravity between two masses be affected if the separtion distance between them were doubled and decreased by one-half?

The force of gravity between two masses can be calculated using the equation:

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

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the separation distance between them.

Let's assume that the masses of the objects (m1 and m2) remain constant. Now, we need to consider the impact of changing the separation distance (r).

1. If the separation distance is doubled:
- If you double the separation distance (r), the force of gravity will decrease by a factor of 1/4 (1/2 * 1/2).
- This can be understood by looking at the denominator of the equation (r^2). When you double r, the denominator becomes four times larger, resulting in a force of gravity that is one-fourth of the original value.

2. If the separation distance is decreased by one-half:
- If you decrease the separation distance by one-half (r/2), the force of gravity will increase by a factor of 4 (2 * 2).
- In this case, the denominator of the equation becomes one-fourth of the original value, resulting in a force of gravity that is four times larger.

So, when the separation distance is doubled, the force of gravity decreases by a factor of 1/4; when the separation distance is decreased by one-half, the force of gravity increases by a factor of 4.