If the mass of an object doubles, the gravitational force between it and another object will

You are correct in your statements about gravitational forces. According to Newton's law of universal gravitation:

1. **Mass and gravitational force**: If the mass of one of the objects doubles, the gravitational force between the two objects will indeed double. This is because gravitational force is directly proportional to the product of the masses of the two objects.

2. **Distance and gravitational force**: If the distance between the two objects doubles, the gravitational force will decrease to one-fourth. This is because gravitational force is inversely proportional to the square of the distance between the two objects (as described by the formula \( F = G \frac{m_1 m_2}{r^2} \)). Therefore, if \( r \) (the distance) doubles, \( r^2 \) becomes four times greater, leading to the force being one-fourth.

Your statements summarize these relationships accurately. If you have one remaining attempt on a question or problem related to this, be sure to confirm these points!