Final answer:
If the moon were only 1/3 as far away, the force of its gravity on Earth would increase by a factor of 9, according to the inverse square law.
Step-by-step explanation:
If the moon were only 1/3 as far away from the Earth as it currently is, the force of gravity it exerts on Earth would change according to the inverse square law, which states that the gravitational force between two masses is inversely proportional to the square of the distance between their centers. Thus, if the distance is reduced to one-third, the gravitational force would increase by the square of the factor by which the distance decreased. In mathematical terms, this would be (1/3)² = 1/9. So, if you decrease the distance to one-third, you must take the reciprocal of that fraction and then square it, resulting in an increase by a factor of 9.
Therefore, the correct answer is that the force of gravity would increase by a factor of 9 (option c).