Final answer:
If Star Conner's diameter decreases to one-eighth while its mass remains constant, the gravitational force at its surface would increase by a factor of 64 due to the inverse-square law.
Step-by-step explanation:
If Star Conner contracted to one-eighth of its previous diameter without losing any of its mass, the gravitational force at the surface would increase. This is because gravitational force is inversely proportional to the square of the distance from the mass's center, as per Newton's Law of Universal Gravitation.
When the star's diameter decreases by a factor of 8, the radius decreases by a factor of 8 as well. Since the radius is squared in the law of gravitation, the force of gravity would increase by a factor of 64 ((1/8)² is 1/64, so when taking the inverse, it multiplies the force by 64).
The gravitational force at the surface of a star would increase if the star contracted to one-eighth of its previous diameter without losing any of its mass. As the star contracts, the distance between a point on the star's surface and its center decreases, while the star's mass remains the same.
According to the law of universal gravitation, the force of gravity is inversely proportional to the square of the distance. Therefore, as the distance decreases, the gravitational force increases.