Final answer:
The gravitational force between two asteroids changes by a factor of 2/3 if one doubles in mass, the other triples, and their distance triples.
Step-by-step explanation:
When two asteroids exert gravitational force on one another, the magnitude of the force can be calculated using Newton's law of universal gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
If one asteroid doubles in mass and the other triples, the force would increase by a factor of 2 x 3 = 6.
However, if the distance between them is tripled, the force would decrease by a factor of (1/3)² = 1/9.
Therefore, the net change in force would be 6/9 or 2/3 of the original force.