Final answer:
When one mass is doubled, the gravitational force doubles. If both masses are doubled, the force quadruples, resulting in a force of 72.0 N from an initial 18.0 N. Both asteroids experience the same force, but the lighter one has greater acceleration.
Step-by-step explanation:
The gravitational force between two objects can be computed using Newton's law of gravitation, F = G(M1M2/r2), where F is the gravitational force, G is the gravitational constant, M1 and M2 are the masses of the objects, and r is the distance between the centers of the two masses. When one mass is doubled, the new force can be calculated by substituting 2M for M1 or M2, leading to Fnew = G(2M1M2/r2) = 2F. If both masses are doubled, the force becomes Fnew = G(2M12M2/r2) = 4F. Thus, if the initial force is 18.0 N and both masses are doubled, the new force will be 72.0 N.
Regarding asteroids, when one asteroid has twice the mass of the other, they both experience the same gravitational force but the lighter asteroid experiences greater acceleration due to Newton's second law, F = ma, where m is mass and a is acceleration.