Final answer:
When an astronaut moves twice as close to the moon, the gravitational force increases by a factor of four, resulting in a new gravitational force of 400N.
Step-by-step explanation:
The question is asking about the effect of changing distance on the gravitational force between two objects, which according to Newton's law of universal gravitation, is proportional to the inverse square of the distance between their centers. Since the force of gravity acting on the astronauts is initially 100N, when the astronaut moves 2× closer to the moon, the distance between them decreases to half. As per the inverse square law, the gravitational force would increase by a factor of 22, or 4 times the original force. Thus, the new force of gravity would be 100N × 4 = 400N. This illustrates a fundamental principle in classical mechanics within the realm of celestial mechanics.