Final answer:
If the distance between Earth and the Moon doubled, the gravitational force between them would be reduced to a quarter of the original force due to the inverse square law in Newton's law of universal gravitation.
Step-by-step explanation:
The students' question relates to the concept of gravitational force and how it changes with the distance between two celestial bodies, such as Earth and the Moon. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (F ≈ m1 × m2 / r²). Therefore, if the distance between the Earth and the Moon were to double, the gravitational force would not be halved but would actually reduce by a factor of four, or become one-fourth of the original force. This is because the distance d is squared in the gravitational equation (F ≈ 1 / d²), leading to a decrease by the square of the factor by which the distance increases. Doubling the distance between the Earth and moon would thus reduce the gravitational force to (1/2)2, or 1/4 the original force.