The gravitational force between two objects is described by Newton's law of universal gravitation, which is given by the formula:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (Earth and the Moon in this case), and
- \( r \) is the distance between the centers of the two objects.
If the distance \( r \) doubles, the formula becomes:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2} = \frac{1}{4}F \]
This shows that the gravitational force would be reduced to one quarter of its original value.
So, the correct response is: The gravitational force between Earth and the Moon would go down by a proportional amount.