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