The gravitational force between two objects, such as the Earth and the Moon, is described by Newton's law of universal gravitation, which states that the force \( F \) between two masses \( m_1 \) and \( m_2 \) is inversely proportional to the square of the distance \( r \) between them:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant.
If the distance between the Earth and the Moon doubles (\( r \) becomes \( 2r \)), the gravitational force changes as follows:
\[ F' = G \frac{m_1 m_2}{(2r)^2} = G \frac{m_1 m_2}{4r^2} = \frac{1}{4} F \]
This means the gravitational force becomes one-fourth of the original force when the distance doubles.
Therefore, the correct answer is:
The gravitational force between Earth and the Moon would go down by a proportional amount.
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