When the mass of an object doubles while keeping the distance between it and another object constant, the gravitational force between the two objects also doubles.
According to Newton's law of universal gravitation, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant.
If \( m_1 \) (the mass of one object) doubles, making it \( 2m_1 \), then the new gravitational force \( F' \) becomes:
\[ F' = G \frac{(2m_1) m_2}{r^2} = 2 \left( G \frac{m_1 m_2}{r^2} \right) = 2F \]
Thus, the gravitational force between the two objects increases and doubles when the mass of one object is doubled, assuming the other mass and the distance between them remain constant.
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