The gravitational force between two objects is described by Newton's law of universal gravitation, which states:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force between the two objects,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.
If you double the mass of one of the objects (let's say \( m_1 \) becomes \( 2m_1 \)), while keeping the other mass \( m_2 \) and the distance \( r \) the same, the new gravitational force \( F' \) can be calculated as follows:
\[ F' = G \frac{(2m_1) m_2}{r^2} \]
This can be simplified to:
\[ F' = 2 \cdot \left(G \frac{m_1 m_2}{r^2}\right) = 2F \]
Thus, the new gravitational force \( F' \) is twice the original gravitational force \( F \). Therefore, if you double the mass of one of the objects while keeping the distance constant, the gravitational force between the two objects will also double.