The gravitational force between two objects is given by Newton's law of universal gravitation, which states:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects, and
- \( r \) is the distance between the centers of the two objects.
If the mass of one object (let's say \( m_1 \)) doubles while the other object's mass (\( m_2 \)) remains the same, the new gravitational force \( F' \) can be expressed as:
\[ F' = \frac{G \cdot (2m_1) \cdot m_2}{r^2} \]
Comparing this to the original gravitational force \( F \):
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
We can see that:
\[ F' = 2 \cdot F \]
So, if one object's mass doubles and the other object's mass stays the same, the gravitational force between the two objects will also double.
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