The force of gravity between two objects is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.
If the mass of the Earth (let's call it \( m_1 \)) doubles, then:
- New mass of Earth = \( 2m_1 \)
- Mass of the Sun remains \( m_2 \)
The new gravitational force \( F' \) would be:
\[ F' = G \frac{(2m_1) m_2}{r^2} = 2 \left( G \frac{m_1 m_2}{r^2} \right) = 2F \]
This means that the force of gravity would double if the mass of Earth doubled.
Therefore, the correct response is:
The force of gravity would double.
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