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. The formula is:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the force of gravity,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the Earth and the Sun),
- \( r \) is the distance between the centers of the two objects.
If the mass of Earth doubles (let's denote the original mass of Earth as \( m \), then the new mass is \( 2m \)), and the mass of the Sun remains constant, the new force of gravity would be:
\[ F' = G \frac{(2m) m_{Sun}}{r^2} \]
From this we can see that the force of gravity will also double since the mass of the Earth is now \( 2m \) instead of \( m \).
Therefore, the correct response is:
The force of gravity would double.
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