The force of gravity 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,
- \( G \) 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 the Earth (let's say \( m_1 \)) doubles, the new mass becomes \( 2m_1 \). The mass of the Sun (let's say \( m_2 \)) remains the same, and the distance \( r \) does not change.
Plugging this into the equation, 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 the force of gravity between Earth and the Sun would indeed double.
Therefore, the correct answer is:
The force of gravity would double.
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