The force of gravity between two objects is described by Newton's law of universal gravitation, which states that the 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 given by:
\[ F = G \frac{{m_1 m_2}}{{r^2}} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the Earth and the Sun), and
- \( r \) is the distance between the centers of the two objects.
If the mass of the Earth (\( m_1 \)) doubles, then the gravitational force \( F \) becomes:
\[ F' = G \frac{{(2m_1) m_2}}{{r^2}} = 2 \times \left( G \frac{{m_1 m_2}}{{r^2}} \right) = 2F \]
This means the force of gravity would double.
So the correct response is:
The force of gravity would double.
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