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 force of gravity,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the planet and the Sun),
- \( r \) is the distance between the centers of the two objects.
If the mass of the planet is cut in half, let's denote the original mass of the planet as \( m_1 \) and the new mass as \( \frac{m_1}{2} \).
The new force of gravity can be expressed as:
\[ F' = G \frac{\left(\frac{m_1}{2}\right) m_2}{r^2} \]
We can see that the new force \( F' \) would be:
\[ F' = \frac{1}{2} G \frac{m_1 m_2}{r^2} = \frac{1}{2} F \]
Thus, when the mass of the planet is cut in half, the force of gravity between that planet and the Sun would decrease.
Therefore, the correct answer is: The force of gravity would decrease.
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