The gravitational force between two objects is governed 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 them. The formula is:
\[ F = G \frac{m_1 m_2}{r^2} \]
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 their centers.
If the mass of one object (say \( m_1 \)) decreases by one-half (to \( \frac{m_1}{2} \)), while the second object's mass (\( m_2 \)) remains the same, the new gravitational force \( F' \) can be expressed as:
\[ F' = G \frac{\frac{m_1}{2} m_2}{r^2} = \frac{1}{2} G \frac{m_1 m_2}{r^2} = \frac{1}{2} F \]
This shows that the new gravitational force is half of the original force.
Therefore, the correct answer is:
The gravitational force decreases by one-half.
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