The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses of the 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,
- \( r \) is the distance between the centers of the two masses.
If one object's mass decreases by one-half (let's say \( m_1 \) is halved), the gravitational force changes as follows:
\[ F' = G \frac{(m_1/2) m_2}{r^2} = \frac{1}{2} \left(G \frac{m_1 m_2}{r^2}\right) = \frac{1}{2} F \]
This means the gravitational force between the two objects decreases by one-half.
Therefore, the correct response is:
The gravitational force decreases by one-half.
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