A

Step 1: The gravitational force \( F_g \) between two objects is given by Newton's law of gravitation:
\( F_g = G \frac{m_1 m_2}{r^2} \)
where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between their centers.
Step 2: Analyzing the equation, we see that the gravitational force depends on the product of the masses \( m_1 m_2 \), the gravitational constant \( G \), and the inverse square of the distance \( r^2 \). Hence, the force explicitly depends on:
- The product of the masses (Option B)
- The gravitational constant (Option C)
- The distance between the masses (Option D)
Step 3: However, it does not depend on the sum of the masses. Therefore, the correct answer is Option A.
Therefore, A.