The variable that has the largest effect on the gravitational force between two objects is:
A) mass
According to Newton's law of universal gravitation, the gravitational force \( F \) between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation 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, and \( r \) is the distance between their centers.
Therefore, mass greatly influences gravitational force, making option A the correct answer.