Final answer:
Students used physical experimentation to determine variables affecting gravitational force, as demonstrated by Henry Cavendish's experiment, which measured the torsion caused by gravitational attraction between masses.
Step-by-step explanation:
The method that students used to determine the variables affecting the gravitational force between two objects was physical experimentation. Specifically, Henry Cavendish conducted an experiment using an apparatus that allowed him to measure the gravitational attraction between two spheres suspended from a wire and two stationary spheres. By observing the amount of torsion (twisting) in the fiber when varying the distances between the masses, Cavendish could test the dependence of the gravitational force on distance and the masses involved. This kind of experiment is challenging due to external factors like vibrations, which can interfere with the measurements of such a weak force as gravity.