Final answer:
The spring constant (k) is the factor that affects elastic potential energy but not gravitational potential energy; it is related to the stiffness of the spring and is unrelated to gravitational forces.
Step-by-step explanation:
The factor that affects elastic potential energy but not gravitational potential energy is the spring constant (k). The spring constant is a measure of the stiffness of the spring and directly influences how much energy is stored in the spring when it is compressed or stretched. Gravitational potential energy, on the other hand, depends on the mass of the object, the acceleration due to gravity, and the height from which the object is positioned relative to a reference point.
Therefore, the correct option among the choices given is A) spring constant. The acceleration due to gravity, distance from a given position, and amount of matter in the object significantly affect gravitational potential energy, whereas the spring constant is specific to elastic potential energy and does not influence gravitational potential energy.