Three identical small spheres, each of mass m, are fixed at the corners A, B, and C of an equilateral triangle of side length L. No other objects are nearby.
Answer the following without performing any numerical calculations.
(a) For sphere A, state the direction of the gravitational force exerted on it by sphere B and the direction of the gravitational force exerted on it by sphere C. Explain how you determined each direction.
(b) Describe the direction of the net gravitational force acting on sphere A. Use symmetry arguments to justify your answer.
(c) Do spheres B and C experience net gravitational forces of the same magnitude as sphere A? Explain your reasoning in terms of the spatial arrangement of the masses.