A small object (blue) is placed along the x-axis, equidistant from two identical massive objects (black).  Due to the symmetry and gravitational attraction, it oscillates as shown below.

(a) What is the net force on the blue object as a function of x and r where r is the distance from a black object.?

(b) At what position is the net force on the blue object zero?

(c) What is the mass of each of the black objects?

(d) When the blue object is at the equilibrium point (which point is that?), does the system have potential energy?

(e) Is the potential energy of the system (all three objects) equal to twice the potential energy of one black object and the blue object?


mblue kg

animation time step, dt, s



Kinetic, gravitational potential, and total energy as a function of time.