A particle of mass 3m is located 1.00 m from a particle of mass m. You put a third mass M so that the net gravitational force on M due to the two masses is exactly zero. Is the equilibrium of M at this point stable or unstable for points along the line passing through M and perpendicular to the line connecting m and 3m?
F = GMm/r^2
The Attempt at a Solution
I found that the answer is stable equilibrium by drawing a free body diagram, because there is a net downward/upward force pointing to the initial point. However, will M move in a straight line towards the initial point? How do I derive this mathematically? Thanks!