Two particles are located on the x-axis. Particle 1 has a mass m and is at the
origin. Particle 2 has a mass 5m and is at x=L. A third particle is placed somewhere
along the line connecting particles one and two, but not necessarily in between the
two particles. Where on the x-axis can the third particle be located so that the
relative magnitude of the gravitational force on both particle 1 and particle 2
increases by the same amount? (Put another way, the ratio of gravitational forces
should be the same for both particles after particle 3 has been added.)