1. The problem statement, all variables and given/known data At a ertain point between earth and the moon the total gravitation force exted on an object by both planets is 0. The earth - moon distance is 3.84 x 10^5 and the moon has 1.2% of the mass of earth. Where is this point located. 2. Relevant equations Fg=GmM/R^2 3. The attempt at a solution So i drew a diagram and put the distance R between the earth and the moon and the object somewhere closer to the moon. I then wrote that the distance from the object from the earth is (R-X). I then said that the distance from the moon to the object was X. Sine it says the Gravitational force exerted on the object at a point is the same... i get Fgm=Fge (GmMm)/(X^2) = (GmMe)/(R-X)^2 x<R i simplify this too X^2 = (R-X)^2 0 = 0.988x^2 - 0.024RX + (0.012)*R^2 if i put this into the quadratic formula i get values x= 0.5 and x = 9327.44m Now if my answer are correct, does this mean that both are answers? so i would say? this point is located 9327.44 meters from the moon and 374.672.56 meters from earth. and this point is also located 0.5 meters from the moon and 383999.5 meters from the earth? but at this second point it couldn't match my first point cause the force of gravity from the earth would decrease while the force of gravity on the moon would increase so how could the force exerted be the same??? Anyway i would appreciate any help i can get.