71See, When you fire the projectile from the surface along the line joining their centers , it experiences force if gravitation from the two spheres as a result of which it has some deceleration [Note that forces on it are unequal] . At some point P on this line, the Field Intensity due to both the spheres is equal. Now just when it crosses that point, it is automatically attracted towards the bigger sphere.
So, In conclusion you need to provide only that much energy so that the particle could just cross the Point P.
