Is there a way to place a satellite in-between two planetary bodies such that the force from each gravitational pull is effectively nullified? In other words, is there any type of situation that would allow for us to place a satellite in-between orbits of two planets such that it wouldn't be moving at all? Is there any way to maintain this state for an extended period of time (the answer here can be in terms of any arrangement of planets, not in terms of our solar system).
I was thinking that if you had a planet orbiting closer to the star at a slower speed and one further from the star at a higher speed such that their orbits synchronized, you may be able to place a satellite between the two and maintain solar orbit indefinitely with no degradation, is this a dumb train of thought? Taking this further, I haven't read much about Lagrange points, but theoretically is there any planetary configuration that allows for a constant Lagrange point that never moves whereas most change with the orbit of the bodies in question?