The gravitational perturbation affecting the outer planets in your solar system is outside your solar system but affecting all your planets steadily, and by more than a gravitational pull. There is confusion, in understanding the nature of the Planet X eccentric orbit and the effect it and your Sun's dark binary twin have, because man is struggling to reconcile this new information with existing astrophysics theories and the math formulas used to describe them. Somehow they all must fit, and they don't. The problem lies with the theories and formulas, though few throw them aside as then they feel adrift, without an anchor. The insecure slam shut the doors, close out new information, and develop the closed-mind syndrome recently under discussion here on sci.astro. For those not closed minded, we will describe the eccentric orbit of Planet X, between your Sun and its dark twin. This unlit binary sun lies some 18.74 times the distance from your Sun to Pluto, at a 11 degree angle from the ecliptic, in the direction of the constellation of Orion. Though farther away, twice the distance or more, from where Planet X rides at the moment, it is a large gravitational giant, and thus between these two binaries Planet X is caught in a highly elliptical orbit. This orbit does not fit into man's astrophysics theories, and thus it cannot be described by the math used by man to describe comet or orbit behavior. Yet the orbit makes sense, if one puts the dictates of man's current theories aside.
There is a desk-top toy composed of several metal balls hung in a line from a wooden frame, which when set in motion causes the end balls to swing out, then return to bump all the balls in the row until the ball on the opposite end swings out in an equal manner, thence continuing until gravity wears the motion down to a stop. This toy is a simple example that an object will stop, when "escaping" a gravity pull, and return toward that gravity pull by reversing its course. That most known planets or moons go around their gravitational giants is due to a phenomena of gravity we have termed the Repulsion Force, though it is simply gravity particles spurting out from large bodies such that they are kept apart like two fire hoses turned on one another. Planet X, like the balls in the desk-top toy described, slings back and forth between its two gravitational foci, returning on almost exactly the same path. Its momentum causes it to overshoot a focus, then like the balls in the toy, to return on the same path after coming to a full stop. Why would it not do that, when both foci are directly behind it? This is equivalent to the end ball in the toy, dropping back toward Earth due to gravity. When approaching one of its suns, Planet X picks up speed, as the end ball does when dropping, and thus acts like a comet when coming through the solar system. It shoots through the solar system, its speed causing it to bypass the sun. Once past, with both gravitational pulls behind it, it stops, as the end ball in the toy does, and then returns on the same path, as the end ball does.
This is not a curved orbit, it is a sling orbit, and for those who would argue that such an orbit cannot exist, we would point to the desk-top toy, where the end ball returns so precisely that it connects with the other balls in the toy line-up so that the motion repeats itself with only gravity bringing it to an eventual halt. The back and forth sling is a return trip, as the toy demonstrates. The difference between Planet X and the desk-top toy is that the toy had its major gravity pull in the center, bringing the motion to a stop, where Planet X has dual gravitaional pulls at the ends of its sling orbit, which keeps the slinging motion going.