A great way to understand the process of planet detection, is to visualize something we are probably all familiar with. That is, when you twirl an object such as a yoyo over your head on a string. As the yoyo goes round and round in circles I behaves much like the moon as it encircles the Earth, or Earth as it orbits the Sun. The centrifugal force built up by the yoyo as you twirl it, is what gives you the feeling that it is pulling away from your hand. The string however, is what keeps it from doing that. If you let go of he string however, the yoyo will in fact go flying off in the direction toward which it was aimed at he instant you released it. Yet as long as yo whirl the string at the appropriate rate, the yoyo will maintain a constant glide at a constant distance about you wrist. The set distance between the yoyo and your wrist that is maintained by the presence of the string, and a speed / centrifugal force of the yoyo's movement, is known as Equilibrium.
In the case of an orbiting planet or moon, the concept of centrifugal force being countered by an equal and opposite attachment force, is identical to that of a yoyo being twirled on a string. The attachment force in this case is the gravity of the larger body; the planet in the case of an orbiting moon; the sun or mother star I the case of an orbiting planet.
Returning to the previous illustration for a moment, you might notice that as you twirl the yoyo, your hand wobbles a bit. If you were twirling a heavier object, your hand would wobble even more. This is caused by the outward pulling centrifugal force of the yoyo as it circumnavigates the opposite pulling force holding it in place. In this case it would again be your fist and the string. In the case of a planet or moon, it would be the star or planet respectively. The wobble however, is still something that occurs even on a cosmic scale. Yet as we peer out at remote stars in space, this wobble is all but imperceptible.
Still, astronomers have learned to detect even the slightest wobbles in stars at great distances. And it is precisely these wobbles or perturbations, when they are observed to follow a regular pattern, that reveal to scientists that the star or planet that they are studying has an orbiting satellite body. Naturally the course of the orbiting body must also shift this way and that as the planet or sun at it's orbital nucleus is caused to oscillate.
Our Sun undergoes quite a bit of oscillation due to the fact that here are several planets in orbit around it. So its apparent wobble would be somewhat kinetic were it to be viewed by an intelligent life form on some distan planet in a far off galaxy. Yet this is the way astronomers are able to detect planets that are otherwise invisible.
In the case of Planet X, the gravity of this enormous object was discovered to be the cause of otherwise unexplainable disturbances in the orbits of Uranus and Neptune. This was a clever method in determining the presence of the massive dark star. Since, even though Uranus and Neptune do not orbit Planet X, the law of gravity still applies.
Every time came Uranus an Neptune came close enough to Plant X as they traversed our Sun, the gravity of the dark star momentarily pulled them near, and cause a slight off tracking or bulge in their solar orbits. The repetition and regularity of this occurrence greatly helped scientists determine the mass and distance to Planet x. At the the time of these calculations in the early 1990's, Planet X was said to be 7 billion miles away. And its size was calculated at 4 to 8 Earth masses.
From a yoyo on a string to a planet around a Sun. The principles of mechanical physics are evidently transferable. Planets, stars and moons wobble the same way yoyo's and hands do.
Furthermore, in the vacuum of outer space, a large extraneous body can cause anomalies in orbital systems that it may pass too close to. That is how astronomers find planets and stars. And it is these same principles, according to a 1992 NASA press release, that led a to strong case for the existence of Planet X or what the Ancient Sumerians called Nibiru.