Halley's comet
Every member of the solar system is held in orbit around the sun by the mutual force of gravity between the object and the sun.
All object except the Sun orbit round the Sun. The moons also orbit round their planets.
The orbit of Eris is 44° from the ecliptic.
The question says that there is an object that's in the solar system that's outside the solar system for half the time. That's a lot like the statement that states: "This statement is false."
The best way to tell the difference is by tracking the object. If the object seems to move in an orbit around the Sun, then it is in the solar system. If not, it is outside it.
If you mean "why don't they orbit other objects in our Solar System", the Sun has most of the mass in our Solar System.
no the moon does not orbit the solar system.
The gravitational force between the sun and each object in the solar system
Gravity combined with the object's "sideways" (tangential to its orbit) motion. The Sun "wants" to pull the object towards it and the object "wants" to fly of into space. When these two things are balanced the object is in a stable orbit.
There is no object on the solar system which is known to take 36514 (what? seconds, hours, days, years?) to orbit the sun.
It is not the dominant object in the neighbourhood of its orbit.
solar system