I have looked on the internet and maybe I am not using the right search terms but I can not find anything concerning this topic.
I am looking because I would think if a massive pole structure were placed in a random assortment of debris going any which direction in space the debris would tend to orbit around it center perpendicular to the direction the pole is pointing.
let me know what you think.
Depending on the dimensions and mass of the linear object you mention, rather than a normal spherical one, at distances relatively far away from the object, space debris would orbit it as though it were spherical.
This is because the centre of gravitational attraction would, in effect be a point and a spherically symmetrical attractive force field would apply.
Much closer in to the object, at the exact mid-point along it's length, assuming it's mass is evenly distributed, I can't think why a piece of space debris would not continue to orbit that given mid-point, given that the space debris was traveliing at just the correct velocity to achieve this orbit, (which is very unlikely).
At any other point (other than the mid point) of a finite length linear object, the gravitational attraction of one side would be greater than on the other, resulting in the orbit of the space debris becoming unstable and eventually the debris would impact the object.
I don't have the background to do it, but a computer model of the system should not be difficult to set up and would illustrate the effects of different variables.
Orbit Modelling From Wikipedia or related, although not very detailed: Orbiter Forum
The shape often doesn't matter. Most orbits are very far away. In the solar system, the sun and planets are modeled as points. Even ones like Earth, which has a large moon. This gave extremely good results.
For example, the orbit of Mercury is close to an ellipse. It is perturbed by the attraction of other planets, primarily Jupiter. Because of this, the perihelion does not occur in the same place every year. It slowly rotates around the Sun, at about 5000 seconds of arc per century. In the 1800's, Astronomers modeled all the effects they could think of and accounted for almost all of the drift. The remainder was a long standing mystery until Einstein predicted that General Relativity would account for the remaining 43 seconds of arc per century.
This is cheating a bit because the planets are close to spherical. We can model the Earth we are standing on as a point at its center. We can calculate our weight to pretty good accuracy.
Sometimes it does matter. There has been a lot of work on orbits of the Moon and other satellites around the Earth. They are close enough and orbits are measured accurately enough that the shape of the Earth does matter.
For a long cylinder, matter would not tend to orbit perpendicular to the axis. The force of gravity would be radially inward. It would have a $1/r$ dependency instead of $1/r^2$. A satellite at just the right velocity would have a circular orbit perpenducular to the axis.
The orbit would not be stable. Any deviation from the perfect speed, and it would fly off into space or crash. See https://en.wikipedia.org/wiki/Bertrand's_theorem and An intuitive proof of Bertrand's theorem
If the orbit was tilted with respect to the axis, it would have a screw shape. There would be no restoring force along the axis, so it would keep any along-axis velocity.
For more information about orbital mechanics, Goldstein is a good advanced book.
