I would have to see a screenshot. There are too many things going on in your description to figure out how the comp is set up.
I would have approached this project using nulls and parenting. Parent a layer to a null, rotate the null == perfect circle. Nothing to it.
It's also important to know if you are doing this in 3D space.
Thanks Rick for responding.
Screen-shots, and video in the replies.
I don't think you need all those nulls. They're great for a lot of things, but they appear to be superfluous in this case. If your colored circles are supposed to follow a different circular motion paths, and the circles' anchor points are at their centers, you shouldn't need anything else.
Sorry, but this is one of those "why bother with AI at all?" things you could have just as easily created all your circles with AE's native tools like the Circle effect or shape layers (though stellar orbits rarely ever are perfect circles). Anyway, presumably your tangents flip around because you transformed your paths in AI in an odd way like scaling them by -100% or you have applied a certain appearance, so check that...
So I took your illustrator screenshot as a template, created a single shape layer and a single null parented them together and set up the first orbit. I then selected both the null and the shape layer, duplicated the layers (Ctrl/Cmnd + d) then moved the duplicates to the top (Ctrl/Cmnd + ]), turned off visibility on the first pair and then adjusted the position of the second null to the center of the second orbit, moved the shape layer to the second orbit path and did it again. Precisely 12 minutes later I had this:
A little adjustment of the shape layer colors and the speed of the rotation and you've got it with not much trouble. Like Mylenium said, this can be done entirely inside AE with very little trouble.
Everyone – thank you to all who responded.
A personal thank you to Rick for spending time and executing a visual explanation.
It turns out my video wasn't published originally, if you need more information click: http://www.dailymotion.com/video/x1dba60_a-letter-1_creation
To answer your questions: the Earth's orbit refrence is a simile.
I understand the process seems irrational; I being with illustrator because I’m trying to find the exact angle to the center point, in addition to the size of the circle. In other words, a circle has four points, turn the circle the correct amount of degrees and one point starts on the center point (the black dot), the other half ends on the colored dot. The only way I know how to do that is by using a plug-in with illustrator (to get the angle from the colored dot to the center point, and the size of the circle), an analog of this plug-in is not offered in after effects.
My original question: why when I paste the circles (that are already made in illustrator) into the null: position in after effects, some give me a perfect circle, some give me a Bowen knot? I appreciate the suggestions about only in after effects, unfortunately the circle paths were already made in illustrator.
You are getting Bowen knots because some of your paths were either scaled something like -100% or the vertex direction in Illustrator was reversed.
BTW, you can snap to the exact center of a path or mask in CC with the new snapping tools. I just eyeballed the project and with very minor adjustments in about 10 minutes matched the paths nearly perfectly. When designing motion graphics it is important to know when close enough is good enough.
Thanks again Rick for the input,
How would I reverse the vertex direction back?
I have not scaled anything down.
I would put a pair of guides at the center of the old circle, delete it, then hold down the Alt/Option key and drag out a new one using the elipse tool with the shift key held down.