I'm very new to AE so please forgive my ignorance.
I'm trying to get 5 small eclipses to rotate around a larger one. My approach to this was to create (using ALT) another even larger eclipse around the large one and copy it's path to the small circles. However, when I do so, the copied path is significantly smaller than the larger eclipse I created.
Can anyone explain why this is, or failing that, suggest another way of getting the end result I'm after.
Per what you are saying, it should work. Are the ellipses 2D or 3D layers? For 2D layers the path should be exactly the same size as you copied, for 3D layers the camera distance will affect the perceived size.
The mask or path that defines the shape scales with the scale of the object. That seems pretty obvious, but if you copy the path from an object with 200% scale to an object with 100% scale, the new path will be half the size of the other one.
If I were doing what you're doing, I'd create a solid and put an oval mask (I prefer working with solids over shape layers). Put it where I want it in 3d, then duplicate it once (ctrl + d) and move the second one where I want it to be to start it's orbit, then parent it to a null where the original oval is. I'd duplicate it un-parent the duplicate from the null and rotate the null 90 degrees (easily done by holding shift) create another duplicated, un-parent that duplicate and rotate it again. Repeat this as necessary until I've got 4 ovals around the first one exactly the same distance from the center oval and perfectly evenly spaced. You can obviously change the angle to a smaller number to get more ovals. Then link all the ovals to the null and rotate the null.
I hope that helps. Sorry if it's more information than you needed.