After I finished the comment I almost went back to modify that intro, but figured the gist of it would be ok.
What I was trying to do was show how we move from the mental model of dots on a balloon (there is so much space on the balloon! the dots are tiny!) to rings around a ball. In order to make sure the dots don't intersect with each other simply spread them out appropriately. In order to make sure the rings don't intersect each other make some of them slightly bigger, or stretch them a bit.
The resulting orbits are still, approximately, great circles on the same sphere - just perturbed a bit.
What I was trying to do was show how we move from the mental model of dots on a balloon (there is so much space on the balloon! the dots are tiny!) to rings around a ball. In order to make sure the dots don't intersect with each other simply spread them out appropriately. In order to make sure the rings don't intersect each other make some of them slightly bigger, or stretch them a bit.
The resulting orbits are still, approximately, great circles on the same sphere - just perturbed a bit.