Looking for this sci-fi book please help

I was told you guys are experts and locating books. Here is what I can
remember:

earth destroyed distant future ---- many societies of people travel
on man made spheres. live forever have implant that allows them to
communicate with a computer and gives them information

one society visits the a settlement of previous vatican catholic
society ruled by priest and a pope council.

Tensions develop when they are visited by the advanced society.
Eventually, after a group wants to leave the pre- industrielized
society and join the others (rebellion) leaving the other society
short of citizens that could not be sustained, a nucluer bomb is snuck
on board the orbiting society and it slowly sinks out of orbit.
Before it does, survivoirs make way to a rescue craft and start a
new. They have to travel several generatons to another sphere that
is like a backup and reserve in case of problems. They no longer can
live forever but survive based on the training of the computers
education.

The catholic society is detroyed by the fall out of the orbiting spher