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## Main Question or Discussion Point

Trying to compute a 'Chainworld' with simplest possible Newtonian physics but still lost with my lousy math. By 'Cainworld' I mean series of man-made, worlds inspired by classic novel "Ringworld", which orbit around a common center of mass in one, common, perfectly circular orbit. They are held apart by centrifugal force and pulled together by Newtonian gravity. In 'Ringworld' , there is a star at the center of mass. I want no star, just independent 'worlds', a 'chain' of cities held in place only by gravity and acceleration.

Say you start with two cities with masses equal. Both M2. They orbit a common center of gravity with radius R. Now consider three cities with the same total mass as the first two. Do they orbit with smaller radius? What is the smallest possible orbit for unlimited number of cities with total mass equal the original total mass? Surely it has something to do with the gravitational constant, G and is some simple function of our total mass!?

Say you start with two cities with masses equal. Both M2. They orbit a common center of gravity with radius R. Now consider three cities with the same total mass as the first two. Do they orbit with smaller radius? What is the smallest possible orbit for unlimited number of cities with total mass equal the original total mass? Surely it has something to do with the gravitational constant, G and is some simple function of our total mass!?