Cities in space - Singles or clusters?

The only time there is a perfectly circular orbit is
if the mass ratio of the objects is infinite.
However, a torus wouldn't technically have to be in
orbit if it went all the way around the earth; the
pull from earth is the same in all directions. The
strength of the material could be enough to keep it
up. After all, if they can make a bridge on earth
that stands up to 1 gee, then this material should be
able to stand up to the less than one gee at whatever
altitude (at GEO it is only 2.3% of a gee).

If instead these are all GEO satellites, then there
will be some eccentricity to their orbit. However, if
the mass is balanced all the way around, then the
center of mass of the system is equal to the center of
mass of the earth so the orbit would be circular. As
soon as the mass balance is thrown off, the parts of
it try to follow elliptical orbits. If the mass can
be effectively balanced continuously then it might
work.

Regarding the trip to the other side: If one were to
"stop" (change velocity by 3km/s opposite the rotation
of the ring) then yes, it would take 12 hours to go to
the other side. If instead the car continues to
change its velocity in that same direction, then the
ride is much shorter; further acceleration by another
3km/s would cut it down to six hours. Either way
there would be a subesquent acceleration by the same
amount in other direction at the other end. Total net
torque on the ring: zero. And the direction doesn't
matter if the destination is directly on the opposite
side, it takes the same amount of time and energy
either way.

Ed

--- Darren wrote: