Silk density is actually ~1.37 g/cm^3, so derate the above to 14.6 km. IOW, a silk cable can support 14.6 km of rope hanging below it.
Not close to strong enough for a Space Elevator.
I thought space elevators were deployed with space tethers, which are held taut by the planet's rotation and centrifugal force. While mutant silk worm silk still may not be strong enough for a space elevator, it shouldn't depend on the weight of the rope hanging below it but instead the on the centrifugal force pulling in the opposite direction, away from the planet's surface.
They could be practical with known materials on Mars, but there is nothing there worth building one for.
If the silk only need be kept "only" taut, its weight will be perfectly balanced against centrifugal force, so in effect the silk will be weightless. But my suspicion is the tether would necessarily need to be kept taut with extra force, not "only" taught, but with force to put stress on the silk tether pointing outwards and upwards.
I have no idea how one would calculate the required centrifugal force, but perhaps you'll do us all the favor and determine whether or not the silk would be strong enough without being distracted by the weight of all the silk, which is irrelevant due to it being cancelled by centrifugal force.
But literally the only thing holding up almost all of the span from geosynchronous orbit down to the ground is the pure strength of the cable. Centrifugal force would act usefully mainly on parts of the cable that extend out past geosynchronous orbit, to support the whole structure through tension in the cable. The cable inside that orbit would absolutely not be weightless. Its weight per unit mass is of course lower close to geosynchronous orbit, but most of the cable is very far from it.
No. That is ridiculous and wrong.
The cable is not holding up its own weight, the centrifugal force is. The tension comes from the anchor point and the centrifugal force only. Weight is entirely counteracted and is no longer a consideration.
Think of a rotating chain in space, the chain is weightless, but each ring needs to apply enough centripetal force to counter the centripetal force.
Lets focus on the barycenter of the chain.
The centripetal force is limited by the strength of the chain; the centrifugal force is a function of rotation speed, length of the chain, and linear density of the chain.
this means that for any combination of chain type and rotation speed if the chain gets too long it will break.
With a geostationary space elevator you need to build a part of it over geostationary orbit and a part of it below geostationary orbit. the part above will pull the part below and make it "float".
The problem is that the part below needs to be ~100 km long and has still has a weight.
Think of the section of the tether at geostationary orbit as a giant weightless chain link.
The issue is not having that chain link remain suspended, the problem is to have it not break while trying to balance the huge forces.
And in order for a space tether to work at all, that weight must be negated by centrifugal force or the entire thing will collapse to the ground.
all the ~100km of tether below geostationary orbit will have positive net weight by definition. All this weight must be held by tensile strength, whether it comes from a fleet of rockets or centrifugal force is irrelevant.
Again the hard thing is not making it float, geostationary satellites do this already, the hard thing is building a 100km long satellite.
EDIT: said another way consider a chain being pulled apart by two tractors. All forces on the chain cancel each other yet some chains will break and some will not.
Forces are first applied, then propagated, then (vectorially) summed. If the material cannot handle the forces applied it will break.
If you happen to have seen those "Hydraulic press against X" videos you can see how it is not enough to have forces cancel each other in different points.
And to be clear about how this is relevant: for (at least) the first 50km or so the centrifugal force is negligible, so even if
weight + centripetal_force = 0
you have
|weight| + |centripetal_force| = fuckton of force
We will be burning rocket fuel to get to space for the foreseeable future. Better to launch enough to build in-space processing facilities if you're really committed to dual-homing humanity or making space travel more cost effective.
(2 GPa) / (1400 kg/m^3 x 10 m/s^2) = (2e9 N/m^2)/(1.4e4 N/m^3) = (2e5/1.4) m = 140 000 m = 140 km
P = F/A, F = M x g, M = A x L x rho
L = M/(A x rho) = (F/g)/(A x rho) = (F/A)/(g x rho) = P / (g x rho)
If by orbital ring you mean a band girdling the planet and rotating well above orbital speed, magnetically coupled to and supporting stationary structures that reach ground level... I don't see any value in discussing those in this century.