For a permanent darkside platform over Venus, I present to you Jeff Greason's Plasma Magnet Drive which builds upon John Slough 10.1063/1.1867244. It provides a counteracting force wherever there is an ionic wind, which Greason intended for interplanetary transit. I'm stealing that here, for statites, buoyed upon the ions blasting back from atmo.
If staying within Venus' true umbra at 949928 km, we lose solar power - all of it. Photovoltaic panels won't be taking direct sunlight here, although maybe L2 or (more directly) the polar orbiters can spare some reflected sunlight. To compensate we get a chill fit for a superconductor.
In near-vacuum and shade, the best measure isn't blackbody Kelvin. We measure the ambient "plasma" - the ions themselves. The relevant units would be speed, density, and energetic excitation. If "density" is measured in the number of ions rather than in their mass, we'll need composition of plasma as well.
On to what it takes to keep statites in the shadow. We're like SVL2 orbiting the Sun - not Venus. Obviously, Venus' orbits will circle out of the shade. Since we're not orbiting, we need to counteract Venus' gravity force. At the edge of Venus' umbra, that gravity is almost at the planet's L2 edge: [6.673 * 4.867 / 9.02363205184]e-4, that is 0.00036 ms-2. (Not much less than what Earth's would be at that height.) At this altitude we needs add the Sun's gravity at the planet's umbral pinpoint too, at 109.157928 gigameters - 0.01114, so 0.0115 total. Further down, the planet's gravity is stronger (at this SV line, V orbits start 536412 km on down), and it gets warmer... but the planet's induced magnetosphere is stronger too, and we don't bake the magnets. Not until we're in the atmosphere proper.
A star gives off heat and that heat excites ions. Within a solar-system, especially habitable-zone or inward, a craft can capture this outgoing force by a physical sail or by a magnetic shield. Best of all would be to capture these ions. The craft would want force in terms of flat pressure, newtons per square meter; if using a magnet-field, that area will be much larger than whatever area taken by the body of the craft itself but then we might not get to do capture.
Jeff Greason for his drive - using only the solar wind, and at Earth I might add - was touting 2 ms-2 acceleration. Remember that too far down Venus' light umbra, Venus' bulk starts casting an ion umbra as well. I think, though, that 949928 km offers some room to float in, before dropping into the full ionopause.
Since I am no expert in the contents of Venus' trail I've got a number of variables here but even so, I think there's ions enough to fight a 0.0115-0.02 ms-2 pull in those higher altitudes of the umbra. So much more, that I expect to use the rest of the force to turn turbines against the darkside magnetosphere (potential-difference of ten volts, I hear) and generate power for whatever robots need it. I don't know that a permanent human colony lives in this frosty environment but, it may not have to.
Venus' statites in this long and narrow cone will store volatiles and perhaps capture its own hydrogen, dumping it downwell for orbital stations to harvest as they fly by. That delta-V will be easier where the stations are in the higher altitudes and the statites, lower.
This is also where Venus-based astronomers do coldweather astronomy. The astro crew live on L2 and communicate thence.
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