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You obviously could do this, by fudging $\epsilon$ suitably. However this idealised greenhouse model is wrong for Earth and is probably wrong for Mars as well. It's wrong for Earth because the atmosphere is not optically thin for long-wave radiation (infrared), so you simply can't consider the atmosphere as a single layer like this. Instead you have to ...


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No, I don't think so. As you say, the pressure is highest in Io's volcanic plumes at 40 nanobar (4 millipa) at most. That's equivalent to the pressure about 115 km (72 mi) above the Earth's sea level. At 120 km / 75 mi the atmospheric drag becomes more significant but it doesn't cause a re-entering craft to glow, so you're wrong unless the craft is going at ...


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Dependng on the tide, you could be partly or completely in the water, as an orbit of sea level perigee is measured through your center line of mass, unless your vacuum tunnel also penetrates the water, and then there are all this places with solids above sea level.


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Maybe I'm not understanding the question correctly, but it sounds like to me that you are describing "Orbital Ring". You can find more about them at Orbital Rings on Wikipedia. There is a great video about it on Orbital Rings by Isaac Arthur on YouTube. He does a good job of describing physical limitations vs engineering limitations. Sorry for the ...


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Yes, if you could build the vacuum tunnel. For example, the Sentinel 1A satellite (which currently orbits the earth every hour or so) is designed to maintain its orbit within a 100m diameter virtual tube, fixed with respect to the surface of the earth, for a decade. (Like many other remote sensing DInSAR satellites, the quality and usefulness of the data it ...


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According to an article by Geoffrey Landis (http://www.geoffreylandis.com/moonair.html), oxygen and nitrogen are removed from the Moon within about 100 days, due to the combined effects of sunlight and the solar wind. However, if the atmosphere is thick enough, then this effect would no longer occur.* In this case, the gases would last for thousands of years....


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I would say, in some sense, such large vacuum structures already exist, for example, LHC. Right now they are only used for orbiting protons, nuclei, etc., but one can use similar structures for larger objects, if the latter are charged (or magnetized) preliminarily. @Russell McMahon mentioned electromagnetic steering here.


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