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It was discussed many times in several threads here the ability of a certain body to retain earth standard atmosphere, w/o domes, for earth standard timescales of billions of years.
Having in mind the papers of G.Nordley for the smaller bodies: http://www.sfwa.org/members/Nordley/Gra … ravity.pdf ;and of Stevenson conserning the interstellar planets: http://www.gps.caltech.edu/faculty/stev … ...ets.pdf ; it`s obvious that much smaller than Earth bodies could retain 1 bar/300 K N2/O2 atmosphere at the surface for billions of years. The trick is to have effective 'clod trap' above the troposphere and the exobase particle`s termal velocity to be less than 20% the exobase escape velocity...
But how much smaller? What`s the minimum of body`s escape velocity and surface gravity?
Norley`s formula puts Titania, Oberon, Charon, Rhea, Umbriel, Ceres, Vesta, Pallas, Ariel, Iapetus, Dione, Tethis... some of the newfound transneptunians in one group of ~3% +/- 30% of earth`s gravity.
If we examine , say Charon and Tethys we`ll see that this is the lower surface gravity+escape velocity limit for terraformability of the round bodies. I mean their ability to hold earth-like open-sky atmosphere for earth-like timescale.
Charon: surface gravity of 3.75% earth`s or 26.66 times smaller than earths; radius of 593 km (diameter - 1186 km); mass - 1.9 E 21 kg; surface area of 4 400 000 km2 ~ India+South Africa, ~EU in 2007, ~half Brazil...
The Charon`s troposphere should be 250-300 km high in order on surface its air weight to push with 1 Bar. Say, the surface temperature is about 300 K and falls quickly to the earth`s -50 degrees Celsius at the tropopause`s 'cold trap' and contineaus to drop fast with the hight. The remaining 20% of the atmosphere`s mass via strato- and mesosphere manipulation is so cold that it lies within several hundred km from surface, hence - let the the exobase is at 1000 km from the Charon center. On that hight the escape velocity is 500 m/s - within the bullet speeds range. The thermal velocity of N2 ( we take this as minimum cause O2 is heavier hence slower and assume that the water is effectivelly sequestered in the troposphere by the 'cold trap'...) should be ~<100 m/s which corresponds to ~<17 K absolute temperature of the exobase. The mean surface temp. of Pluto-Charon is 40 K, but this is not related with the achievable exobase temperatures. Of course too close to the sun minor body very difficultly will be made to have so close and clod exobase, but some cryo-refrigeration measures are still possible.
Tethys: surface gravity - 0.16 m/s2 or 61.31 times lower than earth`s, radius - 530 km ( diameter - 1060 km), mass 6.176 E 20 kg; surface area ~ 3 500 000 km2. Put earth-like atmosphere, 'cold trap' it at the tropopause (~600 km high) for hydrogen retention... The exobase arrange at 1500 km from the body`s center. There the escape velocity is 230 m/s, so the N2 thermal velocity should be under ~50 m/s, responding to under 3 K !!! the temp. of the background universal radiation... which although is not unachievable for advanced exobase-cryorefrigeration tech... Notice that if exobase could be transperant for the background microwaves and it`s thermal velocity could be kept under the limit.
So, bodies with lower than ~1% of the earth`s gravity can not be terraformed without domes. According to the Gibor Basri`s taxonomy of the planetary mass objects ( planemo ) every selfgravitating to roundness obect is planemo. This minimum of gravity corresponds to 400-700 km diameters for the smallets possible planets, depending on the density of the substance - bigger icy, smaller rocky - hence some of the smallest possible icy planets can not hold atmosphere around them without far under 1 K exobase refrigeration. But in wider sense -- it appears that in principle every planemo could be terraformed = provided with 1 bar N2/O2 room-temperature at surface air without cap over which air cover to withstand billions of years untill sufficient refrigeration is kept.
It is obvious that lower requirement for atmosphere`s lifetime in enormous degree ease the task...
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Your far-ranging discussions suddenly caused me to think of one configuration I've not heard about before: A small planetoid, such as you specify, surrounded by a balloon suitably attached and pressurized, and the entire assembly rotated so as to be able to walk on the inside surface of the balloon. I leave the possible advantages and disadvantages of such a scheme open for discussion by any who wish to go out on a limb. . . .
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You mean the whole bubble surrounding the planetoid to be like a giant Bernal sphere?
It would be inhabitable just around its equator - comperativelly narrow strip - and can not have diameter bigger than several hundred kilometers with the existing material. With diamond perhubs up to 5000 km. With quarz - which satisfies the eventual transperancy requirements ~700 km.
If one provides the gravity via axial rotation - you don`t need a planetoid within. Such scheme will suffer also the Ring-world decease - with gravity zero within the sphere, slightly disturbed - the rotating sphere will colide with the 'inbody'...
My point is that if the body is too low massive to selfround itself under its own gravity -- it doesn`t worth to be terraformed externally. Such planetoid - rocky or icy - easier can be made into rotating colony: by total disassembly and utilization of its mass as construction materials, by cavitating it via dig out operations or blowing it in huge baloon after semi-melting it in the focus of a concentrating mirror...
The bodies over the roundness bound - i.e. with diameter bigger than ~400 km. are different thing. Inherently they have surface gravity of ~ or >1% gees and surface area of ~ or > than half a million km2 ( i.e. ~France ). As was shown in my back-of-the-envelope calculations the exobase temperature of such mini-planets if aired should be equal or lower than the background microwave temperature of 3K in order to preserve atmosphere indeffinitelly long. But this assumption is based only if we relly upon the gravity retention only. AS in the example with the Earth - it catches and holds the solar wind iones MAGNETICALLY up to planetary 5-6 diameters where the gravity is also ~1 % of the surface value. My idea is that with several superconductive mag-sails landed on surface to form planetary belts, or with very lightweight orbital rings system - magnetically active, or via huge surface magnets, specially designed mag-field can hold the atmosphere from escaping or constantly to re-enter it WITHOUT solid materials cover.
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