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Gravity Balloon retired working file

AlanSE May 16th, 2016 (edited) 156 Never
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  1.  *** Working Post List and Development ***
  2.  
  3. running set in 2016
  4. - movement of tubes relative to walls
  5. - angular momentum management for ball balloon frame construction
  6. - scaled experiments possibilities
  7.  
  8. new set for Jan 2015
  9. - construction from single sheet from Bowers article    posted
  10. - orientation of the rotating tubes             posted, might want to revisit
  11. - logistical throughway in middle (of tubes? what was I thinking here?)
  12.  
  13. running set from unknown time:
  14. - laminar versus turbulent      shelved
  15.                                         desired order
  16. - friction buffer pressure management       4   touched on
  17. - end seal of friction buffer placement     5   preliminary designs posted
  18.     - end current management
  19. - simple argument for friction buffers      1   finished
  20. friction buffer stability
  21. - comparisons for friction buffer stability     2   touched on
  22. - scaled experiments that would test stability  3   finished qualitative
  23.  
  24. - central technical challenges for gravity balloon  6   finished
  25.     Stability of balloon can't possibly be a show stopper
  26.     flow dividers much less established and more dubious
  27.     thermal issues might run into mild hangups
  28. - friction sheet design for stable operation        abandoned
  29.     if found to be completely unstable
  30.     if flexible sheets unstable
  31.  
  32. transit posts
  33. - computer code reference for GB        mostly stalled, started some on porting VB code for all subjects
  34. - comparisons of hierarchy
  35.  
  36.  
  37.     Topics contained in this file
  38.  
  39. Living in a mixed-gravity world -   pretty passionate, good math problems
  40.     rush hour in a space habitat
  41.  
  42. - natural circulation viability relative to population size     posted
  43. - heat transport in overall system              posted
  44.  
  45. Gravity Balloon Stability
  46. Small Bubble Perturbation Stability
  47. Use of 1 km scale Gravity Balloons  migrated
  48.  
  49. Reference values for space colonies
  50.     Eros
  51.     Phobos
  52.  
  53. Population argument for space-based living
  54.     1. Spacesteading is needed for the progress of humankind
  55.     2. Practicality of many people moving off-planet
  56.  
  57. news blurb for the newcomers    -   Space-faring humans could find the inside of asteroids the best habitat
  58.     Summary of all other topics
  59.     specific history of the idea
  60.  
  61.  
  62.  *** nothing currently written ***
  63.  
  64. Gases in Asteroids and Pressure Management          mostly have paper to go off of
  65.     drilling asteroids for gases
  66.     low movement, but high permeability or something
  67. The different "kinds" of pressure, and asteroids
  68.     addressed a little in access tunnel
  69.     still really big topic that will plague discussion
  70.  
  71. Stability segments  organization unclear    have really good writing, need  illustrations
  72.     Introduction, motivation, and organization of stability topics
  73.     small bubble stability
  74.         internal surface
  75.         external surface
  76.     surface pullback stability
  77.     rock / air mixing stability ?
  78.     small mode
  79.     large mode
  80.  
  81. Versus topics
  82.     - gravity balloon versus space stations
  83.     - gravity balloon versus Mars colonization
  84.     - life on Earth versus off of Earth
  85.  
  86. Place within history
  87.     Gravity balloon in the context of 20th century space
  88.         when will we start to use gravity for productive uses?
  89.     Long term population growth argument for Spacesteading
  90.         the term has bare Google results, so should write about
  91.  
  92. Balloon part        (internal)
  93.     equations of motion for things in the space
  94.     Citification in space
  95.  
  96. Artificial gravity tubes    (internal)
  97.     Cross-structures, but divide up arguments
  98.         would allow staged gravity by floor
  99.         needed for high density without reinforcing outside (covered somewhat)
  100.  
  101. birds in artificial gravity
  102.     what about birds in the gravity balloon itself?
  103.     could they survive? http://www.youtube.com/watch?v=w4sZ3qe6PiI
  104.  
  105. radiation of the gravity balloon
  106.     is there such thing as too little radiation?
  107.  
  108. Where the gravity balloon comes in space development
  109.     Time frame for building a gravity balloon
  110.     Spacesteading with gravity balloons
  111.  
  112. Derivative ideas-       Want to cover alternative proposals, of similar but not quite the same thing
  113.     Ridiculous kinematic designs -  spinning pressure against gravity
  114.     1 km class asteroids for radiation shielding -  Small gravity balloons
  115.     general asteroid scale and usefulness
  116.  
  117. Evolutionary technology track for development of asteroids
  118.     How do you drill an asteroid
  119.     Asteroid gas extraction - like oil wells
  120.  
  121. The problem of Nitrogen and (to a lesser extent) Hydrogen
  122.     A big block of Nitrogen proposal
  123.     Phobos low case for Nitrogen already figured out:
  124.     55,134,893.62 tons
  125.     would take on order ~ 50,000 launches
  126.  
  127. Energy Source and Heat Sink
  128.     Space nuclear power with PACER
  129.     Supercomputers and many other things enabled with large radiators
  130.         consider economics of capital versus extracted temperature
  131.  
  132. Orientation of space colonies
  133.     Exclusive with rotating to reduce pressure (would be nuclear model)
  134.  
  135.     Posted topics
  136.  
  137. finished posts up to 4/17/2013
  138. Candidate Bodies to use as a Gravity Balloon
  139. Turbulent Friction Buffers
  140. Good set of Bounds for Colebrook-White Numerical S...
  141. A Robust Method for Numerical Solution of the Cole...
  142. More on Friction Buffers
  143. How Far Can Light Travel in an Endless Atmosphere?...
  144. Gravity Balloon Pressure-Volume Curve and Rotation...
  145. Access Tunnel
  146. Introduction to the Gravity Balloon
  147.     added since that update
  148. best candidate objects for the gravity balloon:         wrote and posted separately already
  149. The curious world of artificial gravity:                migrated, broke off from other post
  150. Price of Floor Space in a Artificial Gravity Habitat:
  151. What would a giant space habitat look like?
  152. How Many Asteroids Would it take to House all of Humanity?
  153. Material stress management in oblate asteroids
  154.     1. Irregularity of asteroids by mass
  155.     2. Gravity balloons with irregular asteroids
  156.  - energy \ space habitat ultimate population limit
  157.  - physics and space questions
  158. posted end of 2014:
  159. Rockfill
  160. Transit overview
  161.  
  162. ************************************************************************************
  163.  
  164. ---------------------
  165.  
  166. title: make the overall case for the thing
  167.     want to get to the point as quick as possible, preferring 3rd one
  168.  
  169. Space-faring humans could find the inside of asteroids the best habitat
  170. The internal pressure of asteroids could be used for super large space stations
  171. Using asteroids to contain breathable air is our best option for space settlement
  172.  
  173.  
  174. Living anywhere other than on the surface of Earth for an indefinite amount of time is an idea far into the future, BUT, we have overestimated just how far out it is due to neglect of the inside of asteroids as a place to contain breathable air.  The pressure at the center of an asteroid scales with the square of its diameter which is a relationship that holds for the center of all planets too.  By selecting an asteroid with a size that gives a workable center pressure, you get a very large container for air.  By doing this with an asteroid (as opposed to going underground on a planet) you also have zero gravity, which has huge scaling benefit, as well as dramatically simplifying the structural design of the system.  This type of asteroid could be converted to a space settlement.  Once access to the center of the asteroid is established, the walls can be either excavated or simply "pushed" out to make it ultimately like a balloon, but one held together not by the tension of the wall, but the gravity of the walls, thus the "gravity balloon".  Here, I want to give a basic rundown of the idea and some context.
  175.  
  176.  
  177. Why this is better than the alternatives
  178.  
  179. Currently, our presence in low Earth orbit is extremely limited-stay.  Two ways lengthen the amount of time we can stay away from Earth include:
  180.  - Rotating space stations for artificial gravity
  181.  - Traveling to a new terrestrial environment, and setting up there
  182. Both of these have significant problems with radiation protection.  But that's solvable, going underground, and surrounding things with rock.  Put radiation aside, not a deal-breaker.  For both of these ideas, scalability is the deal-breaker.
  183.  
  184.  
  185. Where would this fit in the picture of space development
  186.  
  187. Probably on the 100s-of-years scale, but long before terraforming a planet is a reasonable option, which is closest to the million year scale as far as anyone can tell.  I outlined in a post the candidate objects for a gravity balloon in another post.  There are two possible objects in Mars orbit, and then many more starting with the inner edge of the asteroid belt.  It is a perfectly valid criticism that we are not near the capabilities to start drilling into asteroids today, but this applies to any form of space development or settlement.  We can send probes to the relevant objects today, but the next stumbling block is in-situ resource development.  If that is accomplished (or "when", not if), then the next major steps are artificial gravity and radiation protection.  These are needed to have semi-permanent stays, so that we can do the real heavy development of space.
  188.  
  189. My imagination
  190.  
  191.  
  192. Where did this idea come from
  193.  
  194. I came to this idea "organically" as I was contributing to Physics Stack Exchange.  You can read my original question.  This was the first I had ever thought of it, and I even tell how combined other ideas to get there.
  195. [link]
  196.  
  197. Do I know what I'm talking about?  I am very encouraging of discussion of the ideas here.  The core case for it, however, clearly seems strong enough for me to say that this is a notable absence in literature on space habitats.  That's why I made this blog!  I am getting a higher degree in engineering, although an (mostly) unrelated field.  It is my hope that my Physics SE contributions dispel any idea that the physical merit comes from a solid understanding.  Individual ideas are even cross-checked with other experts there, and you can even add some answers yourself!
  198.  - idea1
  199.  - idea2
  200.  - idea3
  201. This idea does not exist in a vacuum (figurative meaning) in the slightest, but it is entirely born and grown on the internet.
  202.  
  203. How did I become obsessed with this problem?  Actually, long ago I became obsessed with a different space-habitat problem.  It was that of a rotating self-bound torus.  Now, people even have videos of versions of this idea.  It certainly could exist, but over the years, I've become more in-tune with the remaining deal-breakers.  Ultimately, it's hard to argue it's better than the alternatives.
  204.  
  205.  
  206. Have other people had this idea?
  207.  
  208. Of course they have... or at least similar things.  The idea of settlement in the inside of asteroids is fairly common, although I have no far searched in vein for the pressure motivation.  I'm still not convinced that it has never been considered.  Among the educated, the pressure profile of the inside of an asteroid is a common discussion, and perfectly obvious from a physics perspective.  The idea of "inflating" an asteroid is pretty straightforward from there.  My conception of the friction buffers will probably be harder to find president for.  There are other variations, however.  You could use a lower density gas, and I wouldn't be surprised if someone went to this idea before the multiple concentric sheets I have described.
  209.  
  210. Major topics I've been addressing:
  211.  - The engineering argument for the habitat (covered in the introduction)
  212.  - Construction of an access tunnel between space and the inner volume
  213.  - Transport of light into and throughout the inner volume
  214.  - Energy and material requirements to address the fluid friction from rotation
  215.  - Closest objects in the solar system that could be used for a gravity balloon
  216.  - How a mixed gravity environment would be useful for settlement and commerce
  217.  - Stability of the construction
  218.  
  219. Central claims for a gravity balloon
  220.  - use the self-gravity of an asteroid to hold in air of a space colony excavated at its center
  221.  - build rotating structures for artificial gravity within that space, with open ends to the air
  222.  - surround this structure with concentric sheets that rotate at staged speeds to reduce friction
  223.  - concentrate sunlight into a mirror-lined tunnel to transport light inside
  224.  
  225. ------------
  226. Living in a mixed-gravity world
  227.  
  228. Rotating a space station to create artificial gravity creates an Earth-like environment, but the fixation on imitating Earth has limited the possibilities we've envisioned.  Imagine you've built a 100,000 population habitat.  Then what?  On Earth, cities are not static.  There's no modular way to expand rotating habitats.  Let's say that you built a habitat next to it.  Okay, now you need a spaceship to travel between them.  What kind of demand do you expect for this travel?  What about when you have 100s or 1000s of these habitats at the L2 point or something along those lines.  How many airlocks are you going to have?  Will all incoming ships enter at the axis of rotation?  As in the famous 2001 scene?  
  229. http://www.youtube.com/watch?v=q3oHmVhviO8
  230. They can't.  Once you get above a certain (small) volume you can't continue that anymore.  Not to mention, the desire to make larger habitats conflicts with the need for efficient transportation from one habitat to the next.  No matter how large you make the habitat, you only have one axis of rotation.  To engineer an access point not on the axis of rotation, you may need some fancy space maneuvers.  But if you do that, what about the propellant availability?  You might be building a weak atmosphere in your neighborhood if you have too much volume, and there are things that could cause to go wrong with that.
  231.  
  232.  
  233. Only Access to Gravity is Important
  234.  
  235. People don't want a gravity environment, they want ACCESS to a gravity environment.  In fact, there's nothing wrong with zero gravity, even encountered on a periodic basis.  It presents no ill effect on human health because preservation of bone mass through resistance is nothing urgent.  The human body loves to take breaks from gravity.  Swimming and sleeping have always been part of human existence.  If quick access to zero gravity was possible, that would also become part of human existence.  The anime series PlanetES painted a vision of this rather well.  In that world there are many rotating space stations in low Earth orbit where people work.  The cost of launching staff into space is very high, therefore extremely prolonged stays are necessary, therefore artificial gravity is necessary.  Still, they don't sleep in the presence of artificial gravity.  Why would they?  On any excursions, they go right back to zero gravity.  The vision of PlanetES is very much a no-frills business-oriented world.
  236. http://omohide.com/2876/planetes-review-2/
  237.  
  238. [images of space station 7]
  239.  
  240. The visions of O'Neil and others have given a nod to the concept.
  241. http://en.wikipedia.org/wiki/Gerard_K._O%27Neill
  242. There exists the concept of a staged gravity world, where standing in different locations gives you a different weight.  Also, making this ramp lead up to the transfer area to zero gravity parts makes sense.  However, if you look at some visions, it's a little bit of a difficult case to make.  Particularly for the designs mirrored in the Gundam series.
  243. http://en.wikipedia.org/wiki/File:Spacecolony1.jpg
  244. There just isn't much of a provision for rapid transport back and fourth between gravity, zero gravity, and to space.  It makes some sense to think that people would want to spend more and more time in a gravity environment as the infrastructure and means to do this improved.  But then again, this might be hubris on our part in a sense.  Maybe people will eventually find gravity boring.
  245.  
  246. The gravity balloon allows for relatively fast transfers between zero gravity and rotating tubes, although the friction buffers still present complications.  An important difference between rotating something in-atmosphere versus in space is that in-atmosphere is virtually failsafe.  There are no leaks that can cascade and kill every inhabitant.  The gravity balloon envelope itself would leak very slowly and unspectacularly.  Even if a rotating tube was completely destroyed, a 500 m diameter tube only rotates at around the terminal velocity on Earth.  If there was sufficient space between structures it would slow down such that collisions were gentle bumps.
  247.  
  248. There are still unique considerations for a practically endless zero-gravity environment.  You wouldn't want to get stuck floating in the middle of it.  Of course you can also build up enough speed to hurt yourself in a number of ways.  One of the things I would worry most about, actually, is the problem of completely stagnant air, which is something we already have to deal with in Earth orbiting space stations.  Ironically, a pretty good solution to maintain air movement and filtration is to use centrifuges, and the artificial gravity tubes might do just fine.  Just like any HVAC system, the global movement of air would have to be given consideration, and this river of air could even be used for transport of things over large time frames.
  249.  
  250. Travel to and from places in a massive weightless atmosphere is a major theme in the Sun of Sun book series.
  251. http://www.kschroeder.com/my-books/sun-of-suns
  252. I've bought the books and I hope to give a rundown of what is good from a physics perspective.  The amazement, however, is unmistakable.  Being in a tiny space station is one thing, but much larger environments would be a different feel entirely.  Even extremely light equipment would allow you to fly around with a feeling probably closer to sailing or swimming than flying.
  253.  
  254.  
  255. Movement in Open Zero Gravity
  256.  
  257. For objects of any considerable size moving at any considerable speed, the drag scales with the square of velocity fairly universally.
  258.  
  259.  
  260. The Industrial Use of Zero Gravity
  261.  
  262.  
  263. The Value of a Mixed Environment
  264.  
  265.  
  266.  -- rush hour in a space habitat --
  267.  
  268. (would like pdf of distances traveled)
  269. Could deliver pizza from tube to tube.
  270.  
  271. -------------
  272. Gravity Balloon Stability
  273.  
  274.  
  275. We're not finished yet, because we need to think harder about what kind of dynamics would push for the collapse of a gravitational balloon.
  276.  
  277. I want to start with a space-engineering case that often comes up which bears a good deal of resemblance to the gravity balloon - the proposal to keep air on-world by draping a sheet over the atmosphere.  You could imagine this applied to Mars, although it's not necessary and most terraforming proposals don't call for it.  Its atmosphere would be leaked on the scale of millions of years.  The moon might be a better example, as the atmosphere would quickly fly off.  It's thinkable (from a physics perspective) that you could manufacture a giant sheet in the shape of a sphere.
  278.  
  279. Perhaps you would start with the sheet resting on the ground.  Then you would start adding air beneath the sheet.  Initially, the air will go where ever you push it (with the surface taught), just like we are familiar with on Earth.  It behaves this way because there is no density gradient.  This would be the same as if you inflated a balloon around a basketball.  The basketball can bounce around, it doesn't care what side it's on.  The sheet becomes a sphere quickly since there is no pressure on the other side, just space.  As a tangent, this reminds me of the game with the parachute I played in gym class as a kid.
  280. http://en.wikipedia.org/wiki/Playground_parachute
  281.  
  282. Ah, but the moon is not a basketball, it has gravity, so it affects the equilibrium location of the sheet.  If you imagine a pressure differential throughout the gas,  the moon will want to come to rest in the exact center of the balloon.  That will be absolutely true if the membrane has negligible mass.  You would want the membrane to have significant mass-thickness because honestly, its radius of curvature is so low that it would be difficult to make it strong enough to hold in any significant amount of pressure by its material strength alone.  The membrane would exert no net gravitational force on the moon regardless of how heavy it was, because it is spherically symmetric and the moon is on the inside.  That means that the pressure dynamics would dictate its resting location and the moon would rest in the center, assuming the sheet doesn't move.  However, that's a bad assumption.  The sheet would move if the atmosphere pressure was exactly supporting the gravity of the sheet.  Think about it, if upward force from pressure exactly equals downward force from gravity, any nudge can move it as if there is no gravity.  Because of this, real stability can only be accomplished through either material strength, or additional methods.
  283.  
  284. As you continue to think about it, it becomes apparent that it's really quite hard to accomplish the goal of keeping the atmosphere contained without invoking massive material strength.  My favorite work-around is to imagine sandbags on a string like an anchor.  The sandbags would rest on the ground most of the time, and would be connected to the membrane by means of a rope that spanned the entire height of the atmosphere.  This would be stable, but it would also require material strength.  Thankfully, however, it doesn't have the problem of a gigantic radius of curvature.  It would mirror the fundamental hard-to-break PV relationship I mentioned in the introduction post, where the volume in this case is the volume of the atmosphere.  That's still a lot better than the volume of the planet.  Plus, the tug you need (tension) in the wire is only just enough to have stability and weather the periodic fluctuations in atmosphere pressure.  So from a mechanics perspective this would still be "cheaper" than the alternative of just building rigid structures because gravity helps.
  285.  
  286. So far there is one assumption that I will need to break, which is that the mass in the sheet is "tied" to its location in the sheet.  Imagine that we have an infinitely thin sheet held up by pressure, and then throw a bunch of balls on the top.  The balls clump.  This is the behavior you see in a water bed.  When you put objects on a water bed, those objects pull each other closer as if they have "gravity".  In reality this is a form of instability, and a relevant one to the present picture.  If the mass distribution won't obey you, then that can be a problem.  If part of the sheet starts to sag, then if the mass on top of the sheet isn't nailed down, it will follow the sag and lead to failure.
  287.  
  288.  
  289. Raleigh-Taylor Instability
  290.  
  291. The topic of a balloon around a large gravitational body seaways into the issue of the Raleigh-Raylor instability, which is a local concern which can grow to be bigger.  I continued to reference a membrane, but in the extreme, you can imagine no membrane, and the surface holding the pressure in being simply a liquid.  This is intuitively unstable to us all, and it illustrates the concept of differentiation.  The gravity balloon is a proposal that works against differentiation, but we need to get detailed about what kinds of ways you can do this.  The above method creates a "hard" Raleigh-Taylor instability.  Movement leads to a first-order force.  Once the matter moves, other matter immediately wants to move in to take its place.  To get to that, I had to assume some large source of gravity at the center - the planet, and this is how the gravity balloon is different.
  292.  
  293. http://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/HD-Rayleigh-Taylor.gif/400px-HD-Rayleigh-Taylor.gif
  294. [conventional Rayleigh-Taylor instability]
  295. http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Taylor_instability
  296.  
  297. For the gravity balloon, the idea of "working against differentiation" means something different.  At the inner wall, there should be almost no gravitational field.  Actually, there is a field from the air inside, but this is easy to calculate and is almost always extremely small due to the fact that air is around 1000 times less dense than the asteroid rock.  Provided that we assume that there is a clear boundary between the rock and the air, the structure is extremely stable in this local sense.  To explain this further, I will use some illustrations.  On the inner wall of a gravity balloon, the gravitational field only starts growing at the onset of the wall, moving outward.  This is as opposed to the first example in this post, and the conditions under which the Raleigh-Taylor instability is usually formulated.
  298.  
  299. [gravity balloon field]
  300. [other example]
  301.  
  302. In the real world, however, there isn't necessarily a clear dividing line between the solid rock and the air.  To have a truly stable location situation, the field would have to be pronounced in the opposite direction, and clearly that's no the case.  For instance, imagine a rock on the edge of the gravity balloon.  This rock was supposed to be part of the wall, but on the inside of the wall is zero gravity.  If it is chipped off, it has no motivation to hang around the wall, it will just float around.  It takes nothing more than a gentle blow to keep it there (even if it weighs tons), but it doesn't necessarily have this force.  Thus, we conclude that there has to be something to keep the mixing from happening.
  303.  
  304. Actually, this topic ultimately comes down to a much more harry detail of the real world - rock permeability.  You just can't say that there is rock and then air.  Whatever kind of rock structure you have contains an internal pressure to itself.  In essence, gas permeates the rock.  This is true before you ever drill into an asteroid, and its something that has to be studied and dealt with.  What's worse, the existing asteroid almost certainly has a form of gas permeating its rock, but it's probably not the type of gas you want.  In fact, it necessarily isn't because it's not Oxygen.  That means that, at minimum, your wall boundary has to keep gases from mixing.  If the pressure of the gases were the same, that's not difficult or expensive.  In the real world, however, you would need some differential pressure between the regions - that being the bulk gas on the inside and the rock permeating gas on the other side.
  305.  
  306.  
  307. Conclusions - the Known Unknown
  308.  
  309. We have at least some sense, and I think a pretty decent sense, that we know what we don't know when it comes to the gravitational balloon.  The biggest challenges in terms of the structure engineering and basic excavating are not unknown unknowns, but quantifiable unknowns.  If this was actually going to happen, it's very obvious that we would want to know properties of the asteroid:
  310.  
  311.  - The clump size and tumbling behavior, if it's not globally rigid
  312.  - The rock permeability
  313.  - The gaseous composition deep within
  314.  
  315. There have already been studies that come up to the doorstep of these concepts.  For instance, the subject of asteroid outgassing is directly a product of the permeability and the gas content. [reference]  Generally we have a sense that these items differ among asteroids.
  316.  
  317. The rest of the unknowns can't get much clarity until you start discussing the actual method you're going to employ to make a gravity balloon.  As I mentioned briefly before, you could move material from the inside to the outside either by mining inside and throwing the pieces out the airlock.  Alternatively, you could just add more gas to the interior (you would never think of doing this if the entire asteroid was a rigid structure).  For this method, there would need to be a lot of push-and-pull between design of the excavation method and acquisition of knowledge about the target.  There very little known about how an asteroid reorganization would take place through a direct push from the center, but it would involve the concepts discussed here.  Reorganization of the material would increase gas mobility, and probably cause a huge amount of outgassing, which would then decrease the pressure of rock-permeable gas on the other side of your wall boundary, which would then affect what materials you could use for the gas boundary.  How you would deal with the asteroid inflation as the inner wall surface area increased is also thoroughly unknown.  I have my speculations, of course.
  318.  
  319. ----------------------------------
  320. Small Bubble Perturbation Stability
  321. Small Bubble Stability
  322. Global Stability Requirement
  323. Small Station Stability
  324. Small Balloon Stability
  325. Stability against Bubble Movement
  326.  
  327. In a simplistic sense, we can imagine the asteroid rock behaving like a fluid.  As we know from literal pictures of 10km-scale asteroids, this is just simply not a good assumption, but it could be pretty good for rubble piles and other similar things.  Even if it's not a real fluid, it will probably exhibit tumbling behavior.  That is, once the gravitational fields produce a "slope" beyond a certain degree then the asteroid rock has a propensity to tumble just like sand.  The problem of stability is a multifaceted problem, and there are many ways to propose to perturb the structure that could lead to collapse.  I will get into those specifics later, but for this post I will formally address a very specific perturbation.
  328.  
  329. Let's imagine that the inner sphere of air is no longer at the direct center of the asteroid, and it is offset some amount.  As already discussed, there are properties of the inner surface that we can't known without specific design information, and these would be relevant.  It needs to be considered how such a displacement of the inner volume would affect the inner wall stability, as well as material movement on the surface of the asteroid.  The inner surface would be affected by creating a non-zero gravitational field on the wall, which invalidates some of what has already been said about the "weak" form of the Rayleigh-Taylor instability.  The inner and outer surfaces are no longer equipotential in this circumstance.
  330.  
  331. [global instability illustration]
  332.  
  333.  
  334. Tumbling Angle
  335.  
  336. Fig. 2 in this paper gives a frequency distribution of the slopes of the surface of Lutetia
  337. http://www.sciencedirect.com/science/article/pii/S003206331100300X
  338.  
  339. It's also helpful that it gives the slope of repose for
  340.  - sand
  341.  - talus (or scree)
  342. http://en.wikipedia.org/wiki/Scree
  343.  
  344.  
  345. Outer Surface Redistribution
  346.  
  347. If you mentally model the outer surface as a fluid, it will want to correct the deviation from equipotential.  That will cause it to move material away from the "shallow" side and toward the "deep" side, exasperating the effect further, demonstrating a true instability.  As far as I can tell, this general nature of instability would necessarily require active control.  Thankfully, the control may only need to be exercised extremely infrequently and could be done by a rover very slowly dragging a big boulder from one side of the surface to the other.
  348.  
  349. ------------------------
  350. Gases in Asteroids and Pressure Management
  351.  
  352. Some relevant concepts:
  353.  
  354.  - Sorption: as in the absorption of a liquid into a rock, for instance
  355.  
  356. from
  357. http://forum.nasaspaceflight.com/index.php?topic=28768.240
  358. bottom line is that NEAs have mostly lost water through sublimation due to the temperatures.
  359.  
  360.  
  361. -----------------
  362. Population argument for space-based living
  363. Spacesteading is needed for human progress and Earth
  364. Gravity balloons are needed for humanity's long term future
  365.  
  366. Could break up into two
  367.     1. Spacesteading is needed for the progress of humankind
  368.     2. Practicality of many people moving off-planet
  369.  
  370.  
  371. The Earth had 300 million people in the year 1,000.  This context is generally missing when looking at history.  Particularly, it makes a difference when considering what a society was capable of.  The building of the great pyramids sounds a lot more impressive when you consider that the population of the entire world was only around 7 million people, a minuscule 0.1% of the population today.
  372. http://en.wikipedia.org/wiki/World_population_estimates
  373.  
  374. Contextualized that way, a lot of things start to make more sense.  Technological and societal progress accelerated an a previously unknown rate in the 18th and 19th centuries, and this is obviously a consequence of there being more people.  It is less obvious how the population was sustained in the first place, and why that boom did not happen earlier.  the history of human civilization is a dance between population and technology.  A semiconductor manufacturing plant would be incomprehensible in scale to a businessman of the 19th century.  A large fraction of our economy consists of projects that would have been flagrantly impossible in the ancient world, due to the organizational constraints alone!  Once you consider the broader economic interconnections with other businesses in the supply chain, basically everything about modern life would be possible with the smaller human population of the ancient world.
  375.  
  376. In those prior 1,000 years, population increased by a factor of 23.  That means that for every one person who was alive 1,000 years ago, 23 are alive today.  If that trend were to continue until year 3,000, there will be 163 billion.  Estimates of carrying capacity of Earth vary, this is clearly beyond that.  If you apply the factor one more time, you find an estimate of Earth's population in the year 4,000 to be 3.8 trillion people.
  377.  
  378. But how realistic is that?  After all, low birth rates that come with better education are a hallmark of the modern developed world.  So there's probably little desire for humans to reproduce at that rate anyway - but there's a flaw in this logic.  If a generation is 30 years, that's 33 generations over 1,000 years.  The equation for the multiplication factor is a straightforward exponential.
  379.  
  380. (birth rate)^(generations) = factor
  381. \left( \text{birth rate} \right)^{ \left( \text{generations} \right) } = \left( \text{multiplication factor} \right)
  382. http://quicklatex.com/cache3/ql_22501753b969bc6311f80d7c7e401eff_l3.png
  383.  
  384. This reproduction rate I used here somewhat of an abused version of corrected birth rate.  You have to correct birth rate for mortality and sex ratio, which still apply regardless of how advanced a society is.  Scientifically, we have a term for the birth rate which yields a constant population - replacement rate.  If you look at the relevant literature, you find the following equation for this:
  385.  
  386. http://en.wikipedia.org/wiki/Total_fertility_rate#Replacement_rates
  387. http://link.springer.com/article/10.1023%2FB%3APOPU.0000020882.29684.8e
  388.  
  389. TFR_R \approx. (1 + SRB) / p(A_M)
  390. http://quicklatex.com/cache3/ql_64f0b6b55055398dd8e7e2e5d262ae99_l3.png
  391.  
  392. TFR_R -     replacement value for total fertility rate, which is about 2.09 for developed nations
  393. p(A_M) -    probability of surviving to the mean age of fertility schedule, about 98% for developed nations
  394. SRB -       sex ratio at birth, about 1.05 for humans
  395.  
  396. I'm not interested in only constant population, but a geometrically increasing population.  I would like to find the birth rate that gives the multiplication factor I referenced.  The functional replacement rate I used earlier will functionally be the fertility rate divided by the replacement fertility rate.  Using this logic and combining the two previous equations we get:
  397.  
  398. \left( \text{multiplication factor} \right)= \left( \frac{TFR}{TFR_R} \right)^{\left(\text{generations}\right)} = \left( TFR  \frac{ p(A_M)}{(1 + SRB)}  \right)^{\left(\text{generations}\right)}
  399. http://quicklatex.com/cache3/ql_d18dd0a101d138469906b25dafa2913a_l3.png
  400.  
  401. I've already given all the numbers for this assuming a developed nation, so with some rearranging we can find a direct formula for the birth rate (TBR) necessary to continue the population growth rate for 1,000 years that I talked about.
  402.  
  403. TRF = \frac{ ( 1 + SRB ) }{ p(A_M)}  \left( \text{multiplication factor} \right)^{\frac{1}{\left( \text{generations} \right) } } = \frac{1+1.05}{0.98 } \left( 23 \right)^{\frac{30 }{1000 } } \approx 2.3
  404. (1+1.05)/(.98)*(7/.3)^(30/1000)
  405. http://quicklatex.com/cache3/ql_c10f376413f12e6e1928fd2a0d8799e8_l3.png
  406.  
  407. This number, which will skyrocket the human population to the 100s of billions of people is 2.3, which is actually only slightly higher than the raw replacement rate of 2.09.  That leads to a population growth rate of 0.5%, as opposed to 0.0%.  This is the compounding returns.  Only a slight deviation from replacement rate will turn society into something completely unrecognizable in a reasonable amount of time, an amount of time that is actually small compared to the length of time over which humans have had written records.
  408.  
  409. TFR_R:
  410. Europe          2.097
  411. More developed regions  2.091
  412. North America       2.085
  413.  
  414. current fertility rates
  415. Argentina   2.25
  416. Mexico      2.21
  417. Costa Rica  2.10
  418. Utah        2.449
  419. 15 states have over 2
  420. 4 states have over 2.2
  421.  
  422.  
  423. There are several advocacy groups for moving humans into space.
  424.  
  425. http://ssi.org/
  426. http://100yss.org/
  427. http://www.nss.org/ National Space Society, formerly L5 Society
  428. http://mars-one.com/en
  429. http://en.wikipedia.org/wiki/Mars_to_Stay
  430.  
  431.  
  432. Other people have made the population argument before.  It was predicted that the population of Earth could near 16 billion by 2050, and that space could then be an immediate relief to this pressure.  Then the ratio of population in space to the population on Earth was envisioned as diverging to an incredible multiple.
  433. http://mike-combs.com/space/TCoS.html
  434.  
  435.  
  436. What would happen to Earth?  Re-wilding.
  437.  
  438. as per Geoge Monbiot
  439. http://www.monbiot.com/2013/05/24/feral-searching-for-enchantment-on-the-frontiers-of-rewilding/
  440. http://www.monbiot.com/2013/06/04/rewilding-made-simple/
  441.  
  442.  
  443.  -- Practicality of moving lots of people into space physically --
  444.  
  445. Let me describe a simple calculation that is surprisingly compelling.  Take the mass of the Soyuz command module and divide by the number of passengers.  Now you have the mass per astronaut needed to get people into low Earth orbit.  Now, take the mass of the payload that a large rocket can deliver to Low Earth Orbit (LEO).  This can be the Apollo rocket family, or it could be the SpaceX Falcon Heavy rocket.  Divide that mass by the mass per astronaut to get a human into LEO.  That gives a number in terms of astronauts.  It gives the number of astronauts that a large rocket could send into LEO with present-day technology.
  446. http://en.wikipedia.org/wiki/Soyuz-TMA
  447. Soyuz-TMA   5,000 kg        1,666 kg/person
  448. Falcon Heavy    53,000 kg to LEO    32 people
  449. Saturn V    120,000 kg to LEO   72 people
  450.  
  451. I read about this proposal from a group advocating for reuse of shuttle external tanks.  Their logic was that 100 people could be ferried up to an orbital station.  Now that's an incredible thought.  We have commonly taken people up in groups of 3 or 7.  We have not even begun to seek the economies of scale that come with building transferring vehicles with a large human capacity.  In this context, the idea of putting 100,000 people on Mars starts to sound a lot less crazy.  Even if you imagine that we only take up 50 at a time, which is entirely possible with the reusable Falcon Heavy, that will be 2,000 seperate launches.  That's a lot of launches, but if we're using reusable rocketry hardware that can be flown once every day (again, which is a possible future), then we're left with putting up nearly 20,000 people into space each day.
  452. http://www.astronautix.com/craft/stsation.htm
  453. http://news.bbc.co.uk/2/hi/science/nature/293366.stm
  454.  
  455. -- start xkcd --
  456. xkcd has entertained this topic, with the hilarious title of "Everybody Out".  There is, however, a glaring error with the method used there.  It was assumed that chemical rockets would lift the people from the surface of the Earth to a speed that puts them beyond the gravity well.  This is what's needed to escape Earth's gravity, but we're not confined to doing it with chemical propellant.  We're also not confined to lifting those propellants from the surface of Earth.
  457. http://what-if.xkcd.com/7/
  458.  
  459. In fact, if your destination is something like Eros, it would be much more preferable to bring the propellant from the desination, instead of the starting point.  Even if that's not appealing, it's still possible to lift from LEO to further in the solar system using more efficient engines.  One option is a simple ion drive that's powered by the sun's light.  This would take a longer time, but the equipment could also be reused fairly consistently.  Another option is to use nuclear propulsion in a way that's less dramatic than the oft-cited Orion.
  460. -- end xkcd --
  461.  
  462. Launch costs are high, but a streamlined process isn't as crazy as we might think.  Current thinking is that the Falcon Heavy could lift 53 metric tons to space at a cost of $83 to $128 million.  If you use the Soyuz number above, that comes out to $2.5 million per individual sent to Low Earth Orbit.
  463. http://www.spacex.com/falcon_heavy.php
  464.  
  465.  
  466. Interstellar Travel is Unhelpful
  467.  
  468. at speed of current Voyager spacecraft: 62,136 km/hr
  469. Alpha Centauri is 4.3 ly    -> would take 74,000 years to get there
  470. http://www.universetoday.com/15403/how-long-would-it-take-to-travel-to-the-nearest-star/
  471. best case scenario is 85 years
  472.  
  473. http://en.wikipedia.org/wiki/Planetary_chauvinism
  474. http://www.quora.com/Mars-planet/Is-Mars-worth-mining-for-Earth-purposes
  475. Most of Earth's human population is suffering from what G. O'Neill called planetary chauvinism
  476.  
  477. http://spacefrontier.org/
  478.     "The Space Frontier Foundation is an organization of people dedicated to opening the Space Frontier to human settlement as rapidly as possible."
  479.     "Our goals include protecting the Earth’s fragile biosphere and creating a freer and more prosperous life for each generation by using the unlimited energy and material resources of space."
  480.     "Our purpose is to unleash the power of free enterprise and lead a united humanity permanently into the Solar System."
  481.  
  482. ----------------------
  483. Eros colony
  484.  
  485. http://answers.yahoo.com/question/index?qid=1006050210699
  486.  
  487. "At least 1.2 acres per person is required in order to maintain current American dietary standards."
  488. 1 acre:     sqrt(4 046.86 (m^2)) = 63.6149354 meters
  489. 1.2 acres:  sqrt(1.2 * 4 046.86 (m^2)) = 69.6866702 meters
  490.  
  491. will have 0.6 acres per person in 2050
  492. http://dieoff.org/page40.htm
  493.  
  494.  
  495.  -- farmland requirement for specific crops --
  496.  
  497. http://www.localharvest.org/blog/15945/entry/calories_per_acre_with_apples
  498. At half a bin, or 500 pounds per tree and with 200 trees per acre, the calorie
  499. value of commercial apple production jumps to 100,000 pounds per acre, or 23.6 million calories per acre
  500.  
  501. http://www.waldeneffect.org/blog/Calories_per_acre_for_various_foods/
  502. potatoes are 17.8 million calories per acre
  503.  
  504. http://answers.yahoo.com/question/index?qid=20071028131143AAiPmqb
  505. believes 1/8th of an acre per person
  506.  
  507. (1 calorie / acre) / (2000 calories/person-day) / (365 days/year)
  508.     -> c/a / (2000*365) gives (people/acre)
  509.  
  510. crop        calories/acre   people/acre
  511. potatoes    17.8e6      24.4
  512. apples (high)   23.6e6      32.3
  513. other source            8
  514. NSS             31.25
  515. NSS2    1000 lbs
  516. NSS3    15400
  517.  
  518. also have NSS source on farming
  519. http://www.nss.org/settlement/ColoniesInSpace/colonies_chap09.html
  520. crop    state   bushels tons
  521. wheat   Kansas  65  1-3/4
  522. corn    Iowa    140 3-12
  523. International Rice Institute    Philippines 16 tons
  524.  
  525. This higher yield was obtained by a longer growing season and higher rainfall.
  526. 320 acres for 10,000 people
  527. 100 acres for 10,000 people, more optimistically
  528.  
  529.  
  530. me: imagine a lower gravity case for farming.
  531. a = omega^2 r   -> omega = sqrt( a / r) -> omega = 0.198 Hz -> 1.89 rpm
  532. so, standard velocity for Earth gravity is 49.5 m/s
  533. for half gravity you get 24.74 m/s = 55.36 mph
  534. so it might be better to lower it even further
  535.  
  536. my previous requirement found (63 m)^3 for each person.
  537.  
  538.  
  539.  -- floor space for non-farm activities --
  540.  
  541. floor space needed per person for non-farm activities:
  542. http://www.engineeringtoolbox.com/number-persons-buildings-d_118.html
  543. 18.5 to 55.8 m^2 per person residential
  544.     still only about 1.3% of an acre at most
  545.  
  546. alternative approach:   city population density
  547. http://en.wikipedia.org/wiki/List_of_United_States_cities_by_population
  548. for high-density >100k person city
  549. ((1 mile)^2) / 10 000 = 258.998811 m^2 per person
  550.     = 6.4% of an acre
  551.  
  552. Another reference on population density and N2 concentration from NSS
  553. http://www.nss.org/settlement/nasa/75SummerStudy/Chapt3.html#Atmosphere
  554.  
  555. for the 1/8th of acre farming claim = 12.5% of an acre
  556.  
  557. use     m^2 m   acre
  558. apartment   55.8    7.5 1.3%
  559. >100k city  259.0   16.1    6.4%
  560. NSS minimum 40.0    10.0
  561. NSS agriculture 20
  562. farming case    505.9   22.5    12.5%
  563.  
  564.  
  565. could add those up for about 20%, or about 5 people per acre
  566. less generous would be 10%
  567. 12.5+6.4 = 18.9
  568.  
  569.  
  570. from post on inflatability
  571. Object      M (kg)  rho (kg/m3) R inner (km)    V (km3)
  572. Phobos      1.07E+16    1876    4.74        447
  573. 433 Eros    6.69E+15    2670    4.33        340
  574.  
  575. from post on abundance
  576.             ISS     Geometric Mean  Earth
  577. V (km3) per person  0.0000001   0.000237847 0.565714286
  578. V (km3) for all humans  700     1.7E+06     4.0E+09
  579. Side length (m)     4.6     62.0        827.1
  580.  
  581.  
  582. Eros comes out to   340/0.0017 =    200,000
  583.  
  584. then consider the land use requirements:
  585.     -> at 1/5 acre per person, that comes to 40,000 acres
  586.     -> 161.9 km^2
  587.     -> calculate tube length for diameter of 500 m = 103 km
  588.     -> 340^(1/3) = about 7.0 km on one side
  589.     -> 103/7 = 14.8 tubes within a cross section
  590.     -> 7^2 = 49 km^2 for total cross section
  591.     -> 49/14.8 = 3.3 km^2 cross section for one tube
  592.     -> sqrt(3.3) = 1.8 km^2 side-length of single lattice
  593.         compared to 0.5 km tube diameter
  594.         area ratio is 13 to 1
  595.  
  596. Eros dimensions:    34.4 × 11.2 × 11.2 km
  597.  
  598. 4.33x2 = 8.66 km diameter   ->  8.66/11.2 = 77% of its waist
  599.                     25% of its length
  600. total volume:   2.505618e+12 m^3 = 2,505 km^3
  601. inner volume:   340 km^3
  602. inflated vol:   2845 km^3
  603. uninflated radius:  5.6 km
  604. inflated radius:    8.8 km
  605.             ...which still falls short of length, only 50%
  606.  
  607.  -- reflector requirements --
  608.  
  609. Use the farmland area as the demand for sunlight.  That is 1/8th acre per person.
  610. population  area        area (km^2) diameter (km)   tube D (m)
  611. 1,000                       0.8
  612. 10,000      1,250               2.5     11.8
  613. 20,000      2,500 acres 10.1        3.6     16.68
  614. 200,000     25,000      101.        11.3        52.8
  615. 1 million   125,000 acres   505.8       25.4        118.
  616. sqrt((20000/8 acres)/Pi)*2
  617.  
  618. Will increase if corrected for distance from the sun.  Eros is at 1.78 AU.  Maximum sunlight concentration is
  619. ((radius of the sun)/(1 AU))^2  = 0.00002161441
  620.  
  621. Can compare the diameter of the overall collector versus the mirror area needed to line the tube.  The radius in both cases is sqrt(A/Pi).  So divide these, consider that the area is corrected by the sunlight concentration factor.  Also consider the length of the tube is l, which is on the order of 10 km.
  622. 2 Pi r_i l / Pi r^2     = 2 sqrt(f) ( l / r )
  623. sqrt(f) = 0.0046
  624.  
  625. This means that the collector reflector will be of comparable area to the tube mirrors when we hit the point that this equals 1, where l is 10 km.  Then take 2 sqrt(f) times 10 km to get 0.092 km, or 92 meters.  This means that the tube mirrors would be a small cost compared to the overall collector even with a population of around 1,000 people.
  626.  
  627. ----------------------------
  628. Energy cost of excavating an asteroid
  629.  
  630. A logical opposition to the idea of a gravity balloon is that moving the (fairly dense) rock out of the center and onto the perhiphary or into the outer fractures would take energy.  The statement is self-obvious, so the real question is "how much?"  It turns out, you'll get the same answer as if you just did a simple pressure over volume integral.  For the sake of completeness, I want to cover that with a little bit of rigor here.  So the two methods used to approach the problem are:
  631.  
  632.  - integrate the pressure of the center cavity from zero volume to final volume
  633.  - subtract the gravitational binding energy of the initial state from the final state
  634.  
  635. -------------------
  636. Space Settlement material constraints of different types
  637.  
  638. NSS Journal's
  639. Paths to Space Settlement
  640. http://www.nss.org/settlement/journal/NSSJOURNAL_PathsToSpaceSettlement_2012.pdf
  641.  
  642. This publication mentioned a number that caught my eye, because it was quite similar to numbers I was publishing myself.
  643.  
  644. "Asteroidal resources are easily sufficient for orbital settlements with a total livable surface area from 100-1000 times the surface area of Earth"
  645.  
  646. There are a lot of issues with assumptions baked into this number.  Since it's a simple statement of surface area, it's easier to actually just back-calculate what they're assuming for the amount of mass available.  In previous posts, I've habitually assumed 10 meters of water equivelent thickness for shielding material, but this assumption will vary by source.  After all, the logic is that 10 meters will buy you shielding equally as good as Earth's atmosphere, and there's no real good reason for that requirement.  After all, Earth's atmosphere isn't the same everywhere, and different altitudes will see variations of 20-40% easily, even constraining the discussion to large population centers.  So it becomes a question of your acceptable tolerance for radiation, and the answer will probably tend to within the range of 2 to 8 meters.
  647.  
  648. I'll use 5 meters.  This is really saying 5 tons per square meter.  The surface area of Earth is trivial to find, multiply that by the proposed ratios in the quote:
  649.  
  650.  - 100x ->  5.112e16 m^2    ->  2.319e20 kg
  651.  - 1000x ->     5.112e17 m^2    ->  2.319e21 kg
  652.  
  653. These are not small values.  You'll have to travel quite some distance to find a single asteroid with this much mass.
  654.  
  655. asteroids close to 2.3e20 kg    mass (kg)   rank
  656. Pallas  2.11E+20    2
  657. Vesta   2.60E+20    3
  658.  
  659. asteroids close to 2.3e19 kg    mass (kg)   rank
  660. Davida  3.84E+19    7
  661. Sylvia  1.47E+19    8
  662.  
  663. In neither case does the target asteroid fall off the top 10 list.  You might ask the question of how much it would take to produce only 1 Earth equivalent of space, and that would be 2.3e18, of course.  This is still quite notably larger than Eros or Phobos.  You would still have no choice but to make the trek to the asteroid belt if this is your requirement.
  664. https://en.wikipedia.org/wiki/433_Eros
  665.  
  666. Naturally, that's a fairly meaningless requirement.  The mass in our solar system is very unequally distributed among different bodies.  If we assumed we had the capability and will, we could fill the inner solar system with settlements made of materials from our own moon.  With a mass of 7.3e22 kg, the idea of material scarcity is far from relevant.
  667.  
  668. -----------------
  669. The design space between caves and gravity balloons
  670.  
  671. Caves are attractive for space colonies, particularly for relatively near-term manned bases.  Any time you start to talk about a permanent colony, underground habitats start to become very relevant very fast.  This would be particularly true for something like Mars One, where people would stay indefinitely.  A lifelong stay would bump up against the radiation limits we could responsibly expose people to, so it makes all the more sense to put more material above the people.
  672.  
  673. Objects to consider:
  674.  - Earth
  675.  - Mars (?)
  676.  - The moon
  677.  - Ceres
  678.  - Vesta
  679.  
  680. --------------
  681. The role of density in the gravity balloon pressures
  682.  
  683. The fundamental equation that dictates the pressure in a body due to self-gravitation has been stated several times on this blog.  In this post, I want to focus on the fact that the density is a squared term, and the massive impact that has on assumptions we use.
  684.  
  685. [equation]
  686.  
  687. It is helpful to reformulate this into the small and large cases.  The small case applies when the balloon in the center of an asteroid is very small in diameter compared to the entire thing.  The large case applies when the opposite is true.
  688.  
  689.  
  690. ----------------
  691. set of posts after the principle of mediocrity post:
  692.  
  693.  - bridges in space, using rotation to fling things
  694.  - how orbital inclination factors into the geography of our solar system
  695.  - Most promising main belt asteroids to live in
  696.  
  697. bridges in space:
  698.  
  699. The Coriolis force is a straightforward concept, but some of what you read online about it is a little confusing.  I think the Physics Stack Exchange question had the most coherent summary of the concept.  You can clearly pick out the tangential (Corolis) and radial acceleration terms.
  700. http://physics.stackexchange.com/questions/383/derivation-of-the-centrifugal-and-coriolis-force
  701. a|R = a - 2 omega (cross) v_R + omega^2 R
  702. The second term is corollis force there.
  703.  
  704. It's often mentioned that space elevators would have a dual-use of launching things deeper into space  This is easy because the counterweight is already beyond GEO, and going much further on an extension of the tether would obviously put your beyond escape velocity.  I worked with calculations for this case, and I was surprised by the fact that I couldn't justify any benefit from using a space elevator as opposed to a bare cable.  There is the Oberth effect, where accelerating something starting at a lower gravitational potential can pay off in terms of in the final speed, so one might expect to see that here.  But you don't.
  705.  
  706. Okay, planetary bodies don't benefit us much through tricks of gravity, but they still can give us their angular momentum, which can be used to move things around the solar system.  A logical concept is then to attach a rope to a rotating body, and then use this to fling payloads at high velocities to their destination.  But refer back to the equation with Coriolis force in it.  This might not work so easily.  A solution may be to put extra tether connections between the main tether that counters the centrifugal force and a tangential point on the body.  I have asteroids in mind myself.  This would result in something like the following illustration.  I think there's a cute similarity to bridges.
  707.  
  708. [ asteroid bridge ]
  709.  
  710. A certain type of scheme that resembles this was outlined for Phobos.
  711.  
  712. http://hopsblog-hop.blogspot.com/2012/09/beanstalks-elevators-clarke-towers.html
  713.  
  714. I tried to calculate the deflection due to the moving material.  Problem is, this depends on the throughput.
  715.  
  716. del(r) = omega v_R m_frac r^2 / ss
  717.     predicated off the standard space elevator stuff
  718.  
  719.  
  720. While I'll leave a comment there, I do want to talk about the most obvious problem with this here.
  721.  
  722. lambda(r) \propto exp(U(r)/ss)
  723. U(r) = 1/2 (omega*r)^2  = 1/2 v^2
  724. lambda(r) \propto   exp( v^2 / (2*ss) ) = exp( sqrt( v/sqrt(2*ss) ) )
  725.  
  726. Wikipedia actually has quite a good section on the subject, with many of the topics I was going to cover myself
  727. http://en.wikipedia.org/wiki/Space_tether#Practical_materials
  728.  
  729. Ra  -   radius of asteroid
  730. r   -   radius of payload
  731. fundamental requirement is a fration:
  732.  
  733. Fr / Ft >= r / Ra
  734. omega^2 r / ( 2 omega v_R ) >= r / Ra
  735. v_R <= omega Ra / 2
  736.  
  737. Final radius needed for release is dictated by the desired final flight velocity and the spin rate.  This will give the travel time needed to get from the surface of the asteroid to the release point.  That number will then be the logistical constraint on how many payloads can be fired per unit time.
  738.  
  739. vf = omega Rf
  740. Rf = vf / omega
  741. t_{load} = Rf / v_R = vf / omega * 2 / ( omega Ra ) = 2 vf / ( omega^2 Ra )
  742. t_load = 2 vf / ( omega^2 Ra )
  743.  
  744. Have other equations for the ratio of the tether mass to the payload mass.
  745. Of course, this ignores the potential due to the gravity of the asteroid itself.  However, on a order-of-magnitude comparison, we don't expect it to be much.  Most asteroids (and certainly most close ones) have escape and orbiting velocities on the scale of speeds on the interstate.  In comparison, the square root of the specific strength of Kevlar is on the scale of km/s.
  746. need to use Application.WorksheetFunction.
  747.  
  748. alpha = v / sqrt( 2 * ss )
  749. Mt / Ml = Pi * alpha * erf( alpha) * exp( alpha^2 )
  750.  
  751.  Hohman transfer:
  752.  
  753. \Delta v_1 = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2 r_2}{r_1+r_2}} - 1 \right),
  754. \Delta v_2 = \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2 r_1}{r_1+r_2}}\,\! \right) ,
  755.  
  756. The one thing left to consider is the required radius.
  757.  
  758. Rf = omega / vf
  759.  
  760.  
  761. --------------
  762. Delta V and cost to get to the asteroids
  763.  
  764.  
  765. In space, "far" may be best quantified by how much propellent it takes to get to some place.  This process of switching from one orbit to another is quantified well by hohlman transfer orbits, which have a corresponding change in velocity.  The velocity then feeds back to the rocket equation, which with you can calculate the size of rocket you'll need, more or less.
  766.  
  767. Asteroids make this topic about as complicated as possible, due to the fact that they are also highly inclined to the solar system's plane.  If a planet had inclination of the magnitude they often do, it would be considered quite abnormal.  The distribution is really all over the place.
  768.  
  769. If that wasn't enough, there are more complications that can be thrown in:
  770.  - Oberth effect if starting from the moon or Earth (for instance)
  771.  - Gravity assists
  772.  
  773. For a cursory analysis, I prefer to ignore the possibility of gravity assists.  After all, even if you do an assist, that will probably increase the total trip time.  At least in the case of a direct transfer orbit, you constrain the travel time to half of a full orbit.  This might turn out to be an important detail for asteroid trips, particularly for heavy industry activities to the asteroids.  The year length for those bodies can be upwards of 3 or 4 Earth years.
  774.  
  775.  
  776. --------
  777. Friction buffers could be spherical
  778.  
  779.  
  780. --------
  781. Classification of Gravity Balloon Types
  782.  
  783. R/t ratio
  784. 12.5 % ratio makes it Phobian
  785. 90 % ratio makes it Paxian (possibly)
  786. between is Anahitan
  787.  
  788. Pressure ratios that define these
  789. Phobian     < 1.0435
  790. Anahitan    < 4.445
  791.  
  792.  
  793. --------
  794. posts located elsewhere that still need to be done:
  795.  
  796.  - Revised friction buffers math, accounting for changing circumference
  797.     started on, is actually kind of hard
  798.  - Travel stuff, after building integrator for the different cases
  799.     that would be complicated, but it would be fun
  800.  
  801.  - Artificial gravity inside pressure boundary  just more on the tubes
  802.     gravity tube access and containerization
  803. - Relationship between
  804.     + absolute magnitude
  805.     + albedo
  806.     + density
  807.  
  808. -----
  809. Material Requirements for Most Simple Habitat
  810.  
  811. In-situ resource utilization would always be preferable to delivering materials from Earth, and this is the type of assumption that O'Neil and others make for their proposals of permanent space habitats.  However, we might not want to assume the technological capability in order for the concept to have any immediate social impact of convincinesss.  Even if we can use space resources, there may be production bottlenecks to deal with which still place a premium on good design that conserves resources.
  812.  
  813. Conserving resources and using the natural forces of nature to our advantage is the basic philosophy behind my proposal of a gravity balloon with in-habitat rotating tubes for artificial gravity.  For that reason, I think that a brief material accounting of a "startup" habitat might be a helpful addition.
  814.  
  815. While maintaining conservatism, I'll still use the most promising design cases for the gravity balloon here.  For example, we would expect to use a habitat of the ideal porosity if going as far as the asteroid belt.  That's not exactly an example of claiming "extra margin", because it's certain that such an object exists, we just haven't characterized it yet.  For the tubes, we can wave away the need for a massive cooling system, because I've
  816.  
  817. Things that need materials:
  818.  - the Liner, need more area than just the sphere surface area, "wrinkled"
  819.  - Kevlar
  820.     + tethers for access
  821.     + tube main structural material
  822.  - explosives to break the rock
  823.  - liquid nitrogen
  824.  - liquid Oxygen (?)
  825.  - sails
  826.  - rigid members for tube frame
  827.  - sheets   Does syran wrap have sufficient breaking length?
  828.  
  829. Optimization problem:
  830.     How small to blast the rocks to
  831.     balance of explosives versus liner
  832.  
  833. https://commons.wikimedia.org/wiki/File:Alternate_truncated_cube.png
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