Tuesday, April 16, 2013

Candidate Bodies to use as a Gravity Balloon

You could formulate the concept of the gravity balloon as a completely man-made construction.  Quite simply, once a space station grows to the scale of a Death Star, it make sense to stop building rigid walls as a pressure boundary, and instead design around the self-gravitation.  To fit into a realistic picture of the future of humanity, however, we need to make direct references to objects that we could use to hold an Earth-like atmosphere with minimal processing.  I touched on the availability of candidate objects in the introduction.  Since then I've delved into the knowledge base of asteroids to give a much more comprehensive picture and I hope to communicate that here.

The Obvious Candidates

Suitable bodies for the creation of a gravity balloon are extremely numerous in our solar system, however, they're not at the doorstep of Earth.  This is logical since the evolution of life required that Earth was not regularly hit by such bodies.  For what it's worth, the KT extinction event is thought to have been caused by an asteroid 10-15 km in diameter.  The factoid is interesting because it demonstrates that the minimum size needed to create a livable internal pressure in an asteroid is greater than the size that can cause mass damage on Earth, should it fall.

433 Eros

Predictably, the inner solar system is mostly devoid of the sweet spot of asteroids between about 20 and 60 km in diameter, the size necessary to contain a breathable atmosphere.  One notable exception is Eros, which is a fairly large asteroid that currently hangs around the orbit of Mars and could one day impact Earth.  Naturally, it's received a good deal of attention due to its unique status.  It is large enough to turn into a gravity balloon with an initial internal pressure of 70% of Earth's sea-level pressure, if it were spherical (density is reported to be 2.67 g/cm3, and is used in the calculations).  However, the shape clearly shows that it's not perfectly differentiated.  This isn't exactly a problem for a gravity balloon, since it just demonstrates that its material has tensile strength comparable to the gravitational forces.  This could be used to the advantage of people working with it, and could also make excavation somewhat more difficult.  It would definitely be one of the top targets of future asteroid hunters.

Eros, asteroid at about 1.46 AU, weighing 6.7 x 1015 kg

I also want to include a second scale of about 60 to 80 km (diameter).  These wouldn't be an ideal place to build a habitat right away, but with specific combinations of gases, humans can tolerate the pressures.  If such an object was inflated significantly, the pressure would decrease anyway.  Of course, development of that class would be relevant much further out in the future.

Phobos (moon of Mars)

Of the moons in the inner solar system, Phobos is the only suitable one.  Mercury and Venus are thought to not posses any natural satellites.  We could still discover some, but our efforts up to this point would have caught a mass lager than a 20 km diameter for either of these, so we're out of luck there.  Earth's moon is vastly too large by comparison (and Earth's second moon is vastly too small).  Development of infrastructure on the surface of the moon could, of course, be vital to space development but it couldn't hope to approach the flexibility that you could have in the inside of a gravity balloon.  Ultimately, you could consider the possibility of breaking up larger bodies to turn them into multiple gravity balloons, but this would require monumental capability, probably on the scale of what's needed for terraforming.  So for now we're just left with Phobos out of all the moons in the inner solar system, and I predict a central pressure of about 60% Earth's sea-level pressure.  The density is 1.88 g/cm3, and it is at least somewhat close to spherical.

Phobos, moon of Mars, about 1016 kg

This candidate has lots of positives.  For one, it's the only one that's currently being considered for manned missions by NASA.  While it's not likely that we'll be drilling over a kilometer into it anytime soon, this offers a connection with current buildup of space efforts.  Also, since there are significant public figures who are interested to see a million settlers on Mars, why not a million inside Phobos?  After all, the latter could turn out to be a better idea - less difficulty in mining and moving material, radiation protection without claustrophobic caves, and a full Earth gravity.  One of the major drawbacks is the fact that Phobos lies in a gravity well, in close orbit of Mars.  The orbital period is only 7.5 hours, as opposed to a full month for Earth's moon.  That makes it difficult to travel to and from other destinations in the solar system.  Because of that, Eros could have an advantage in energy budget for travel.  Tidal forces are also particularly strong, which would be an interesting technical complication.

Inner Edge of the Asteroid Belt

Now we're past Mars' orbit (1.66 AU) and we only have two workable candidates.  It's true that there are others, both comets and asteroids, that occasionally swoop into the inner solar system at the closest point in their orbit, but these would be energetically difficult to reach, just like far-flung candidates, so I'm excluding them.  In more scientific terms, I'm only interested in the location of the semi-major axis, which is a reasonable proxy for the energy required to reach them.  The area with a great abundance of suitable gravity balloon candidates starts where the asteroid belt begins.  To make the point, I gathered data on all asteroids within my size criteria (about 10 to 80 km diameter) and a semi-major axis closer than 2.5 AU.  This was done using the JPL small-body database search engine.

As far as I know, this data doesn't include any mass, and with good reason - mass is difficult to calculate, and often inferred from brightness.  They do give the calculated GM form of mass, calculated from orbital behavior, but this is only feasible for extremely large asteroids and almost none in my search criteria had that data.  That means all I had was diameter, but this isn't a huge problem.  I assumed a density of 1.3 g/cm3, which is largely thought to be representative of asteroids, or at least conservatively low for the majority of them.  With this density, I find mass, and use the methods I've previously described to find their internal pressure at the center.  I graphed this internal pressure over the semi-major axis values, which gives a good picture of the abundance of candidates throughout the inner solar system, up to 2.5 AU, covering some of the inner edge of the asteroid belt.


For the line that represents the limit of habitability, I'm using about 0.34 atmospheres, which is taken from Skylab.  In that mission, they didn't use Oxygen gas exclusively, but the Nitrogen content was much lower than on Earth.  That worked for them, although there are lingering concerns about using that type of atmosphere.  For a gravity balloon, the reasons likely be different, because the gasses that you can get access to are fundamentally limited since you're only interested in in-situ resources.  Oxygen gas would be comparitavely easier to make, so for early stages of self-sufficient space development it is thinkable we would use such a low atmosphere pressure.  Importantly, doing so also broadens the types of candidates that can be used.

The density assumption obviously causes errors, but for the majority of these, we don't actually have better data.  Give it another decade and that may change - this is one of the things I find most exciting about the subject right now.  A good example of the innacuracy is Eros, which is shown to be below 34% of sea-level pressure in the graph, which is obviously not the case.  Its density is very high, and that's why its in the wrong place.  Otherwise, the spead of pressures observed here reflects the general abundance curve of asteroids.  When I did the search, I included objects as low as 10 km diameter, just for illustrative purposes.  I then removed all those below the habitable pressure line from the set.

Even though these are all the same semi-major axis, they're not all the same since some orbits are more elliptical than others.  In order to illustrate this, I ordered the candidates from the reduced set (not all shown on that graph, about 50 in total) by the perihelion and plotted the perihelion and aphelion.  This shows that many of the candidates in the set have a nearly circular orbit, but on the other extreme, some come as close as about 1.7 AU.

Spread of Orbit Characteristics within the Selection Criteria


It's not immediately clear to me whether a more highly elliptic orbit is more or less favorable as a destination.  On the one hand, uniformity throughout its year would be nice, but it's possible that more highly elliptical orbits could offer opportunistic trips.  Either way, for the moment I selected the 9 candidates with the closest perihelion, just to have a small list to cite.

Asteroids within the Set with Closest Passes
(done with Tableizer)
AsteroidPerihelion (AU)Aphelion (AU)Inclination (deg)D (km)M (kg)P (atm)
323 Brucia1.673.1024.235.83.1E+160.75
220 Stephania1.742.957.631.12.1E+160.56
234 Barbara1.802.9715.443.85.7E+161.12
1108 Demeter1.803.0524.925.61.1E+160.38
916 America1.812.9211.133.22.5E+160.64
783 Nora1.812.889.340.04.4E+160.93
584 Semiramis1.822.9310.754.01.1E+171.70
219 Thusnelda1.832.8810.840.64.5E+160.96
284 Amalia1.832.888.148.77.8E+161.38

This list is somewhat arbitrary, so I'll also give the entire list.  If you want, you can search for the number and get information in public databases.  These are all the candidates that met the selection criteria:  67, 585, 198, 142, 584, 284, 261, 270, 186, 248, 432, 306, 113, 138, 126, 1963, 161, 623, 234, 182, 118, 435, 219, 131, 136, 783, 282, 495, 302, 877, 556, 189, 732, 474, 930, 323, 178, 376, 249, 169, 916, 757, 220, 1244, 1159, 572, 273, 1650, 917, 364, 565, 853, 443, 470, 1108, 1296, 908, 3345

If you continue to go further out from 2.5 AU, there are many many more.  Right now I'm not interested in those because, for one, they're more difficult to access from Earth, and two, they don't receive as much light.  Even at a distance of 2.0 AU, you receive 1/4th the sunlight as Earth.  Being able to continuously generate solar power without interruption from night is a benefit, but it may only break even the the common isolation values of about 208 W/m2 at 2.5 AU.  Everything in this post is intended to answer the question "where would you build a gravity balloon".  Phobos, Eros, and the above group are an obvious starting place, but beyond those it is less obvious.

Access to these Objects

It's hard to move something as large as the asteroids I'm talking about here.  NASA is currently working on a plan where they'll bring a near-Earth asteroid into orbit around the Earth-moon system.  But this plan calls for moving an object 7 meters in diameter that is already near-Earth.  For a gravity balloon, we're talking about objects 20 km in diameter, that are not near Earth.  The scope of moving such a thing is orders of magnitude beyond reasonability, and I place in the same fesiability category as terraforming - scale being in the millions of years.  So we're stuck with working with them in-place.

In order to give a good technical argument, I wanted to give the Delta v budget associated with accessing these places.  A complication, however, is that there isn't a single value associated with this.  To get from Earth to the surface of Phobos, for instance, one would have to travel out of Earth's gravity well, work against the gravity of the sun to get to Mars, descend to Phobos orbit, and then climb down Phobos' gravity well.  These are 4 components but the first one is identical for all possible locations.  Because of that I'm only going to focus on the latter 3, for purposes of comparison between the candidates.
  • Delta-V needed to get to its orbit around the sun
  • Delta-V needed to get to its orbit around its planet (in the case of a moon)
  • Delta-V needed to descend to its surface
The first one is the real difficult one to calculate.  For that, I'm using the Hohmann transfer orbit equations from Wikipedia.  I'm combining the terms for the initial and final thrusts, giving the following expression.


In this calculation, r1 will be the orbiting radius of Earth, because we're interested in missions starting from Earth, and r2 will be the semi-major axis of the destination object, which I've already tabulated.

For the case of reaching a planet's moon, we need a variation on the above formula.  To do this, I'm equating the r2 value to infinity and r1 to the orbit of the moon.  This isn't very accurate because it ignores everything about gravity assists and probably aerobraking, so it should be taken with a grain of salt.


To get the delta v for reaching or leaving the surface of an asteroid (with no atmosphere), that's just the formula for escape velocity.

With all these, we can get a simple table of the Delta-Vs.  In a simplistic sense, the values are addative, if you consider that a spaceship has to get to one location, stop, then go to the next.  Real life isn't exactly so simple, but this is the best I will do for now.  We also need to qualify that significant work is needed to get away from the Earth in the first place.  Low Earth Orbit costs about 10 km/s to begin with, and then from there to escape is on the order of 4 km/s.  Due to the rocket equation, however, accelerating 2 kg to 4 km/s is much much easier than accelerating 1 kg to 8 km/s.

Delta-V in (km/s) for sun, planet, and the object
ObjectR (km)M (kg)amoon R (km)sunplanetself
Phobos11.11.07E+161.529,377 5.5890.8850.011
433 Eros8.46.69E+151.46-5.07200.010
323 Brucia17.93.13E+162.38-10.02700.015
220 Stephania15.62.05E+162.35-9.90400.013
234 Barbara21.95.70E+162.39-10.04100.019
1108 Demeter12.81.14E+162.43-10.17800.011
916 America16.62.50E+162.37-9.96700.014
783 Nora20.04.36E+162.34-9.89400.017
584 Semiramis27.01.07E+172.37-9.99500.023
219 Thusnelda20.34.54E+162.35-9.92800.017
284 Amalia24.37.84E+162.47-10.32000.021

The main takeaway from this chart is that the propulsion needed to travel from Earth to the object dominates.  The value for the stellar Delta V for Phobos is just that of Mars.  Compare to a more accurate Delta-V, which includes some of the more harry real aspects of the real solar system.  The sum of all the transfers to get to Mars, I find comes out to 0.7+0.6+0.9 = 2.2.  This is much lower than the 5.5 I found, which is unsurprising considering the factors I didn't consider.  This also begs an interesting question, as to whether travel to Eros would actually be easier than travel to Phobos, and it looks like not, unless you are possibly considering the effort to get back to Earth (which should be more for Phobos).

Inflatability

So far I've only considered the challenge of getting to an asteroid, drilling to the center, and setting up shop there no matter how big of a volume.  This wouldn't be very useful in the long run unless the favorable scaling factors over rigid pressure boundaries could be exploited at some point.  Thus, it's a good question to ask how large of a volume could you get out of these objects before your pressure limits stopped you.  I've already covered the mathematics of doing this in previous posts.

The requirement of the maximum size will be that it has a pressure equal to what the Skylab space station had, about 34 kPa.  Then with some root finding routines, the inner radius that gives this pressure (given the object's mass and density) is found.  That then implies the internal volume.  This is fairly straightforward, and here are the numbers I obtained.

ObjectM (kg)rho (kg/m3)R inner (km)V (km3)
Phobos1.07E+1618764.74447
433 Eros6.69E+1526704.33340
323 Brucia3.13E+1613009.843993
220 Stephania2.05E+1613006.13966
234 Barbara5.70E+16130016.1417620
1108 Demeter1.14E+1613001.4312
916 America2.50E+1613007.811994
783 Nora4.36E+16130013.159525
584 Semiramis1.07E+17130024.7863773
219 Thusnelda4.54E+16130013.5810489
284 Amalia7.84E+16130020.2034507

I wanted a good way to illustrate this, since a large inner volume is the entire point of the gravitational balloon.  In the following illustration, I made the size of a dot proportional to the inner volume in a graph of the mass versus inner radius.  This means that the volume follows directly from the radius, as per 4/3 Pi R3, but the inner radius isn't a direct function of the mass because the densities of the objects can be different.  Indeed, this is why Phobos and Eros are outliers.  I had actual densities for those two while the inner-belt asteroids were assumed to be the same, so they lie on the same (imaginary) curve.  You can even see how Eros maintains almost the same volume (dot size) as Phobos, in spite of having much less mass.  This is because the effects of self-gravitation are greater for Eros, because it has a higher density.


The takeaway from this graph staring you in the face is that the potential size of a habitat grows very fast with size of the asteroid you use.  About half of the potential volume comes from Semiramis alone.  That's not even the largest in the group, out of the larger group of 50 or so asteroids in the inner edge of the asteroid belt, there are candidates much much larger than that.  If you've read my previous posts, you may be wondering how Semiramis can give such a large volume compared to my original large reference case in the introduction.  That's because I used a pressure of 0.8 atm in that case, and 0.34 atm here.  The latter might be somewhat uncomfortable, it's hard to say, but for the most near-term prospects of in-situ resource utilization, it's probably the most reasonable assumption.  It would be much smaller if you required 1 atmosphere, and Phobos and Eros would be entirely unusable.

In closing, I discovered a few things that I wasn't entirely certain of before.  Firstly, Phobos and Eros are quite inflatable if you use an atmosphere with reduced Nitrogen concentration.  In fact, at around 9 km inner diameter that would be quite spacious, larger than any other space habitat would could possibly hope to build, and large enough to build artificial gravity tubes.  Also, I was surprised by the sudden increase in density of large asteroids at around 2.2 AU.  Obviously this is because of the clearing effect of Mars, but it's still interesting.  There are lots and lots of options around there.  Finally, the difficulty to travel to those asteroid belt candidates is much more burdensome than the Eros or Phobos options.  Those two are probably the best we've got for anything near-term in the absence of other information.  But that other information could be substantial.  You would obviously have your pick of compositions if you went as far as the asteroid belt and that could also reduce the amount of equipment that has to be hauled in the journey, as well as the difficulty of actually manufacturing the atmosphere.

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