December 18, 2011

The Friedlander Cold Crown –A Cold Trap For The Lunar Poles--Solid Oxygen For Lunar Capture And Export

Guest post by Joseph Friedlander

This article discusses the problem of preserving the Lunar vacuum despite huge industrial use. Lunar ‘atmosphere’ might frost out to an artificially enhanced ‘cold trap’ at the Lunar Poles. The proposed mega-engineering plan is to create 40 kilometer high walls around the lunar poles to make the poles colder and trap billions of tons of frozen oxygen.

The basic idea revolves around the fact that many polar craters have (for at least part of the year) so little sunlight (principally upon the rim) that simple seeing of a remote sunlit cliff above is enough to heat up and evaporate away any volatiles below upon the dark clefts of the polar crater floor. Shackleton’s floor has gotten down to 88-86 Kelvin, but oxygen sublimates over 54 Kelvin for example. (And as we shall see in this article, really above 21 Kelvin)

WHY this is needed--

You may know of the work of Geoffrey Landis who published a technical and popular version of his work on degradation of lunar vacuum.

The takeout for this is oxygen (primary waste gas from lunar rock refining) can travel around the moon in around 47 hours (450 hops at 160 km each, taking 380 seconds between bounces)

On the night side of the moon, the typical temperature is only 100K. Molecules thus take six times as long to diffuse across the same area, and since any given molecule will spend six times as long on the night hemisphere as on the day hemisphere, the gas reservoir on the night side will be proportionately greater

Landis estimates that emission of only 10000 tons of oxygen a day would result in much slower escape of oxygen (no longer say 90 days, more like thousands of years)
That is only say 10 million tons of moon rock being vigorously deoxygenated per year. That might be enough for one large 10000-person base but is very disappointing in terms of a massive new lunar civilization.

There would still be a vacuum on the Moon but the quality would be low enough that many processes would be hampered without artificial vacuum chambers (thin walled to be sure)

Landis gives the mechanism of escape blocking oxygen buildup --For the heavier gasses, though--like oxygen and nitrogen--the gravitational escape lifetime in the atmosphere is thousands of years.

While the moon will lose atmosphere over geological time spans, it could hold onto gas for a very long time by human scales. For these gasses a different mechanism removes them from the lunar atmosphere. The unfiltered light of the sun ionizes the gas molecules, and the ionized molecules are then quickly swept away by electric fields associated with the solar wind. This occurs in a time span of approximately 100 days. When the atmosphere gets thick enough this mechanism stops happening--but the gas generation needed to make it "thick enough" is something like 10,000 tons/day--considerably higher than anything produced in our lunar industrial facility--at least in the next century or two.

Joseph Friedlander here again --What I wanted was a way to deoxygenate gigatons and teratons of lunar rock with impunity for a massive Lunar industrial buildup. (Which I have explored and hope to explore in various Next Big Future articles on Moon colonization)

The way for that to remain plausible was to find a way to trap oxygen at the Lunar Poles and freeze it out. So the Moon itself would do the garbage disposal for us. We would fry rock at the equator hot enough that the oxygen would escape—and it would flee to the poles, not ruin our good vacuum for thousands of years.

And right now it is a very high quality vacuum

Right now the entire Moon’s atmosphere is only--10 tons-- of all kinds of gases (yes you read correctly--the landing stage of the LM each time doubled the ambient!)

Lunar Polar area pictures--

The darker areas in these pictures are where the trap would be, the lighter areas the areas to have their sunshine blocked by the reflector fence sunshades--

'Friedlander Cold Crown', a reflector fence would enable a few hundred thousand square kilometers of cold trap)--a circle of complete darkness About 6-7 times vertical exaggeration—really only 40 kilometers high--

Adam Crowl: The area of a circular annulus on the surface of a sphere can be computed via 2piR^2(cos(a)-cos(b)) where angles a & b are taken from the vertical axis. Thus, covering both poles, the area from 80-90 degrees North/South (a=0, b=10) is 1.5% of the whole. That little equation also means half the … surface area is within 30 degrees of the Equator (a=60, b=90). That region has a net gain in heat from the Sun, while North and South of 30 degrees have a net loss over the course of a year.

Illustration of Friedlander Cold Crown on Moon—double reflective sun fence, outer deflects sunlight, inner deflects infrared of outer one. On the ground within 10 degrees of either lunar pole, no surface sees anything other than 3K background radiation of space. It gets cold. Oxygen escaping from massive deoxygenation does ballistic hops of around 160 km all across Moon, hits several times within the Cold Crown, cools down enough for capture.

Area within between 80-90 degrees north and south (within inner fence) is 1.5% of lunar surface, a good fraction of the size of the State of Michigan.

Hi, this is Joseph Friedlander in a guest article for Next Big Future. Recently I had a brainstorm about the lunar atmosphere buildup problem (while thinking of lunar industrialization)

Now oxygen liquefies around 90 K, and if the Moon had an atmosphere we might enjoy picturesque photos by starlight of liquid oxygen lakes on the Lunar Poles—but of course there is vacuum—no vapor pressure—and for something to remain there it has to freeze solid.

And until recently 90K was about the limit of known Lunar cold--

For Shackleton Crater, the average temperature was determined to be about 90 K,A reaching 88 K at the crater floor. Under these conditions, the estimated rate of loss from any ice in the interior would be 10^−26 to 10^−27 m/s.

but of course that is water ice, not oxygen ice… so the possibilities weren’t there.

Adam Crowl of kindly pointed me out to this paper on using solid oxygen to extend LOX storage times.

Adam said,

“This paper covers a lot of the properties. Wikipedia's triple point temperature is wrong, oddly enough. Usually it's accurate. Heat capacity declines linearly when oxygen transitions from its warmest solid phase (freezing at 54.4 K) to the next phase at 43.8 K.

...there's a vapour pressure diagram in torr (mm Hg) down to ~20 K.”

This is a 1968 study on behavior of solid oxygen as storage medium (nice charts including vapor phase charts)

Joseph Friedlander here again, basically here is that chart here—you see that below 21K vapor pressure drops off a cliff.

So we need oxygen to be solid for easy capture—but until recently the hope of temperatures that low—colder than Pluto—were ‘good luck’ to find on the Moon.

All of a sudden the possibilities expand. Note this new experiment and the map it produced: Note that nearside is warmer at lunar night (lighter vs darker blue in
the right image) my guess is because of the Earthshine! (half 1/20000th sunshine
on average)

New Temperature Maps Provide a 'Whole New Way of Seeing the Moon'

DIVINER cold temperature map of Moon

Diviner Lunar Radiometer Experiment, is making the first global survey of the temperature of the lunar surface.

Diviner has obtained enough data already to characterize many aspects of the moon's current thermal environment. So far, the instrument has revealed richly detailed thermal behavior throughout the north and south polar regions that extends to the limit of Diviner's spatial resolution of just a few hundred yards.

"Most notable are the measurements of extremely cold temperatures within the permanently shadowed regions of large polar impact craters in the south polar region," said David Paige, UCLA professor of planetary science and principal investigator of the Diviner Lunar Radiometer Experiment. "Diviner has recorded minimum daytime brightness temperatures in portions of these craters of less than -238 degrees Celcius (-397 degrees Fahrenheit). These super-cold brightness temperatures are, to our knowledge, among the lowest that have been measured anywhere in the solar system, including the surface of Pluto."

Friedlander here again—the BBC covered it and gave a closeup of the temperature map—for Hermite Crater

========================BBC on HERMITE CRATER===============
…lowest summer temperatures in the darkest craters at the southern pole to be about 35K (-238C); but in the north, close to the winter solstice the instrument recorded a temperature of just 26K on the south-western edge of the floor of Hermite Crater. the lunar poles they receive no direct sunlight and the coldest places don't even receive any indirect sunlight," Prof Paige said.
"In other words, only what little radiation may be scattered from some distant cliff gets down into these areas; and they just cool off. Finally, they reach equilibrium temperature down at those low values."

(My emphasis)
======================/BBC on HERMITE CRATER

Friedlander here. So the idea of building sunshade fences—a Friedlander Cold Crown around the poles of the Moon occurred to me—because if 26k could be achieved (in winter and dark) with no special equipment, no isolation floor (many vacuum separated levels insulating the cold load from the ground)—just naturally with plain rock and regolith—

Then solid oxygen safe 20K temperatures might well be achievable year round in large areas around the Lunar Poles-- with a little help—build a sun fence to keep the sunlight away from distant cliffs, and then the polar night is eternal and unending, and the nearly unlimited cold has wonderful industrial possibilities.

Ideally there would be massive volatile capture (more below on that). The limit might be the emissivity of oxygen ice grain surfaces that can change (larger grain size is more emissivity, smaller is lower)

This page estimates lunar polar deep subsurface temperatures to be around 160 K or -110 degrees C.

The temperature drop is limited by conduction of heat from layers several meters below the surface, which maintain a roughly steady average temperature that can also be determined from the Stefan-Boltzmann law. In this case 'I' represents the incoming solar energy averaged over a full day-night cycle
Iave = 1366cos(θ) / πW / m2
so at the equator T is about 296 K, or a comfortable 23 degrees C if you bury yourself sufficiently. At 60 degrees that drops to 249 K or -24 degrees C. The average subsurface temperature near the poles (85 degrees and higher) would be below 160 K or -110 degrees C.


At 85 degrees the equilibrated temperature drops to 214 K or -59 degrees C. At the lunar poles there are believed to be regions which never receive direct sunlight. If they don't receive significant warming from higher elevation surfaces that are in direct sunlight, they would be equilibrated only with the thermal background radiation of deep space at 2-3 K (-270 degrees C), and would likely form cold traps holding volatile materials.

Joseph Friedlander here again --Obviously the selenothermal (equivalent of geothermal) gradient being 160 K below at some arbitrary depth did not stop 26 K on the surface from being achieved, so (especially with dust grains separated from vacuum as insulation) there is plausibility that 20K could be achieved.

Note what the sun fence does—it blocks the sun (outer fence) and the infrared leaking through the outer fence (inner fence)

So the area from 80-90 north and south—because the Moon’s tilted only 1.5 degrees and not 23.5 degrees—NEVER SEES THE SUN, and indeed never sees a cliff in distant sunlight if this Friedlander Cold Crown gets built.

But if you are going to build a sun fence you need to know how high to build it.
Dynamic range of topography--
The dynamic range of Mercury's topography (from highest high to lowest
low) is 9.6 kilometers, with a pretty narrow range about the mean. For
comparison, the Moon's is 19.9, and Mars' is 30 kilometers – so she
pointed out it's easy to remember Mercury 10, Moon 20, Mars 30."

Friedlander here again --I think the Earth like the Moon must be close to 20 incidentally—minus 11 for the deepest trenches, plus 9 for the highest mountains—

So to build the sun fence we needed data on lunar topography.

Lunar Reconnaissance Orbiter (LRO) topographic maps of lunar elevations
High Resolution Global Topographic Map of Moon

› Related story and imagery from Arizona State University!.html

LROC WAC color shaded relief of the lunar farside (NASA/GSFC/DLR/Arizona State University).
WARNING HUGE 70 mb tiff files—I have prepared smaller JPGs

Orthographic projection centerd at 0° longitude and 90° latitude.
Orthographic projection centered at 0° longitude and -90° latitude.

Joseph Friedlander here again –the Lunar South Pole –is the rougher one. (Note the deep blue South Pole - Aitken Basin, , Main ring diam: 2500 km, Depth: 8.5-12 km, largest crater known in the Solar System, which forces the sun fence to be higher to compensate (you also have many more high mountains to completely shade near the

South Pole than the flatter North Pole) here--

Color scale legend for LROC Color Shaded Relief (NASA/ GSFC/ DLR/ Arizona State University).

From my reading the north is flatter, relief range appears to be around 4 kilometers at absolute maximum. And by not making the shading fence perfectly round you could almost count on 2 kilometers in relief range on the modified route. For the South Pole up to 10 kilometers in relief range might be needed but 5 kilometers in relief range on the modified route.

Around the south pole the deep Aitkin basin complicates things, as the pix show
Note that 10 kilometers of relief does not necessarily mean a 10 kilometers high fence (all that is needed is for all to be in shadow--

So I wrote poor Adam Crowl again,

Adam said,
The Moon's axial tilt is why the crater walls get lit up. How does one's reflective fence avoid that issue?

I replied, If the shadow of the fence in the worst case of local 'summer' never gets below the top of the hills, the crater walls are always dark, so the issue never arises.

We discussed the correct height for the sunshade—

Adam said,
If the poles are at the selenodetic datum…

Remember the curvature of the moon. Imagine a triangle side through the pole and another side a radius at 80 degrees. Thus that radius is the hypotenuse when the sunlight is dead-level grazing the Pole at 5 km altitude from the Moon reference radius, thus (1738+5)/(cos(80))-1738 = 26.9 km high wall is needed. Depends on the actual altitude of the Pole.

(For 6 km elevation of highest South pole mountains---)
More like 36 km for 1.5-degree tilt….
Throw in the axial tilt and your shade wall is HUGE…

…Might be possible to shade the polar craters even more than they are at present, but how much cold-trap that can be created, I am unsure. …the shades ..they have to stay cold too, else their IR glow will heat the cold-trap!

A 40 km high shade wall—sun fence--- Friedlander Cold Crown around the poles of the Moon would be the equivalent of a nearly 7 km tower in engineering terms—but minus wind loads it would be far easier to engineer. It would be a huge project:

The lunar civilization require to build it grows more and more impressive as we regard it--—nearly 8000 km of fence, thousands of towers, around 300000 sq km of reflective foil—massing 30 million tons at least. It would need a massive industrial capability on the Moon—but enable a yet greater one.

For current lunar atmosphere, Landis gives ten million molecules/cubic centimeter (half nanotorr) during the lunar day 100,000 molecules/cubic centimeter during the lunar night, This corresponds to pressures from 0.001 nanotorr

Joseph Friedlander here again --In my view what would happen is that all this ‘lingering’ nighttime gas would basically flee to the cold trap and be frozen out. Remember it has to stay at solid oxygen temperatures, not liquid oxygen temperatures. Normally it would evaporate when daylight hit it on the head or on a distant cliff and contribute to atmospheric buildup (ruining good industrial vacuum)—but building a Friedlander Cold Crown would actually collapse lunar vacuum levels down to nighttime levels in the day! –cold enough that solid oxygen’s sublimation rate would be negligible.

This would enable (after some years buildup) massive solid oxygen cutting packaging and export to space industry and colonies.

You literally could carve oxygen ice with heated wires, confine it to a closing-hatch tank, launch it and let it thaw to liquid oxygen in the tank on its’ journey to a space depot.

The solid oxygen would pile up in the crater. (Through anti-sublimation, frosting up) and we could do incredibly intense industry (refine teratons of lunar rock and deoxygenate it,) at the equator and if the snow down time was reasonable, you could maintain usable vacuum at defined seasons of the year. (Otherwise a mere 10000 tons a day of oxygen could begin a buildup to degraded vacuum conditions as Landis says above—processing a mere 10 million tons of lunar rock a year could do that--) and we have a limit either on vacuum levels or industrial levels. So truly massive industrial levels WITH good vacuum depends on some technology like I am trying to prove here.


The "snowout" issue
How do you calculate how rapid "snowout" can be handled, in other words, what is the
radiative capacity of the shadowed crater per square kilometer?

For example, people have speculated about the 'sun going out' (neglecting, or not, the
heat retention capacity of the oceans, and the energy trapped in the radiative layer
of the Sun)—discussing only cooling of the gas, not latent heat of the oceans--

A relatively simple calculation would show that the Earth's surface temperature would drop by a factor of two about every two months if the Sun were shut off. The current mean temperature of the Earth's surface is about 300 Kelvin (K). This means in two months the temperature would drop to 150K, and 75K in four months. To compare, the freezing point of water is 273K. So basically it'd get too cold for us humans within just a few weeks.

Focusing only on an imaginary Earth atmosphere (again, neglecting the heat of the oceans) 5 million gigatons at current temperatures this implies ~8 months to freeze Earth’s air to ~10 meter deep oxygen/nitrogen ice.

This has been described as ‘freezeout’ or collapse of an atmosphere, something like it is expected by many observers for Pluto.

Adam Crowl and I discussed this—


The other problem is that gas molecules lose energy with each impact with a surface colder than they are. But how many impacts are required? A cold trap only allows 1 impact, which implies it has to be darned cold to work, if at all. Water and CO2 get trapped by getting very cold before they encounter the poles, very cold being relative to their respective sublimation points. Oxygen?

Of course, the actual area of the moon inside the Friedlander Cold Crown (assuming 80 north and south to be the boundary) is 1.5% of the lunar surface or 1/67 or so of it, so the question is whether or not (as Adam Crowl puts it, that the night-time equilibrium temp of the rest of the Moon may be too hot to ever let oxygen cool down enough to stick in one go. )…

We really need a proper estimate of "sticking probability" for 'warm' O2 molecules at 120-100 K to stick to solid O2 at 30 K. Then work out the likely flux. If the O2 is bouncing around at 200 m/s (160—JF) and there's 10,000 tons of it zinging around,(now there is 10, JF) then an estimate of the flux can be figured out. That seems the better way forward.

Joseph: Darn it you're right, but hope is not lost, because the very nature of a random walk gets it back there again and again for multiple captures. Certainly if an entire polar area is shaded (with radius 1738 km what is the area between 80 and 90 north?--off the top of my head I will guess around 1% of the lunar surface, about the size of the state of Michigan) so if both poles are done, it seems to me that 2% will be cold traps and 1/50 of all bounces that come say from the night hemisphere and are pre-cooled might have a bigger chance to stick after (say) 4 or 6 slowdown collisions WITHIN the cold trap, 160 km being the hop distance.)

By radiation arguments alone once solid oxygen sticking began it would become contagious.frostout may be slower than expected if many cold impacts are needed for each molecule. Maybe 10? (for 1/10 the frost rate?)

Ironically, a dense atmosphere (cut off from sunlight) aids its' own collapse! On a Earthlike planet with no oceans, the atmospheric collapse would be rapid in my
view, 10 meters of frost in a year.

Based on the earlier estimate of
that the Earth's surface temperature would drop by a factor of two about every two months if the Sun were shut off.
From 300 Kelvin (K). in two months to 150K, four months 75K and extrapolating,
.6 months to 37.5 k, then 8 months to over the 21K oxygen vapor pressure cliff ending at 18.75 (assuming ground heat leaks permit it, but we are talking regolith grains separated by vacuum so I assume it might be possible.

I would love to see national laboratory modeling on something like this. Any takers?

The big question to me would be, what is the total capacity of freezeout per square meter per year? I am guessing 11 tons a square meter of SOX (solid oxygen) but that is only a could easily be 10 x less or even 67 x less (the ratio of non 80 North and South area to the shadowed zones, in this case ballistic transport of particles does our gathering for us but we pay for it in terms of being the radiator for the whole world---

Such a factor of 67 less would still be a respectable 164 kilos of sox per year per square meter 164 kt a square km, so of 30 million sq kilometers of Lunar surface say 448000 cold trap square kilometers capturing 73 gigatons a year of oxygen in SOX form. That’s enough to vigorously deoxygenate 180 gigatons of moon rock a year--major industry (~4 times what we do on Earth today, by mass arguments counting all rock mined—neglecting the fact that the Moon’s cheap solar energy would enable massive reduction of nearly all that rock, not just extracting a few percent as we do here.)

But suppose that the 11-ton per square meter estimate was correct—in that case, we would have nearly 5 teratons (5 million megatons) of oxygen freezeout capabilities and be able to vigorously process about a Phobos (Mars’ larger moon) of moon rock per year.

Either way we should be able to have a huge industrial civilization on the Moon without ruining the ambient vacuum to the tune of needing thousands of years of waiting until it could restore itself.

And of course one final use for this new cold area: Near indefinite cyrogenic storage of anything we want to last a good long time. Seeds, biological samples, you name it. The expense of liquid nitrogen practically guarantees that during a collapse of civilization (say a multi-decade depression, or 50 bad years of war and recovery) any preserved biosamples would perish (the liquid nitrogen preservative in today’s freezing storage companies vaults would evaporate and not be replaced)—but a structure like the Friedlander Cold Crown in vacuum should last for probably tens of thousands of years, presumably by which time some recovery would have occurred.

(Micrometeors probably erode a millimeter per million years, the thinner the reflectors the less long they will last—but they will need replacing probably every 30-100 years because of abrasion—the thinner they are the cheaper to replace—your choice.)

Any other uses to suggest for long term free cryogenic temperatures? Your comments are welcome…

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