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Okay, I was thinking about it during work today and Mal's post back over in Inspirational Sites reminded me.  I think I got a real solution here and the best part is that it plays off the Mecha Fen.
The solution, IMHO, lies in Eureka Seven.
In that anime, there exists in the atmosphere a damn-near magical substance called Transparent Light Particles, or Trapar for short.  These particles were non-toxic, although in great densities it could displace actual atmosphere, but that was a rare occurrence.  the thing is, though, that aircraft/ships and mecha could optionally 'surf' the trapar (it had the odd ability to react energetically with specially treated surfaces, producing lift) or simply pass though it as long as it wasn't too much denser than the air.  Normally, in the anime, they were worried about the trapar not being thick enough.
All that said, what if the Fen could apply it to the atmosphere of Mars?  It could be used to improve the viscosity of the atmosphere, especially in the higher altitudes where that would be very useful.  *Recalls a certain incident involving the Soviets.*  And, hey!  Sky-surfing mecha!  (And just sky-surfing in general.)  What's not to love about that?
The big problem with Mars' atmosphere though is there isn't enough of it. And trapar doesn't seem to have any other qualities other than "hey, you can surf on it." It's not an oxygenating medium, so you can't breathe it. It's not a greenhouse gas, so it won't help trap heat. It's not a UV blocker, so it can't stop the excess solar radiation that the Xavier Protocol grid lets through. And that's what Mars needs for an atmosphere; it has to be breathable, it has to trap heat and it has to block UV.
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
I think the proposal here is more, "why can't we use something like this?" and then add the properties that we need via invoking handwavium, rather than "let's use this literally as it exists in the source material." So let's think about this... A nanopartical "gas", but it kind of binds itself together in a way that keeps it from floating off into space. It acts like a barrier to other gasses, but doesn't impede anything else. Maybe a tuned force field effect for both of these properties? Essentially giving the atmosphere a "surface tension" that holds gasses in. (And which you can surf on.) Once you have that, making it greenhouse and UV-screen would be trivial. I don't think oxygenation would be a good function for it, but that can be handled by some other device. Once you have a lid on the atmosphere, the oxygen is less troublesome.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.
But there's still no damned atmosphere on Mars! That's the problem! Surface tension doesn't do a bit of good when there's nothing underneath it.
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
Well, there's a bit... but it's only 0.00628 times as dense as Earth's atmosphere. The topless towers of Helium would poke through the trapar layer.
--
Rob Kelk
"Governments have no right to question the loyalty of those who oppose
them. Adversaries remain citizens of the same state, common subjects of
the same sovereign, servants of the same law."

- Michael Ignatieff, addressing Stanford University in 2012
Well, we can do something about the density of the atmosphere once the Xavier sats are in place.  The Martian atmosphere's thinner than it should be right now because the solar wind is stripping it away and it has no mag field to protect it.  Of course even with the Xavier sats we're dealing with a place that's got a gravitational pull of about 0.38G so its unlikely we'll ever get an atmosphere exactly like Earth's.
Having something like trapar to help hold in gases and increase the surface pressure would be useful, especially if something can be done to it for UV filtering as Bob suggested.
As to whether or not the towers of Helium stick out of it, that just means they'd have to be sealed.  And they'd have to be very tall for that to happen anyway.  The Martian atmosphere currently has a scale height of about 10.8 km, compared to Earth's 6km.
--
Unlike other cuisines, the Finnish one is most distinguishable by the
fact that none of the major traditional dishes have anything you could
remotely call flavo(u)r, and pretty much the only spice is salt.
    -- Toni Lassila
Martian atmosphere starting from OTL 2010 is 6 millibars on average. Even with aggressive terraforming, the atmosphere ca. Fenspace's 2015 would be... 20, maybe 30 millibars. And that would still be 90% CO2 or more. Compressing that with trapar or a force field would yield a very thin layer, that might not even cover the entire planet, and it'd still be mostly CO2.

For terraforming purposes, having a breathable atmosphere is more important than having a thick atmosphere. And once the one is accomplished, the other will follow in short order. Hell, the main gas can even be trapar; just be ready to manufacture five quintillion tons of the stuff...
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
Oh yes, compressing the existing atmosphere would be kind of silly.  I was thinking more using the trapar to hold in more atmosphere than the planet could realistically hold on to otherwise.  And yeah, you'd need to import/manufacture a lot of air so its definitely a very long term thing.
In any case, so long as we end up with something breathable at ground level we can call the MTP a success.
--
"Did you hear about the guy who bought a Web TV unit, and on the way
home from the store he stopped at the bank. When he got back to his car
he found it had been broken into, and there were now 2 Web TV units in
the back seat."   -(Larry Martell)
Ultimately atmosphere loss to the solar wind or low gravity are very long term problems, like longer than Fenspace as a civilization or even humanity as a species will likely exist long term. Even if we get Mars up to a full 1 atm at sea level, it would take tens of thousands of years for the atmosphere to degrade back to unbreathable levels left to its own devices.

At this stage, holding onto the air is not a big problem. Getting it to the point where it's more than just an annoyance is. It's an interesting irony of handwavium that the more ridiculous feats of planetary engineering, like artificial magnetospheres and planetary rotation management, are easy to pull off but the basic stuff like atmosphere and water generation are still long slogs.
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
Okay. Remedial lessons needed here, because I'm gonna try and cook up a blue hair moment. I'm not thinking of an over-night solution, but something that works within a decade or two would be very nice, eh?

I know we got a high concentration of CO2, but not a whole lot of atmosphere, period. We need lotsa oxygen and nitrogen... what else?
Ok, all this data is from Wikipedia, consider it as accurate as anything from there is.
Martian Atmosphere:
Mean pressure: 0.6 kPa
95% carbon dioxide, 3% nitrogen, 1.6% argon and contains traces of oxygen, water and methane.
A note about the methane, it has a a concentration of about 30 ppb by volume;[url=http://en.wikipedia.org/wiki/Mars#cite_note-methane-94][/url] it occurs in extended plumes, and the profiles imply that the methane was released from discrete region.  Also the implied methane destruction lifetime may be as long as about 4 Earth years and as short as about 0.6 Earth years. This rapid turnover would indicate an active source of the gas on the planet.
Earth's Atmosphere:
Mean pressure: 101.325 kPa
78% nitrogen and 21% oxygen, with trace amounts of water vapor, carbon dioxide and other gaseous molecules.
So we've got a lot of CO2, but we can crack at least some of that to produce more oxygen.  The nitrogen is more of an issue, and either way, there's a lot less atmosphere on Mars than we need so it will have to be imported from somewhere.  This is as opposed to the VTP where the problem is less the lack of atmosphere and more the wrong kind.
--
If at first you don't succeed, put someone else's initials on
the worksheet.
Okay, first, my suggestion about the trapar was not to use it to directly add atmospheric density, but rather as a layer of saran wrap around the entire planet to keep the freshness in and the vacuum out.

Second... we have power to burn in any form that we want. Plus we need to add water to Mars anyway. So why not get more water than we need and crack half or more of it with electrolysis? So we grab iceteroids from Saturn's rings or the Oort cloud (more likely the latter, as the ring fragments are generally rather small). Those not being used for oceans remain in orbit, where they are broken up and fed into electrolysis satellites powered by (energy source of choice); oxygen is fed down through the trapar via a skyhook-like pipeline arrangement and the hydrogen -- well, it can either be set loose in space, refined for fusion fuel, or sold as-is for H-powered vehicles. I won't begin to pretend I can work out the math, but assuming we're using the efficiency of handwavium throughout the process, shouldn't we be able to get a good rate of production?

Nitrogen we handle much the same way; comets are a mix of water and various organic gasses, like ammonia and methane. We tow a few comets in, break them down and feed them into orbital processors, crack the gasses, pipe down the stuff we want in the air, and come up with some efficient way of using up the leftovers.

Sound good? Or am I just blathering?
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.
Methane and the other ethanes; crack 'em down for O2, sure.
Ammonia is too valuable as fertilizer; ship it down in bulk for farming.
And, of course, plant cultures of blue-green algae *everywhere*; the stuff will actually grow in Mars' current atmosphere, given a bit of water, and convert CO2 to O2 while it does.
Shipping CO2 from Venus to Mars will allow for increasing the atmospheric density fairly quickly.
The thing about the trapar layer is, as far as I can tell, it doesn't seem to do anything. If it was dense enough to keep atmosphere in, it wouldn't hold the necessary altitude - it'd be more like a thick, low fog than anything else. And if it was the same relative density as the rest of the atmosphere, it'd be escaping off into space too. Sorry guys, I'm just not seeing it.

As for the oxygen, it's already there (We think, we're pretty sure.) locked up in the regolith and in the icecaps. Once that starts heating up, more and more of that will get released. Plus, once the atmosphere is thick enough to support plants the O2 levels will shoot up thanks to widespread photosynthesis. It's the buffer gas that's the tricky part, since it makes up most of the atmosphere (five quintillion tons, fix that number in your mind).

For buffer gasses & other stray organics, the solution is the stuff in the outer system. A Kuiper object about the size of Ceres that's mostly water and ammonia ices, plus a little methane ice, would do the job nicely. Getting it to Mars would be a bitch and a half, and there'd be some interesting gravitational problems to deal with as well, but that would take care of the missing volatiles. Getting it into the Martian atmosphere is as simple as dragging chunks through the upper atmosphere and letting 'em boil down.

(The hot new sport of questionable sanity: comet drag racing!)
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
M Fnord Wrote:(The hot new sport of questionable sanity: comet drag racing!)
"I live my life a quarter of a light year at a time....
  
Ebony the Black Dragon
http://ebony14.livejournal.com

"Good night, and may the Good Lord take a Viking to you."
M Fnord Wrote:(The hot new sport of questionable sanity: comet drag racing!)
And how did this fun bit of insanity get started?  (^_^)
Benjamin:  Yo!  KJ!  Bet ya can't beat me there!
The rest, as they say, is history.  Wink
  
Actually, there might be a use for trapar... but only on a short-term basis. Use it as a cover over Valles Marineris and terraform the valley before terraforming the rest of the planet. That way, the Marineris opal miners can work in relative comfort until the valley is flooded - inside has Earth-normal atmosphere, outside has Mars-normal atmosphere. And if there are any problems with the terraforming process itself, they'll show up "in testing" when the valley is terraformed.

Heck, it might even pay for itself, depending on how much Martian opals sell for...
--
Rob Kelk
"Governments have no right to question the loyalty of those who oppose
them. Adversaries remain citizens of the same state, common subjects of
the same sovereign, servants of the same law."

- Michael Ignatieff, addressing Stanford University in 2012
Hell, not just the mining facility, but just about anywhere else with a sizable settlement. Cheaper and easier to erect than domes, plus it's low maintenance. Can you imagine how quickly the population on Mars would explode?
I'm still not seeing it. I've looked up every bit of info on trapar that I could find - dug out my old Eureka Seven bootlegs and everything - and all I can see is "it's fog - but you can surf on it!" Domes make more sense, tents make more sense, forcefields make more sense. I just don't get the fascination with making fog you can surf on into something that replaces domes, tents or forcefields. Sorry.
Mr. Fnord interdimensional man of mystery

FenWiki - Your One-Stop Shop for Fenspace Information

"I. Drink. Your. NERDRAGE!"
I can see the point that other things make more sense... but like James May's Toy Stories, some of the things done could very well be done just because "it's gonna be effin' COOL". It's only after the spectacular, but surprisingly non-fatal, failures that the fen involved will come to their senses. Tongue
--

"You know how parents tell you everything's going to fine, but you know they're lying to make you feel better? Everything's going to be fine." - The Doctor
Hey, Fnord? Don't be too literal about the source material. We're taking an idea and riffing on it, and what we might come out with at the end may not look anything like what went in at the beginning. I've never seen trapar before this thread, and nowhere else since, and all my ideas were based on just the idea of making a "lid" to hold air in. In the source it may be a fog, but what I was coming up with was a network of nano-sized force-field projectors that hover above the atmosphere.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.