What-If 0068: "Little Planet"

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Vroomfundel
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What-If 0068: "Little Planet"

Postby Vroomfundel » Tue Oct 22, 2013 1:49 pm UTC

http://whatif.xkcd.com/68/

If an asteroid was very small but supermassive, could you really live on it like the Little Prince?

Samantha Harper


Image

In orbit at jogging speed - how cool is that?

Reminds me of the previous one with the satellite entering its Roche limit but staying in one piece due to tensile strength. If you are on the surface - you just float away!
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Re: What-If 0068: "Little Planet"

Postby davidstarlingm » Tue Oct 22, 2013 1:54 pm UTC

Vroomfundel wrote:Reminds me of the previous one with the satellite entering its Roche limit but staying in one piece due to tensile strength. If you are on the surface - you just float away!

Like the Space Station?

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Re: What-If 0068: "Little Planet"

Postby SerMufasa » Tue Oct 22, 2013 2:22 pm UTC

Did I miss it, or did he not address whether a breathable atmosphere would extend far enough from the planet surface to make it livable?
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Re: What-If 0068: "Little Planet"

Postby jozwa » Tue Oct 22, 2013 2:23 pm UTC

I would have liked to hear how an atmosphere would function. Or is that too sciencey?

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Re: What-If 0068: "Little Planet"

Postby taemyr » Tue Oct 22, 2013 2:45 pm UTC

Overall I feel that Randall fails to answer the question in this case.


OTOH the answer might be simple.

The moon doesn't have an atmosphere. Because it lacks the mass to retain one. The escape velocity of the little planet is significantly lower.

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Re: What-If 0068: "Little Planet"

Postby davidstarlingm » Tue Oct 22, 2013 2:48 pm UTC

SerMufasa wrote:Did I miss it, or did he not address whether a breathable atmosphere would extend far enough from the planet surface to make it livable?

Yeah, I would have liked a more in-depth treatment too.

Interestingly enough, I started a thread about the minimum size of a habitable Earthlike planet on Sunday.

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Re: What-If 0068: "Little Planet"

Postby Tryptophanx86 » Tue Oct 22, 2013 2:57 pm UTC

Oh good, I'm not the only one who wondered why he didn't quite answer the question...

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Re: What-If 0068: "Little Planet"

Postby DaveMcW » Tue Oct 22, 2013 3:05 pm UTC

The average velocity of air is 500 m/s.(http://www.dummies.com/how-to/content/u ... ir-mo.html). You would need to cool it down to a few degrees Kelvin to keep it on the asteroid.

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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Tue Oct 22, 2013 3:13 pm UTC

I was writing about some of this stuff here:

http://space.stackexchange.com/question ... ity-device

The real quandary for this What-If is that there is no obvious material to make these superdense asteroids. Gauss' Law tells us how much mass you'll need, and it is shockingly simple. You find that the mass of the asteroid per surface area must be the same as Earth in order to have Earth's gravity. The calculation is:

(mass of Earth)/(4*Pi*(radius of Earth)^2) = 12 million tonnes per square meter

That's umm... a lot. Sheetrock is about 20 kg per square meter, or 0.02 tonnes. Such an asteroid, suitable for our Little Prince, needs to be absurdly dense. Even if you load it up with Uranium or Osmium, it will fall short. Even a black hole would be unsuitable for a rock as small as this recent What-If because of Hawking radiation. Sure, it would physically work, but once you start the thought experiment, it is actively in the process of a giant x-ray explosion.

What's more interesting is the fact that there is no physical law that prevents such a rock. We just don't know of any material that would work for it. Neutron stars are nice, but since they're held together by gravity, there's little indication that it would hold together well when you scale the mass down. But then again, a neutron star is really more dense than we need. We would like some non-atomic matter that behaves nicely and is really really high density. Maybe if you replaced a material's electrons with muons (which is a nice way to achieve fusion btw), then it would contract the material and make it suitable. But you'll also have to limit the heat production, since such a small body won't have nicely behaved tectonics. It'll just all turn into lava. Then boil away. These requirements are impossible to meet with what we know today, but our knowledge doesn't preclude something that could work. Maybe a supercooled material could do this.

But the atmosphere...

The "gap" between the surface and space for the air is dictated by the gravitational potential. This is the criteria Earth had to fit to keep the sun from boiling off its upper atmosphere Hydrogen too fast, so that it could support life. Earth had to have its large gravitational potential in order for us to be here. As you decrease the size, this potential changes proportional to the square of escape velocity. For Earth this is (11,000 m/s)^2, and for the Little Prince planet is is (5 m/s)^2. If a tossed wrench can fly off the planet, so can a gas molecule.

But why not just build a pressure vessel around it? It can't be that hard, considering its already packed with exotic matter. The only issue is that this can't really be stable. It would be a superdense asteroid bouncing around inside a bubble. But given that you accomplished that, you could play basketball in this strange place. You would probably want a barrier to keep your ball from floating away into space anyway.

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Re: What-If 0068: "Little Planet"

Postby Plasma Man » Tue Oct 22, 2013 3:41 pm UTC

It would probably be hard to play basketball on this asteroid. I imagine it would probably be quite hard to accurately throw a ball that's affected by tidal forces. Best just to stick to dunking it.
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Re: What-If 0068: "Little Planet"

Postby wisnij » Tue Oct 22, 2013 3:56 pm UTC

In Wil McCarthy's Queendom of Sol series, there are little artificial planets like this (called "planettes") made with a core of neutronium stabilized with diamondoid and plot magic. Once you're willing to handwave the stable neutronium thing, the rest of it works out pretty well. (They also have tiny stars built in a similar way -- neutronium, wrapped in wellstone, wrapped in fusing hydrogen.)
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Re: What-If 0068: "Little Planet"

Postby rhomboidal » Tue Oct 22, 2013 4:06 pm UTC

Wait, I thought Tayshaun Prince signed with the Grizzlies...?

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Re: What-If 0068: "Little Planet"

Postby cellocgw » Tue Oct 22, 2013 4:16 pm UTC

DaveMcW wrote:The average velocity of air is 500 m/s.(http://www.dummies.com/how-to/content/u ... ir-mo.html). You would need to cool it down to a few degrees Kelvin to keep it on the asteroid.

Nobody said the air on this microplanet was moving. After all, it'd need something to make it move ("a body at rest" etc).
So if the atmosphere is static, and there's a force of 1G at the planet's surface, and after all gravity obeys the 1/r^2 law, I don't see any reason the atmosphere, once in place, wouldn't extend just as far as it does on earth.
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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Tue Oct 22, 2013 4:43 pm UTC

cellocgw wrote:
DaveMcW wrote:The average velocity of air is 500 m/s.(http://www.dummies.com/how-to/content/u ... ir-mo.html). You would need to cool it down to a few degrees Kelvin to keep it on the asteroid.

Nobody said the air on this microplanet was moving. After all, it'd need something to make it move ("a body at rest" etc).
So if the atmosphere is static, and there's a force of 1G at the planet's surface, and after all gravity obeys the 1/r^2 law, I don't see any reason the atmosphere, once in place, wouldn't extend just as far as it does on earth.


The atmosphere would extend to the same altitude as it does on Earth, and then much higher. That's the problem - it extends to infinity. The gas molecules have to be moving, because that's how gases work. If the gas was cooled to something like 0.0001 Kelvin, then okay, maybe it will behave as you suggest. The problem is that humans have these darn biological limitations and if it gets too far from 293 K they'll start complaining, or die.

So if your planet is intended to have humans walk on it without a spacesuit, it needs to have moving gas molecules, and those need to be well below escape velocity, which they clearly are not here. The alternative way to look at it is to think of pressure, and ignore gas molecule motion itself. Pressure decreases with greater altitude, but really with gravity gradient. The issue is that the gravity gradient isn't large enough between the surface and infinity. If you assume the surface pressure is at Earth sea level pressure, then at infinity altitude it will still be close to that value. If you have a back-pressure far away from the planet, that's not a problem. But we keep assuming that this exists in space, and that's a vacuum, so it will cause the atmosphere to float away.

But hey, we don't have to assume that. We can take this to be Virga - a large zero gravity world that has a fairly constant atmosphere.

http://www.kschroeder.com/my-books/sun-of-suns

This planet will sit in that world, happy as a clam with people playing basketball on it. This author may have even written such an object into his world.

wisnij wrote:In Wil McCarthy's Queendom of Sol series, there are little artificial planets like this (called "planettes") made with a core of neutronium stabilized with diamondoid and plot magic. Once you're willing to handwave the stable neutronium thing, the rest of it works out pretty well. (They also have tiny stars built in a similar way -- neutronium, wrapped in wellstone, wrapped in fusing hydrogen.)


Well you do have to hand wave a lot. The semi-empirical formula gives the basis for how nuclei act.

Image

If you just throw lots of neutrons at the problem, you make A large, and Z small. Then it's the asymmetry term that kills you, which is nearly proportional to A. That comes from the Pauli Exclusion Principle. Maybe if you got enough neutrons, this would change in nature (although neutron stars would seem to disagree). It seems that you would somehow have to get the coefficient lower than the first term - which it is not currently. The best explanation would be to invent some new kind of nucleon that we haven't seen yet. Then pepper the neutron-filled ball with it.

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Re: What-If 0068: "Little Planet"

Postby peewee_RotA » Tue Oct 22, 2013 6:00 pm UTC

In fact, that's where their name comes from—the word asteroid means "star-like."

I'm pretty sure "asteroid" means something that Mark McGwire takes.
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Re: What-If 0068: "Little Planet"

Postby gmalivuk » Tue Oct 22, 2013 6:33 pm UTC

cellocgw wrote:
DaveMcW wrote:The average velocity of air is 500 m/s.(http://www.dummies.com/how-to/content/u ... ir-mo.html). You would need to cool it down to a few degrees Kelvin to keep it on the asteroid.

Nobody said the air on this microplanet was moving. After all, it'd need something to make it move ("a body at rest" etc).
So if the atmosphere is static, and there's a force of 1G at the planet's surface, and after all gravity obeys the 1/r^2 law, I don't see any reason the atmosphere, once in place, wouldn't extend just as far as it does on earth.
The 500m/s average for Earth is entirely a result of temperature (aka average kinetic energy). Actual windspeed is usually a small fraction of that.
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Re: What-If 0068: "Little Planet"

Postby altay » Tue Oct 22, 2013 7:22 pm UTC

Zassounotsukushi wrote:if your planet is intended to have humans walk on it without a spacesuit, it needs to have moving gas molecules, and those need to be well below escape velocity, which they clearly are not here.

What if we built a glass dome around the atmosphere? It would allow us to contain the atmosphere, and the atmosphere would help keep it in position. As long as the planet and glass are perfectly uniform it shouldn't experience a net force, but that's clearly not the case if we have inhabitants. Still, a nice glass sphere around the tiny planet would do a sufficient job containing the atmosphere, wouldn't it?

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Re: What-If 0068: "Little Planet"

Postby Djehutynakht » Tue Oct 22, 2013 7:56 pm UTC

Part of me thinks that Randall didn't completely answer the question.

The other part of me says that if you read the Little Prince it kinda recommends that you not obsess over that stuff.

I should go on an adventure. The foliage is very pretty right now.

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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Tue Oct 22, 2013 8:25 pm UTC

altay wrote:
Zassounotsukushi wrote:if your planet is intended to have humans walk on it without a spacesuit, it needs to have moving gas molecules, and those need to be well below escape velocity, which they clearly are not here.

What if we built a glass dome around the atmosphere? It would allow us to contain the atmosphere, and the atmosphere would help keep it in position. As long as the planet and glass are perfectly uniform it shouldn't experience a net force, but that's clearly not the case if we have inhabitants. Still, a nice glass sphere around the tiny planet would do a sufficient job containing the atmosphere, wouldn't it?


The glass dome is basically what I was getting at.

And actually, I officially change my position on the stability of this construction. The glass dome would tend to remain in place, and not bump up against the asteroid. Of course, you could just tether it with a rope, but something about that sounds less romantic.

The asteroid won't exert any gravitational force on the glass dome itself because of the shell theorem. We're left with the movement of the air to account for. We start out with the asteroid directly in the center of the spherical glass dome. If it moves to the side, then some of the air has to increase altitude relative to the asteroid. This takes work, and we can see that the system is at lowest energy with the asteroid remaining in the center of the glass dome. Of course it would be a fairly small effect, but with no other forces pushing on the dome, it'll keep the asteroid dead-center.

I also like the idea of the thing floating in a nearly endless atmosphere like Virga. That is much more romantic, not to mention, there's no need for structural materials and the stability issues are totally worked out. Virga is claimed to be close to the size of Earth itself, and consists of continuous atmosphere. The author proposes that the walls are made of carbon nanotubes, which is completely pointless. Yes, that would be of sufficient strength to hold in the atmosphere, but you don't need anything of the sort. If the outer envelope were just ordinary lead a few kilometers across, then it will sit there perfectly stable. Considering that lead is the end-state element of matter in our universe, I think it should be obviously plentiful in the future from the perspective of sci-fi writers.

Within such a huge world, items floating around in it would gravitate to the center. That's because the outer shell is canceled by the shell theorem, and the air itself has a lot of mass, but you also fly through the air. That makes everything a long-period harmonic oscillator about the center. That is specifically...

2*Pi/sqrt(4/3*Pi*G*(1.3 kg/m^3)) = 3.8 days

But that's kind of tangential here. What I think is more interesting is putting several of these superdense asteroids near each other. Then, as you jump and hit escape velocity, you can potentially fall down onto another tiny planet. Or even more interesting, you can bounce around the system in some kind of crazy trajectory like we use in rocket science. Just don't let the tiny planets hit each other. They have so much mass that they'll crush anything that gets in-between, and also each other. Then whatever superdense material lies at the center might combine, which probably won't be good. I would suspect that would lead to nuclear explosions, but I don't have the specifics of this variety of unobtainium. Basically, the kind of situation you're looking at is like Super Mario Galaxy. When you land on a planet, you also won't affect its trajectory particularly. They're mass scale is just so much greater than the air or you.

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Re: What-If 0068: "Little Planet"

Postby rmsgrey » Tue Oct 22, 2013 9:30 pm UTC

Zassounotsukushi wrote:Considering that lead is the end-state element of matter in our universe, I think it should be obviously plentiful in the future from the perspective of sci-fi writers.


I thought Iron-56 was the most stable nucleus - in fact, some spot research shows that all known isotopes of lead have decay mechanisms...

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Re: What-If 0068: "Little Planet"

Postby bmonk » Tue Oct 22, 2013 9:33 pm UTC

About small, hyperdense moons or asteroids--I remember reading a story many, many years ago--early '70s?--about a person who leased several hundred particular asteroids, because they were made out of "neutron star matter" and could be used to make habitable moons for very rich persons. Even then I wondered if the matter would explode without a sufficient gravity and pressure well to hold it together. But it was an interesting idea.
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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Tue Oct 22, 2013 9:46 pm UTC

rmsgrey wrote:
Zassounotsukushi wrote:Considering that lead is the end-state element of matter in our universe, I think it should be obviously plentiful in the future from the perspective of sci-fi writers.


I thought Iron-56 was the most stable nucleus - in fact, some spot research shows that all known isotopes of lead have decay mechanisms...


Well that was embarrassing. Should have checked my binding energy per nucleon chart - yes, it's Iron which is the lowest energy. Lead is often the end-state of alpha decay chains, which is irrelevant, but I often have the mental fart of switching the two. It's Iron if you're interested in the universe after some super-intelligence saps up all the nuclear energy, doing simulations of their ancestors who screw up dumb things like this.

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Re: What-If 0068: "Little Planet"

Postby ucim » Wed Oct 23, 2013 12:01 am UTC

bmonk wrote:I remember reading a story many, many years ago--early '70s?--about a person who leased several hundred particular asteroids, because they were made out of "neutron star matter"
Who did he lease them from?

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Re: What-If 0068: "Little Planet"

Postby gene123 » Wed Oct 23, 2013 1:25 am UTC

I have a variation of this question to the math/physics/geology/evolutionary biology geeks here...

Let's not consider exotic matter not possible to sustain under normal temperature/pressure conditions, and instead take the most (or one of the most) dense non-radioactive elements (namely osmium).

If the entirety of Earth was made out of osmium (except, say, the topmost 3km of soil/water needed to sustain life, which is probably small enough to be ignored in calculations to 3 significant digits, but feel free to prove me wrong!), at 25.59 g/cm^3, down from Earth's current mean density of 5.52g/cm^3...

1. How big would the Earth radius be, down from the current 6,371km, in order for the surface gravity to be identical to that of current Earth? The math would have to involve both the increased density (which increases surface gravity) and a smaller radius (which _further_ increases surface gravity), so I'm not sure what the formula would be to calculate this.

2. Ignoring the question of whether such a planet could have formed to begin with, _if_ it did, would it be possible for life and civilization to (a) evolve and (b) sustain itself on such a planet? We can assume a proportional decrease in atmosphere in order to bring down surface pressure to be identical to current one, assuming such an atmosphere could (a) form and (b) sustain itself.

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Re: What-If 0068: "Little Planet"

Postby gmalivuk » Wed Oct 23, 2013 1:38 am UTC

Five times the density means five times the gravity at the current radius, and then holding density constant gravity scales with radius, so 1/5 the radius gets back to Earth gravity. (A bit more at the stated density, which is a bit less than 5x the current value, but then a bit less because compression under the immense weight would raise the density from what it is under normal circumstances.)

I don't know of any reason life couldn't evolve on such a planet, seeing as we don't really know what's required for it to evolve in the first place. At 1/25 the mass and 1/5 the radius, the escape velocity at the surface would be sqrt(1/5) what it is on Earth, or about 5 km/s. That's proportionally about halfway between Earth's and the Moon's, so I don't know what it would really mean for holding onto an atmosphere.
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Re: What-If 0068: "Little Planet"

Postby chris857 » Wed Oct 23, 2013 3:23 am UTC

The real question is what would it be like on a KSP planet? And what could they be made of?

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Re: What-If 0068: "Little Planet"

Postby DaveMcW » Wed Oct 23, 2013 6:37 am UTC

gmalivuk wrote:At 1/25 the mass and 1/5 the radius, the escape velocity at the surface would be sqrt(1/5) what it is on Earth, or about 5 km/s. That's proportionally about halfway between Earth's and the Moon's, so I don't know what it would really mean for holding onto an atmosphere.

That is the Mars scenario, decent gravity but no spinning iron core to generate a magnetic field. Without a magnetic field to protect against the solar wind, the atmosphere would be slowly stripped away over millions of years.

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Re: What-If 0068: "Little Planet"

Postby Arky » Wed Oct 23, 2013 7:36 am UTC

I never thought to see an NBA joke in XKCD, even in the alt-text to a What If. Well played!
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Re: What-If 0068: "Little Planet"

Postby SikaGrr » Wed Oct 23, 2013 8:03 am UTC

Can anyone explain what is the snake that swallowed a hat actually representing?

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Re: What-If 0068: "Little Planet"

Postby Peregrine Crow » Wed Oct 23, 2013 8:33 am UTC

It's a snake that swallowed an elephant, but all the adults that look at it just see a hat.

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Re: What-If 0068: "Little Planet"

Postby Klear » Wed Oct 23, 2013 8:34 am UTC

gmalivuk wrote:
cellocgw wrote:
DaveMcW wrote:The average velocity of air is 500 m/s.(http://www.dummies.com/how-to/content/u ... ir-mo.html). You would need to cool it down to a few degrees Kelvin to keep it on the asteroid.

Nobody said the air on this microplanet was moving. After all, it'd need something to make it move ("a body at rest" etc).
So if the atmosphere is static, and there's a force of 1G at the planet's surface, and after all gravity obeys the 1/r^2 law, I don't see any reason the atmosphere, once in place, wouldn't extend just as far as it does on earth.
The 500m/s average for Earth is entirely a result of temperature (aka average kinetic energy). Actual windspeed is usually a small fraction of that.


That reminds me of the observation that cold wind is made of slow-moving air which is moving fast.

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Re: What-If 0068: "Little Planet"

Postby Chebyshev » Wed Oct 23, 2013 12:56 pm UTC

I love that last color image. Is there some way we could get a higher resolution version?

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Re: What-If 0068: "Little Planet"

Postby davidstarlingm » Wed Oct 23, 2013 1:38 pm UTC

What is the actual average speed of an oxygen or nitrogen molecule over its mean free path at STP?

Can we conclude that with a sufficiently powerful magnetic field, any size and density of atmosphere is more or less possible (given a Mars-like planet, not a LP planet).

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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Wed Oct 23, 2013 4:19 pm UTC

davidstarlingm wrote:What is the actual average speed of an oxygen or nitrogen molecule over its mean free path at STP?

Can we conclude that with a sufficiently powerful magnetic field, any size and density of atmosphere is more or less possible (given a Mars-like planet, not a LP planet).


Well no, and no.

The specifier "over its mean free path" doesn't make a lot of sense there. For a simple ideal gas model (which I'm sure if what you're looking for), temperature and molecular weight determines speed, which is around 400 m/s for an average Oxygen molecule at an average Earth temperature.

The magnetic field is only relevant in terms of the upper atmosphere's high energy molecules. There is an altitude at which the atmosphere reaches an absolute minimum temperature. If we didn't have the sun's rays and particles then this limit would not exist, and the gravity well necessary to sustain a low leak rate would be comparatively little.

But there are two very different actors - photons and protons. Photons are all clustered around the same temperature of 5500 Kelvin or something like that. The protons from the sun are buzzing through at much higher (crazy) energies. If a gas molecule absorbs a photon in Earth's upper atmosphere, it is likely to return to the atmosphere. If it absorbs a proton and is directed in the direction of space, it's gone because the proton will kick it off at well above escape velocity. For the photon, it's not so clear. But even with the protons, it doesn't follow the familiar gas laws, because it becomes an "exosphere", where collisions are extremely rare, so gas molecules just wander around on their own for most of their time.

A magnetic field only prevents erosion from charged particle radiation. It doesn't matter how strong it is, light itself will still get through, and that sets a different type of requirement. If you were in a system that had a brown dwarf star, the photon energy would be less, and a lower gravity well would be necessary - even for the same surface temperature (because surface and upper atmosphere T are very different things). If you were a rogue planet wandering through interstellar space, you would have yet a different kind of limit. But all these "limits" aren't really limits, but just leak rates given the gravity well. For the recent What-If, the leak rate for that gravity well is so great that it would be gone before you had time to scream. We can establish that with the most optimistic assumptions, because the size is so absurdly small.

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Re: What-If 0068: "Little Planet"

Postby davidstarlingm » Wed Oct 23, 2013 6:09 pm UTC

Zassounotsukushi wrote:A magnetic field only prevents erosion from charged particle radiation. It doesn't matter how strong it is, light itself will still get through, and that sets a different type of requirement. If you were in a system that had a brown dwarf star, the photon energy would be less, and a lower gravity well would be necessary - even for the same surface temperature (because surface and upper atmosphere T are very different things).

For a photon flux on the order of what we get from our sun, then, what's the minimum escape velocity in order to maintain a stable atmosphere over a few million years at least?

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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Wed Oct 23, 2013 7:01 pm UTC

davidstarlingm wrote:
Zassounotsukushi wrote:A magnetic field only prevents erosion from charged particle radiation. It doesn't matter how strong it is, light itself will still get through, and that sets a different type of requirement. If you were in a system that had a brown dwarf star, the photon energy would be less, and a lower gravity well would be necessary - even for the same surface temperature (because surface and upper atmosphere T are very different things).

For a photon flux on the order of what we get from our sun, then, what's the minimum escape velocity in order to maintain a stable atmosphere over a few million years at least?


Neglecting charged particle radiation? Well you could do the calculation for escape of a Hydrogen atom. Use the temperature of the sun, and ask what the speed would be from a direct-on absorption of a photon.

sqrt((3 * k * (5778 kelvin)) / (1 amu)) = 12,005 m / s

Earth escape velocity is 11,200 m/s. I do believe this is not a coincidence. Now there are several factors that make this calculation non-ideal:

  • There is still UV radiation, that has more energy than the average
  • Few photons will hit a gas molecule in a direction and scatter at an angle sufficient to impart anywhere near to this full velocity to it
  • Not all atoms it hits will be Hydrogen anyway
  • Not all atoms that get all that speed will be high enough up to make it to space without hitting more gas molecules

It's still quite compelling. It tells us that the loss of atmosphere due to the sun's light might increase rather precipitously if the Earth was even a little bit smaller.

But that doesn't answer your question. Earth's requirement wasn't just for a million years. Its requirement was an anthropic one, that life had the ability to evolve, which entailed billions of years. Many people think that a terraformed Mars could hold an atmosphere for thousands or millions of years. Maybe it actually did this in the past. Solar radiation would cause it to leak to space, but I guess it's sufficiently slow for that scale.

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Re: What-If 0068: "Little Planet"

Postby gmalivuk » Wed Oct 23, 2013 7:21 pm UTC

Is high-atmosphere hydrogen monatomic? If it's H2, then we'd only have 9km/s or so. Which is "good" news for Venus, with its lower escape velocity but more than adequate atmosphere.
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Re: What-If 0068: "Little Planet"

Postby davidstarlingm » Wed Oct 23, 2013 7:26 pm UTC

What if the escape velocity is lower than what you'd need to hang onto hydrogen and helium, but higher than what you need to hang onto diatomic oxygen and nitrogen?

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Re: What-If 0068: "Little Planet"

Postby gmalivuk » Wed Oct 23, 2013 7:46 pm UTC

Actually, we *do* lose helium from Earth in exactly this way. It doesn't react with anything, and it's lighter than almost everything else in the atmosphere, so it goes up to the top and evaporates away. Hydrogen, on the other hand, reacts strongly with things and thus typically ends up in much heavier molecules than H2, so it's safe from the same fate.

(4amu would get an average of only 4km/s from a solar photon, but of course the sun puts out a lot of photons and a lot of them have far more energy than average)

Edit: To get a helium nucleus from stopped to escape velocity requires about 2.5 eV, which any photon with a wavelength shorter than about 500nm will have. The Sun puts out about 25% of its energy at this wavelength or lower, which pretty much means He at the top of the atmosphere doesn't last long there. On the other hand, even monatomic nitrogen is 3.5 times more massive and so requires 3.5 times the energy, or a wavelength below 143nm. Quite a bit less than 0.01% of solar energy is radiated as photons with shorter wavelengths than this, so other atmospheric gases are safe.
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Re: What-If 0068: "Little Planet"

Postby Zassounotsukushi » Wed Oct 23, 2013 9:30 pm UTC

gmalivuk wrote:Is high-atmosphere hydrogen monatomic? If it's H2, then we'd only have 9km/s or so. Which is "good" news for Venus, with its lower escape velocity but more than adequate atmosphere.


This general issue is something I've struggled with a great deal with space exploration topics. It just gets complicated. My primary thinking is that we might just have stray Hydrogen ions by themselves, and those could get hit. That would, of course, decrease the rate of this type of event by many orders of magnitude. There's also the issue that even an H2 molecule that gets stuck in cislunar space might just be blown away by the solar wind (charge interactions), or sunlight. I don't actually know how easily that would happen. If molecules are not regularly disturbed (which I think may be the case), then a molecule rocketed off the top of our atmosphere at 9 km/s will be a Newton's cannonball - meaning that it will rejoin the atmosphere in due time.

But the concept of a stray Hydrogen or Helium atom getting blow away has quite a few orders of magnitude reduction in event frequency by itself. The Helium atom is harder to blow away, but the sun's spectrum still has plenty of photons which are 2x or 3x as energetic as the mean, so we have to recognize that has some event frequency. I feel like the real question is what the photo-absorption mechanism is in the first place, because there's plenty of sunlight.

Ultimately, this is the picture it fits into, these are mass flows in and out of Earth's atmosphere.

Image

Now that I revisit this, the space loss is quite unimpressive. The ISS is about 500 tonnes, which is 5x105 kg. So space only gives us like two ISS's worth of Hydrogen every year. That sounds like the least important fact you might ever learn, but over billions of years, maybe it affected the elemental availability to life?

Oh right, but the Hydrogen gas dissociation energy. I looked that up, and put in terms of velocity, it is this:

sqrt((2 * (4.52 eV)) / (2 amu)) = 20,883.336 m / s

Chemical bonds have a lot of energy. Although, this is what it takes to break two H atoms apart, so it's not really useful for this discussion. Even if a photon from the sun broke apart a H2 molecule, they wouldn't have much kinetic left after that. But we know the space loss is rather low anyway, so I'm kind of beating a dead horse.

Also, Helium use rate is something like 15 million kg per year (by first google result). So if my numbers were right (and they might not be), the Helium isn't actually floating into space. It's really just accumulating in our upper atmosphere, and it'll take the sun a long time to blow it away (okay, maybe 1000s of years, which is like a sneeze to the sun).

EDIT: last post kind of beat me to some of these points, which I didn't see until I submitted.


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