Lower bound for Earthlike planet

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davidstarlingm
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Lower bound for Earthlike planet

Postby davidstarlingm » Sun Oct 20, 2013 1:56 pm UTC

We bring up planet sizes quite frequently on this forum, but this is a question I hadn't seen addressed before, so I thought I'd ask it.

What's a realistic lower bound in radius for a planet that:
  1. Has one g of gravity
  2. Could conceivably have formed naturally
  3. Has an earthlike atmosphere oceans, mountains, weather, and plants
  4. Could support Terran life without modification
It's easy to come up with conditions 1 and 2. A pure iron planet is the densest sort of planet that can possibly form under natural circumstances. Iron is 43% denser than the Earth's mean density; in order to have Earthlike gravity, such a planet would need to have 70% the radius of Earth (which, for the record, is still really really large). But obviously a pure iron planet could not sustain life.

How much smaller and denser can we make the Earth without it ceasing to be Earthlike?

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Re: Lower bound for Earthlike planet

Postby Izawwlgood » Sun Oct 20, 2013 2:27 pm UTC

I'd be more interested in the range of g you could still sustain life on. If you go higher, you'd start seeing smaller organisms form, see fewer flying organisms at that, and if you go too high, you prevent terrestrial life from developing at all.

Conversely, you only really need to maintain high enough g to hold an atmosphere and water.
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Re: Lower bound for Earthlike planet

Postby Tass » Sun Oct 20, 2013 2:43 pm UTC

Izawwlgood wrote:Conversely, you only really need to maintain high enough g to hold an atmosphere and water.


High enough escape velocity, surface gravity is pretty irrelevant to keeping an atmosphere.

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Re: Lower bound for Earthlike planet

Postby Izawwlgood » Sun Oct 20, 2013 3:20 pm UTC

Surely the two are related? Can a planet have high escape velocity but low surface gravity?
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Re: Lower bound for Earthlike planet

Postby Tass » Sun Oct 20, 2013 3:53 pm UTC

Izawwlgood wrote:Surely the two are related? Can a planet have high escape velocity but low surface gravity?


Yes. Look at Saturn.

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Re: Lower bound for Earthlike planet

Postby lightvector » Sun Oct 20, 2013 3:54 pm UTC

Surface gravity should scale as M/r^2, where M is the planet mass and r is the radius. Escape velocity should go as the square root of the necessary kinetic energy for escape, which, integrating, scales as M/r.

So you can increase the escape velocity pretty much arbitrarily while holding the surface gravity constant by making the planet larger and more massive but less dense. Although of course they should still be somewhat correlated in practice.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Sun Oct 20, 2013 4:20 pm UTC

Izawwlgood wrote:I'd be more interested in the range of g you could still sustain life on. If you go higher, you'd start seeing smaller organisms form, see fewer flying organisms at that, and if you go too high, you prevent terrestrial life from developing at all.

I was thinking of what you could change without a human realizing it was a different planet.

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Re: Lower bound for Earthlike planet

Postby Izawwlgood » Sun Oct 20, 2013 6:59 pm UTC

Tass wrote:
Izawwlgood wrote:Surely the two are related? Can a planet have high escape velocity but low surface gravity?


Yes. Look at Saturn.

Hardly really applicable then given we're not talking about gas giants?
I'm still uncertain though how that works? Is the high escape velocity due to atmospheric drag getting off Saturns 'surface'?
davidstarlingm wrote:
Izawwlgood wrote:I'd be more interested in the range of g you could still sustain life on. If you go higher, you'd start seeing smaller organisms form, see fewer flying organisms at that, and if you go too high, you prevent terrestrial life from developing at all.

I was thinking of what you could change without a human realizing it was a different planet.
Oh, I wager people are fairly sensitive to gravity changes, as least able to detect them initially. Assuming you're not talking about raising people on this planet, I think at least some humans have a fairly reasonable grasp of distances as it relates to the Earths curvature. If you put someone on a strikingly larger planet with the same g, someone may notice that the horizon seemed further away?

Do I have that right?
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Re: Lower bound for Earthlike planet

Postby starslayer » Sun Oct 20, 2013 10:07 pm UTC

Izawwlgood wrote:
Tass wrote:
Izawwlgood wrote:Surely the two are related? Can a planet have high escape velocity but low surface gravity?


Yes. Look at Saturn.

Hardly really applicable then given we're not talking about gas giants?
I'm still uncertain though how that works? Is the high escape velocity due to atmospheric drag getting off Saturns 'surface'?

No, it isn't. As lightvector said, surface gravity goes as M/r^2, while escape velocity goes as sqrt(M/r). Increasing the size and mass of the planet while lowering the density will result in higher escape velocity with about the same surface gravity. For terrestrial planets, there's only a certain range you can stick their densities (between pure iron and pure water, basically), but it's plausible for a more massive silicate planet or waterworld to maintain similar surface gravity to Earth.

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Re: Lower bound for Earthlike planet

Postby Tass » Sun Oct 20, 2013 10:07 pm UTC

Izawwlgood wrote:
Tass wrote:
Izawwlgood wrote:Surely the two are related? Can a planet have high escape velocity but low surface gravity?


Yes. Look at Saturn.

Hardly really applicable then given we're not talking about gas giants?
I'm still uncertain though how that works? Is the high escape velocity due to atmospheric drag getting off Saturns 'surface'?


It is applicable because the physics is the same. Sure it might be outside the parameter space that the OP was interested in. (As the ninja above points out terrestial planets kind of need densities between those of water and iron.)

Escape velocity has nothing to do with atmospheric drag. The high value is because of Saturns larger size. Of course in order to have the same surface gravity for a larger planet it will have to be less dense, but because of their different scaling this reduction in density is not enough to keep the escape velocity down. Saturn is heavy but so huge that it is not very dense, this allows it to have a gravity similar to Earths, but more than three times the escape velocity. Likewise you could have a small but very dense planet with the same gravity, but it would have a lower escape velocity.

Basically when you integrate the gravity you have to fight to escape, you find that the energy required is the same as if the surface gravity extended one planetary radius out. The escape energy becomes mgR. See this comic. The depth of the Earths well is its radius. The other bodies wells are their radii times there surface gravities measured in g's.

The result is that for a truly tiny planet to hold on to an atmosphere, it needs to be so dense that its gravity is actually stronger than earths. -The air has such a short distance to travel to freedom so the pull needs to be greater.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Mon Oct 21, 2013 3:58 pm UTC

Tass wrote:Escape velocity has nothing to do with atmospheric drag. The high value is because of Saturns larger size. Of course in order to have the same surface gravity for a larger planet it will have to be less dense, but because of their different scaling this reduction in density is not enough to keep the escape velocity down. Saturn is heavy but so huge that it is not very dense, this allows it to have a gravity similar to Earths, but more than three times the escape velocity. Likewise you could have a small but very dense planet with the same gravity, but it would have a lower escape velocity.

Basically when you integrate the gravity you have to fight to escape, you find that the energy required is the same as if the surface gravity extended one planetary radius out. The escape energy becomes mgR. See this comic. The depth of the Earths well is its radius. The other bodies wells are their radii times there surface gravities measured in g's.

The result is that for a truly tiny planet to hold on to an atmosphere, it needs to be so dense that its gravity is actually stronger than earths. -The air has such a short distance to travel to freedom so the pull needs to be greater.

Hmm. So atmospheric pressure is tied to escape velocity.

Does this mean that if you woke up tomorrow on an alien planet but detected no noticeable difference in atmospheric pressure or gravity, you could safely conclude that the alien planet had roughly the same escape velocity as Earth, meaning it had both Earthlike mass and Earthlike density?

Then again, would we even be able to detect differences in atmospheric pressure? I was up on Pike's Peak a week ago, and the air didn't actually feel thinner....though I was certainly winded after walking only a few dozen yards. Would we even be able to notice thinner air other than the lack of oxygen? Could a higher oxygen-nitrogen ratio make a significantly lower atmospheric pressure unnoticeable?

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Re: Lower bound for Earthlike planet

Postby Tass » Tue Oct 22, 2013 10:07 am UTC

davidstarlingm wrote:Hmm. So atmospheric pressure is tied to escape velocity.


Not really. A lot of other things matter. A planet needs a certain minimum escape velocity to be able to hold on to an atmosphere for geological timescales, but that is no guaranty that the air will be there. Venus is about the same size as Earth, but it has 90 times the atmosphere. Both planets are simply large enough to hold on to what is there. In addition Venus is hot enough to cook oxygen and carbon out of the ground as carbon dioxide in a feed back loop.

Another important thing is magnetic field. Contrary to popular belief we would not be fried by radiation without it, the atmosphere gives ample protection for that. What the field does protect is the atmosphere itself. An air molecule need not be able to escape from a planet on its own, if it can just get high enough to be blown away by the solar wind, and the magnetic field keeps the solar wind away.

Light gasses also escape easier than heavy, and they escape easier the hotter it is. The combination of high temperatures and small magnetic field, has allowed hydrogen to escape from Venus, leaving it without much water, while carbon dioxide and sulphuric acid are heavy enough to stay. Mercury is smaller and has lost practically all. The moon is way to small to hold on to an atmosphere for more than a few million years, a comparative blink of an eye, leaving it with a pressure not much above interstellar space. However, it does still take a few million years for air to escape it, and there is a concern if we begin large scale operations on the moon and use rockets too much, we might ruin the hard vacuum there for the (for humans) foreseeable future.

Titan is quite small, but it is also very cold and far from the sun, which has allowed it to keep a dense atmosphere with lots of hydrogen.

Basically, you planet just has to be large enough, once it is that you are quite free to postulate pretty much any atmosphere you like.

davidstarlingm wrote:Then again, would we even be able to detect differences in atmospheric pressure? I was up on Pike's Peak a week ago, and the air didn't actually feel thinner....though I was certainly winded after walking only a few dozen yards. Would we even be able to notice thinner air other than the lack of oxygen? Could a higher oxygen-nitrogen ratio make a significantly lower atmospheric pressure unnoticeable?


By basic senses it would be hard to notice, though simple experiments and math could do it. In a thinner atmosphere with relatively more oxygen things would burn easier, air resistance would be lower so paper aeroplanes and toy parachutes might behave differently, especially if you are able to time their fall and compare it to Earth. It would not be able to suck water as high up in a tube as the ten meters which is possible on earth, mercury in a sealed tube would sink to a lower height than the ~76cm (iirc) it does on Earth.

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Re: Lower bound for Earthlike planet

Postby mathmannix » Tue Oct 22, 2013 1:38 pm UTC

davidstarlingm wrote:A pure iron planet is the densest sort of planet that can possibly form under natural circumstances. Iron is 43% denser than the Earth's mean density; in order to have Earthlike gravity, such a planet would need to have 70% the radius of Earth (which, for the record, is still really really large). But obviously a pure iron planet could not sustain life.


First of all, this is using the density of iron under standard pressure. I believe a solid planet-sized ball of iron would in fact be a lot more dense than 143% of earth's mean density, although I do not know how to calculate this off the top of my head.

Second, OK, so iron is the most dense element in the sun. But it is not the densest element found in nature; Osmium, Iridium, Platinum, and Rhenium are all at least 2.5 times as dense as iron. (As are Neptunium and Plutonium, which are found in nature in very trace amounts.) So couldn't a planet be formed, theoretically, with a mostly platinum core? This could make the planet a lot smaller and have the same mass as earth. (Or use gold, lead, silver, copper, or nickel. They are all denser than iron. There are 42 elements denser than iron, of which at least 35 are found naturally on earth.)
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Re: Lower bound for Earthlike planet

Postby Tass » Tue Oct 22, 2013 2:36 pm UTC

No. nickel and iron are the densest elements that are common enough to conceivably make up the majority of a natural planet. Of course it is possible if we allow an advanced civilization to gather it for whatever reason, but the OP wanted naturally formed.

Formation history: Regular big terrestrial planet forms, lots of iron and nickel, but also lots of silicon and oxygen. Solar wind blows off volatiles. Huge impact smashes planet, blowing off silicon and oxygen mantle, leaving a dense former core. Comets add back a bit of volatiles to allow for life.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Tue Oct 22, 2013 2:55 pm UTC

Right -- like Tass said, nothing heavier than iron is going to occur naturally in really large quantities, because iron is the heaviest thing that a star can make with exothermal (net energy gain) fusion. Anything heavier requires endothermal (net energy loss) fusion, which can only occur during a supernova.

In fact, it's been recently determined that elements heavier than lead can't even be formed in supernovae. To get these, you actually need something more violent: the collision of a neutron star pair. Thankfully, this happens more frequently than you might imagine. But there's still no (natural) way to get a planet made of anything heavier than iron.

Anybody have an idea how much denser a solid iron planet might be? Earth's solid iron core is supposed to be something like twice as dense as iron at STP.

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Re: Lower bound for Earthlike planet

Postby PolakoVoador » Tue Oct 22, 2013 4:40 pm UTC

Wouldn't the interior of a solid iron planet suffer from absurdly high pressure?

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Re: Lower bound for Earthlike planet

Postby Tass » Tue Oct 22, 2013 4:57 pm UTC

PolakoVoador wrote:Wouldn't the interior of a solid iron planet suffer from absurdly high pressure?


Of course. But less so than Earths core does, due to its smaller size.

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Re: Lower bound for Earthlike planet

Postby mathmannix » Tue Oct 22, 2013 5:18 pm UTC

As Wikipedia says, the earth's inner core is believed to be primarily nickel-iron (again, nickel being heavier than iron), with some other, even heavier elements such as gold and platinum thrown in for good measure. So, denser than pure iron. And I'm imagining a bigger super-earth to start with, that had its mantle and crust blown off in a collision, or unknown solar event, and then maybe later acquired the atmosphere and water necessary for life. Theoretically possible, right?
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Re: Lower bound for Earthlike planet

Postby Tass » Tue Oct 22, 2013 5:25 pm UTC

mathmannix wrote:As Wikipedia says, the earth's inner core is believed to be primarily nickel-iron (again, nickel being heavier than iron), with some other, even heavier elements such as gold and platinum thrown in for good measure. So, denser than pure iron. And I'm imagining a bigger super-earth to start with, that had its mantle and crust blown off in a collision, or unknown solar event, and then maybe later acquired the atmosphere and water necessary for life. Theoretically possible, right?


Since I posted this above:

Tass wrote:Formation history: Regular big terrestrial planet forms, lots of iron and nickel, but also lots of silicon and oxygen. Solar wind blows off volatiles. Huge impact smashes planet, blowing off silicon and oxygen mantle, leaving a dense former core. Comets add back a bit of volatiles to allow for life.


...I guess my answer will have to be: "yes"

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Tue Oct 22, 2013 5:40 pm UTC

mathmannix wrote:As Wikipedia says, the earth's inner core is believed to be primarily nickel-iron (again, nickel being heavier than iron), with some other, even heavier elements such as gold and platinum thrown in for good measure. So, denser than pure iron. And I'm imagining a bigger super-earth to start with, that had its mantle and crust blown off in a collision, or unknown solar event, and then maybe later acquired the atmosphere and water necessary for life. Theoretically possible, right?

The issue is that Earth's core is still more than 90% iron. There's no known natural process that can get a significantly lower proportion of iron.

Given that the pressure at the core of this planet would be lower than the pressure at Earth's core, we can safely say that the average density will be somewhere between 143% of Earth and 286% of Earth. Let's say 250% is a reasonable upper bound; that brings us down to only 40% the radius of Earth.

Would 40% cause a noticeable change in the appearance of the horizon? How much larger would it need to be if it had this for a core?

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Re: Lower bound for Earthlike planet

Postby PolakoVoador » Tue Oct 22, 2013 6:04 pm UTC

Tass wrote:
PolakoVoador wrote:Wouldn't the interior of a solid iron planet suffer from absurdly high pressure?


Of course. But less so than Earths core does, due to its smaller size.


Ok, this time around I did my homework and wiki'ed a bit before posting: for some reason, I was thinking that Earth's core would be smaller than it really is, so our pure-iron planet would be significantly bigger than the core. But my estimating was very wrong, carry on.


davidstarlingm wrote:Given that the pressure at the core of this planet would be lower than the pressure at Earth's core, we can safely say that the average density will be somewhere between 143% of Earth and 286% of Earth. Let's say 250% is a reasonable upper bound; that brings us down to only 40% the radius of Earth.

Would 40% cause a noticeable change in the appearance of the horizon? How much larger would it need to be if it had this for a core?


So, about Mercury's size. Do we have any sort of pictures of Mercury's surface, or very near flybys, or anything like that?

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Tue Oct 22, 2013 7:11 pm UTC

PolakoVoador wrote:
davidstarlingm wrote:Given that the pressure at the core of this planet would be lower than the pressure at Earth's core, we can safely say that the average density will be somewhere between 143% of Earth and 286% of Earth. Let's say 250% is a reasonable upper bound; that brings us down to only 40% the radius of Earth.

Would 40% cause a noticeable change in the appearance of the horizon? How much larger would it need to be if it had this for a core?

So, about Mercury's size. Do we have any sort of pictures of Mercury's surface, or very near flybys, or anything like that?

Nope. Mercury is so close to the sun that it's pretty hard to orbit, let alone land on. Orbital mechanics is a bitch.

I couldn't find any "artist depictions" that accounted for the planet radius.

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Re: Lower bound for Earthlike planet

Postby Tass » Tue Oct 22, 2013 7:37 pm UTC

davidstarlingm wrote:
PolakoVoador wrote:
davidstarlingm wrote:Given that the pressure at the core of this planet would be lower than the pressure at Earth's core, we can safely say that the average density will be somewhere between 143% of Earth and 286% of Earth. Let's say 250% is a reasonable upper bound; that brings us down to only 40% the radius of Earth.

Would 40% cause a noticeable change in the appearance of the horizon? How much larger would it need to be if it had this for a core?

So, about Mercury's size. Do we have any sort of pictures of Mercury's surface, or very near flybys, or anything like that?

Nope. Mercury is so close to the sun that it's pretty hard to orbit, let alone land on. Orbital mechanics is a bitch.

I couldn't find any "artist depictions" that accounted for the planet radius.


But that math is pretty easy to do. I am fairly sure that if you are somebody who is used to being outdoors, especially a sailor or someone who has climbed mountains by the sea, you would notice that something was odd fairly quickly on a planet of 40% radius.

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Re: Lower bound for Earthlike planet

Postby gmalivuk » Tue Oct 22, 2013 7:40 pm UTC

Um...

(No, not from the surface itself, but what counts as "very near flyby" anyway?)
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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Tue Oct 22, 2013 9:04 pm UTC

Tass wrote:
davidstarlingm wrote:I couldn't find any "artist depictions" that accounted for the planet radius.


But that math is pretty easy to do. I am fairly sure that if you are somebody who is used to being outdoors, especially a sailor or someone who has climbed mountains by the sea, you would notice that something was odd fairly quickly on a planet of 40% radius.

Yeah, it's not too tricky. I'm just not sure how to visualize it.

gmalivuk wrote:Um...

(No, not from the surface itself, but what counts as "very near flyby" anyway?)

Hard to tell scale. How high above the surface was the orbiter?

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Re: Lower bound for Earthlike planet

Postby gmalivuk » Tue Oct 22, 2013 9:43 pm UTC

On a fairly featureless surface, from human heght 40% of Earth's radius is still big enough to look like a normal horizon all the way around. The difference would be if you got up high or watched a ship go out to sea, since it would go over the horizon more quickly than on Earth.
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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Tue Oct 22, 2013 10:08 pm UTC

gmalivuk wrote:On a fairly featureless surface, from human heght 40% of Earth's radius is still big enough to look like a normal horizon all the way around.

That's kind of what I figured.

See the ongoing dual world discussion over in fictional science for the "why" of this thread, haha.

Any other observable/noticeable/important differences on a 40%-sized world?

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Re: Lower bound for Earthlike planet

Postby Vieto » Wed Oct 23, 2013 2:54 am UTC

Tass wrote:The result is that for a truly tiny planet to hold on to an atmosphere, it needs to be so dense that its gravity is actually stronger than earths. -The air has such a short distance to travel to freedom so the pull needs to be greater.


Obviously, the solution is to make gravity 10x that of earth's gravity, so we can increase our power levels. :P

On a more on-topic note, I've been making a Matlab calculator for this, where you enter the Radius and Surface Gravity of a sphere, and it gives you the mass, density, and escape velocity (yet to add Atmosphere size). I tested it with Earth's Radius and with g = 9.81m/s^2, and so far it agrees with the wikipedia.

With a 0.4 Earth Radius body, the escape velocity is ~7km/s, compared to Earth's 11km/s. It's density would have to be 14,000kg/m3, compared to Earth's 5,500kg/m3.

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edit: Actually, upon thinking and research, technically the atmosphere would slowely decrease over time unless there was an input, due to the statistical nature of the speed of particles in a gas in relation to temperature. Therefore, The Little Prince's atmosphere would be dependant on his volcanoes outputting enough gas to keep the atmosphere thick enough to breath, although a 15m/s escape velocity won't help him too much...

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edit again to prevent doubleposting. I found This source which, on page 4, has a diagram that suggests that the smallest escape velocity that allows for an earth-like atmosphere would be 1.2 km/s with an upper atmosphere at a temperature of 50K (and I will assume that it is that low due to a lack of solar winds and UV rays heating the upper atmosphere). My model, uppon trying a number of radii, had an escape velocity of 1200m/s at a surface gravity of 10m/s^2 and a radius of 75km. This is pretty small, about 7% the radius of Pluto, but it would have a mass of 8.43 * 10 ^ 20kg (or 843 zettagrams, which is just 1000 times lighter than earth) and a density of 4.77*10^5 Kg/m^3 (47g/cm^3), or roughly 100 times as dense as earth.

For reference, Minmus in KSP is 60km in radius, although because it's density is 1/20th that of our theoretical planet, it would not support an atmosphere as we know it.

Laythe, with a radius of 500km and a gravity of 0.8G, fits within that atmosphere band as well, and would only be 10 times as dense (5.7 kg/m^3) and 1% the mass of earth, despite being half the radius of Pluto.

So in summary, the smallest possible livable atmosphere would be for a planet of 75km radius, but something the size of Laythe is probably more possible, given densities required. In either case, this theoretical planet is going to be made of something dense. Something like Laythe, if it had earth gravity, would be 500km @ 10m/s^2, with density of 7100 kg/m^3 (or 7g/cm^3). The element 'mercury', or the earth's iron core, has a density of 13g/m^3, so if our planet had a core made of mercury, with a silicon crust on top and a nice gas giant nearby to shield it from radiation, it could feasibly exist.

TLDR: Laythe is theoretically possible, as well as Endor or Yavin IV from Starwars, or any other small moon-sized earth-like planet.

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Re: Lower bound for Earthlike planet

Postby PM 2Ring » Fri Oct 25, 2013 1:30 pm UTC

mathmannix wrote: So couldn't a planet be formed, theoretically, with a mostly platinum core?


I'd say that it's possible but extremely unlikely, since generally, the amount of iron released in a supernova explosion will totally swamp the heavier metals. But if a huge flux of neutrons hit the supernova you could certainly boost the amount of platinum group metals (and other heavy metals) produced. And if we're lucky, the iron could get magnetically trapped by a neighbouring magnetar or two while the heavy stuff escapes.

But perhaps we should leave such speculations for the Fictional Science thread. :)

Wikipedia has good info on the typical abundances of the chemical elements here, including this handy chart.
Spoiler:
Image

Note that the abundances are on a logarithmic scale, so iron outnumbers platinum by around a million to one.

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Re: Lower bound for Earthlike planet

Postby PolakoVoador » Fri Oct 25, 2013 2:15 pm UTC

PM 2Ring wrote:
mathmannix wrote: So couldn't a planet be formed, theoretically, with a mostly platinum core?


I'd say that it's possible but extremely unlikely, since generally, the amount of iron released in a supernova explosion will totally swamp the heavier metals. But if a huge flux of neutrons hit the supernova you could certainly boost the amount of platinum group metals (and other heavy metals) produced. And if we're lucky, the iron could get magnetically trapped by a neighbouring magnetar or two while the heavy stuff escapes.

But perhaps we should leave such speculations for the Fictional Science thread. :)

Wikipedia has good info on the typical abundances of the chemical elements here, including this handy chart.
Spoiler:
Image

Note that the abundances are on a logarithmic scale, so iron outnumbers platinum by around a million to one.


Remember, million-to-one chances crop up nine times out of ten.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Fri Oct 25, 2013 2:27 pm UTC

PM 2Ring wrote:
mathmannix wrote: So couldn't a planet be formed, theoretically, with a mostly platinum core?


I'd say that it's possible but extremely unlikely, since generally, the amount of iron released in a supernova explosion will totally swamp the heavier metals. But if a huge flux of neutrons hit the supernova you could certainly boost the amount of platinum group metals (and other heavy metals) produced. And if we're lucky, the iron could get magnetically trapped by a neighbouring magnetar or two while the heavy stuff escapes.

But perhaps we should leave such speculations for the Fictional Science thread. :)

Wikipedia has good info on the typical abundances of the chemical elements here, including this handy chart.
Spoiler:
Image

Note that the abundances are on a logarithmic scale, so iron outnumbers platinum by around a million to one.

I'm more-or-less sold on the iron-core-planet approach, but just for the sake of argument:

Would it be possible for a nearly-molten metal-rich planet to have its constituent elements sort themselves by density? Then, if you had all the iron floating on top of a much-heavier-metal core, you could at least have a setup that might conceivably allow the outer layers to be blown off by proximity to a star, thus reducing the planet to a mostly-heavy-metal core much denser than iron.

Vaguely conceivable?

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Re: Lower bound for Earthlike planet

Postby starslayer » Fri Oct 25, 2013 4:06 pm UTC

Partially. The Earth already went through differentiation like that. Elements do sort of get sorted by density (all the iron is at the center of the Earth, after all!), but they also get sorted chemically. For example, uranium bonds readily to oxygen, so it is more common in the Earth's crust than you might expect based solely on its density. The heavy elements that mostly sank to the core all dissolve readily in molten iron. The rest are more common in the crust than their cosmic abundances might suggest.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Fri Oct 25, 2013 4:14 pm UTC

starslayer wrote:Partially. The Earth already went through differentiation like that. Elements do sort of get sorted by density (all the iron is at the center of the Earth, after all!), but they also get sorted chemically. For example, uranium bonds readily to oxygen, so it is more common in the Earth's crust than you might expect based solely on its density. The heavy elements that mostly sank to the core all dissolve readily in molten iron. The rest are more common in the crust than their cosmic abundances might suggest.

Seems like getting rid of iron is fairly tricky.

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Re: Lower bound for Earthlike planet

Postby learsfool » Fri Oct 25, 2013 8:07 pm UTC

davidstarlingm wrote:
starslayer wrote:Partially. The Earth already went through differentiation like that. Elements do sort of get sorted by density (all the iron is at the center of the Earth, after all!), but they also get sorted chemically. For example, uranium bonds readily to oxygen, so it is more common in the Earth's crust than you might expect based solely on its density. The heavy elements that mostly sank to the core all dissolve readily in molten iron. The rest are more common in the crust than their cosmic abundances might suggest.

Seems like getting rid of iron is fairly tricky.


Hmm. . .

What would happen if the event that blew off the atmosphere and upper layers was fairly early in the developmental process? Would that leave enough denser metals like lead without the oxygen and sulphur to bond with, potentially giving you an even denser core and a body that could be . . . umm. . . would that be almost moon sized?

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Fri Oct 25, 2013 8:17 pm UTC

learsfool wrote:What would happen if the event that blew off the atmosphere and upper layers was fairly early in the developmental process? Would that leave enough denser metals like lead without the oxygen and sulphur to bond with, potentially giving you an even denser core and a body that could be . . . umm. . . would that be almost moon sized?

I would guess that being molten would give the planet a better chance to prefer metal-metal bonds and avoid bonding with oxygen and sulphur, while also giving oxygen and sulfur the chance to outgass and escape into space. There are probably some stars with spectrums where this would be easier to pull off....though my chemistry expertise is very very low.

The tricky bit is still going to be getting the hundreds-of-miles-thick-solid-iron-shell off of the heavy-metal core. That's one job that is entirely as difficult as it sounds.

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Re: Lower bound for Earthlike planet

Postby learsfool » Fri Oct 25, 2013 8:46 pm UTC

davidstarlingm wrote:I would guess that being molten would give the planet a better chance to prefer metal-metal bonds and avoid bonding with oxygen and sulphur, while also giving oxygen and sulfur the chance to outgass and escape into space. There are probably some stars with spectrums where this would be easier to pull off....though my chemistry expertise is very very low.

Moving closer to the center of the galaxy would be an interesting option there. Lots more supernova action happening there, and that's very likely the direction advanced civilizations would head as they started to explore. We're kind of in boondocks as far as star density goes.

The tricky bit is still going to be getting the hundreds-of-miles-thick-solid-iron-shell off of the heavy-metal core. That's one job that is entirely as difficult as it sounds.

Yeah, if you're talking something more like our system it would be easier if at least one event happens when everything's still molten.

We're still fuzzy on some aspects of planetary formation, so you could get away with something plausible but not verifiable from that standpoint. I'd think it'd be easier to go with the 'heart of gold and stuff' route which would at least be a lot stronger than 'neutron star guts' and wouldn't need any real handwavium.

If worse comes to worse, you could just have a galactic culture that experimented in planetary formation a lot. . . causing collisions in some cases and preventing them in others to see what happened until they got what they wanted. (I'm assuming some level of patience or a LOT of exploration is involved here) :)

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Fri Oct 25, 2013 8:52 pm UTC

learsfool wrote:We're still fuzzy on some aspects of planetary formation, so you could get away with something plausible but not verifiable from that standpoint. I'd think it'd be easier to go with the 'heart of gold and stuff' route which would at least be a lot stronger than 'neutron star guts' and wouldn't need any real handwavium.

If worse comes to worse, you could just have a galactic culture that experimented in planetary formation a lot. . . causing collisions in some cases and preventing them in others to see what happened until they got what they wanted. (I'm assuming some level of patience or a LOT of exploration is involved here) :)

The idea is to have a planet which could form naturally even though it would be highly, highly improbable.

I'm still trying to figure out if there are any other consequences of having a planet with only 40% the radius of Earth. Lower escape velocity, so a higher rate of atmospheric loss, but otherwise I can't think of anything.

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Re: Lower bound for Earthlike planet

Postby PM 2Ring » Sat Oct 26, 2013 6:52 am UTC

PolakoVoador wrote:
PM 2Ring wrote:I'd say that it's possible but extremely unlikely, since generally, the amount of iron released in a supernova explosion will totally swamp the heavier metals. But if a huge flux of neutrons hit the supernova you could certainly boost the amount of platinum group metals (and other heavy metals) produced. And if we're lucky, the iron could get magnetically trapped by a neighbouring magnetar or two while the heavy stuff escapes.

[...]

Note that the abundances are on a logarithmic scale, so iron outnumbers platinum by around a million to one.


Remember, million-to-one chances crop up nine times out of ten.

Well, they do on the Discworld, but unfortunately they don't in our universe, due to the chronic shortage of narrativium. :)


davidstarlingm wrote:The tricky bit is still going to be getting the hundreds-of-miles-thick-solid-iron-shell off of the heavy-metal core. That's one job that is entirely as difficult as it sounds.

Hell yeah. Which is why I suggested that we need to separate the iron from the heavy metals well before the ejecta from the supernova start condensing.

To get the high neutron flux required for our heavy metals we probably need either a type Ia white dwarf detonation or a pair instability supernova (see http://en.wikipedia.org/wiki/Supernova#Energy_output). To maximize the chances of actually ejecting the heavy stuff we probably want the explosion to be as asymmetrical as possible. I guess if the exploding star has a close companion star the tidal forces will increase the asymmetry. And if that companion happens to be a magnetar, then we may also get a decent amount of the iron & nickel magnetically trapped by the companion.

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Re: Lower bound for Earthlike planet

Postby davidstarlingm » Mon Oct 28, 2013 3:38 pm UTC

PM 2Ring wrote:
davidstarlingm wrote:The tricky bit is still going to be getting the hundreds-of-miles-thick-solid-iron-shell off of the heavy-metal core. That's one job that is entirely as difficult as it sounds.

Hell yeah. Which is why I suggested that we need to separate the iron from the heavy metals well before the ejecta from the supernova start condensing.

To get the high neutron flux required for our heavy metals we probably need either a type Ia white dwarf detonation or a pair instability supernova (see http://en.wikipedia.org/wiki/Supernova#Energy_output). To maximize the chances of actually ejecting the heavy stuff we probably want the explosion to be as asymmetrical as possible. I guess if the exploding star has a close companion star the tidal forces will increase the asymmetry. And if that companion happens to be a magnetar, then we may also get a decent amount of the iron & nickel magnetically trapped by the companion.

One problem I foresee: heavy stuff like gold, platinum, and uranium can't really be produced in significant quantities in supernovae; you need neutron star collisions to do that.

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Re: Lower bound for Earthlike planet

Postby PolakoVoador » Wed Oct 30, 2013 12:57 pm UTC

New image of Mercury, taken by the Messenger probe, revealed this week by NASA:

Spoiler:
Image


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