# Could this hypothetical xoplanet support life?

## Main Question or Discussion Point

Here is a brief detail on the planet i created.

Mass .218 earths, density 5.62 g/cm3, radius .60 earths, surface gravity is .602 earths
It has 1 moon that has 5% the mass of the main world orbiting 300,000 miles above the surface.
It orbits a sun like star, same luminosity and mass every 342 days, eccentricity is .08
The average temperature is 305 Kelvin
It has 80% water and 20% land, the crust ranges from 5-30 miles thick

I am just wondering if this planet can support a thick atmosphere of carbon dioxide, nitrogen, oxygen, water vapor and some methane. I also need to know if the planet an generate a magnetic field.

The planet i created is currently 3.5 billion years old and it is in a stable solar system that is 50 light years from earth.

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Sure, although earth like life would not survive on this planet i think native life could. It would be hot 305 Kelvin is 89 F and for a global temperature there would be no ice caps at all. There could be plant life if there is alot of cloud cover to reduce the heat. I think your right on the edge of habitability when it comes to temperature.

A rule-of-thumb lower bound to atmosphere retention (derived here) is given by

rm ~ (3/2) (k/G) (1/m_proton) (R/M) T ~ 2*10^14 (R in m / M in kg) (T in K)

where R, M and T are the planet's radius, mass and surface temperature in SI units. The resultant number is the molecular mass, in atomic mass units, below which the thermal kinetic energy exceeds the gravitational binding energy.

Plugging in values for Earth, that yields rm ~ 0.06. Gases with a molecular mass below this value cannot be retained at all (which is meaningless here, since molecular masses are by definition integers). Gases between this value and ten times this value are lost quickly, i.e. within a year or so (still meaningless here). Gases between ten times and a hundred times this value are lost slowly, i.e. within a billion years or so. That means everything with a molecular mass below 6, which covers diatomic hydrogen and helium. Gases above a hundred times this value are retained almost indefinitely.

To get a long-lived Earth-like atmosphere, the lightest gas that has to be retained is diatomic nitrogen, I think, which means a molecular mass of 28 and thus rm ~ 0.3. In other words, you need a planet for which the quantity (R/M)*T is no more than five times higher than it is for Earth. If a shorter-lived atmosphere is sufficient, the quantity may be ten or twenty times higher (for reference, "twenty times higher" corresponds to the Moon, roughly).

As mentioned initially, this is a lower bound. It doesn't stop the atmosphere from, say, being chemically absorbed into the crust or being stripped away by solar wind or any number of other relevant processes which have already been discussed above.
If the planet has water, those molecules (atomic weight of 18) should stay in the atmosphere, too.

Some similar relations:
With the average density ρ, M scales with ρR^3, and the ratio becomes $\frac{T}{\rho R^2}$.

The surface gravity scales with g~M/R^2, and an equivalent ratio is T/(gR).
^ Good point. Evaporating water straight into space doesn't sound very habitable.

And it occurs to me that methane would be again slightly lighter, and should probably be kept too, considering that it's a minor but not insignificant carbon cycle constituent and greenhouse gas.

So, better call it (rm < 2.5 rmEarth) for a long-lived and (2.5 rmEarth < rm < 10 rmEarth) for a short-lived atmosphere. Which means that the Moon isn't even marginally suitable - domed cities it is. :P
Using your values, one gets rm ~ (R/M)*T ~ (0.6/0.218)*(305 K/290 K) rmEarth ~ 2.9 rmEarth

If you're talking about colonization, that's definitely good enough. If you're talking about evolution, it's a little bit outside the stricter limits for water vapor and methane I derived at the end, but should still be close enough for the seepage to be of marginal significance at worst. *thumbs up*

Someone else will have to address magnetic fields, I'm afraid.

How far is it from the star?

^ 0.96 AU, unless I misinterpreted the OP.

The planet in question should be able to support an atmosphere of any gas, so long as it is not heavier than the material making up the planet itself.

whether or not a planet has a magnetic field depends on whether or not it's core rotates, and what it's inner and outer core consist of.

The core would be a iron/nickle and a bit of sulfur mix to lower melting point. The mantle would have more iron in it than earths. So with water vapor not being perminant any idea how long it could last in the atmosphere until total dissapearence?
So for the oceans if the atmosphere was thicker in CO2 or nitrogen say 3-6 bar would the liquid stay or seep also?

So with water vapor not being perminant any idea how long it could last in the atmosphere until total dissapearence?
Very roughly, the range from 2.5 rmEarth to 25 rmEarth corresponds to retention times of billions of years to days. Based on that, my best guess for 2.9 rmEarth would be several billion years for water and a billion years for methane. But the model is very simplistic, so those may be off by several orders of magnitude either way. Millions of years, you can rely on, I'd say.

So for the oceans if the atmosphere was thicker in CO2 or nitrogen say 3-6 bar would the liquid stay or seep also?
The way I'm thinking about this (which may be wrong), a thicker atmosphere would actually be counterproductive. The only thing that keeps the gases bound to the planet is gravity, and increasing the amount of atmosphere isn't going to increase the planetary mass in a significant way until it becomes a gas giant, more or less. Instead, more atmosphere means that it extends farther into space, which makes it more susceptible to stripping, and higher absolute losses due to similar relative loss rates. Bad all around, it seems to me.

Borek
Mentor

The planet in question should be able to support an atmosphere of any gas, so long as it is not heavier than the material making up the planet itself.
Care to elaborate? Hydrogen? Helium?

It would be able to support any atmosphere that would realistically exist in large quantities. Of course, if the atmosphere were more dense than the planet, then the gas would sink and the rock would rise, although I severely doubt that any gas would realistically be this dense

Make sense i could understand leakage in the upper atmosphere. There is one thing i dont get though leakage from the surface because the higher up you get in the troposphere the colder the temperature gets so i would think like 99% of the water vapor would sink back due to colder temps and less heat excitement of molecules That basically what im confused about but i totally get leakage in the upper atmosphere.

Borek
Mentor

It would be able to support any atmosphere that would realistically exist in large quantities. Of course, if the atmosphere were more dense than the planet, then the gas would sink and the rock would rise, although I severely doubt that any gas would realistically be this dense
Hard to deny.

Though it would be cool because with a that leakage maybe some plants if they exist would be able to get water from the vapor instead of just relying on rain haha.

Plus with a magetic field i would think there would be less escape of any gas but without it i doomed.

While denser air does sink there would still be very minimal leakage in the upper reaches of the atmosphere. The colder air concept does play an important role though without the freezing temperatures water vapor would escape much quicker. I do believe that with a denser atmsphere and a magnetic field you would hold onto a thicker atmosphere that could last billions of years. Oxygen co2 and nitrogen will be permenently retained as long as the temperature does not increase. Stay awesome :)

While onomatomanic is right about adding more atmosphere would cause it to grow in height id think that f the molecules were more tightly paked it would be denser that way and the altitude wouldnt change. While the exosphere and thermospheres height may grow te stratosphere and troposphere might stay the same. Its very interesting to think about.

There is one thing i dont get though leakage from the surface because the higher up you get in the troposphere the colder the temperature gets so i would think like 99% of the water vapor would sink back due to colder temps and less heat excitement of molecules That basically what im confused about but i totally get leakage in the upper atmosphere.

Temperature does drop with height in the region familiar to us (up to 10 km), but this trend doesn't continue indefinitely. Once you get above 100 km, the temperature begins to climb in earnest due to the absorption of hard UV light (which is why we don't get any of that down here).

Whether 99% of the water vapour sinks back isn't the issue at all. Sinking or no sinking, 99% of the atmosphere are close to the planet's surface, simply because density decreases with height. The issue is what happens to the 1% above that. If there is a mechanism which allows this fraction to rapidly escape, then another 1% of the remainder will have to rise to take its place, which will escape by the same mechanism, and so on until there is nothing left. One hundred times "rapidly" is still pretty rapid, if you see what I mean.

Anyway, I'm not sure I understand your thinking here. Why should water vapour sink down due to temperature decreasing with height? The decrease affects all gases, not just water, and since they can't all sink at the same time, none of them can sink at all, it seems to me. Obviously, if the water vapour gets the chance to precipitate into droplets, this no longer applies and it falls (as rain) rather than sink - maybe that's what you meant?

Though it would be cool because with a that leakage maybe some plants if they exist would be able to get water from the vapor instead of just relying on rain haha.
Space plants? I agree that the idea has a certain appeal, but if water leaks at that sort of rate, your planet is pretty much screwed, I think. :tongue:

Plus with a magetic field i would think there would be less escape of any gas but without it i doomed.
Yes, having a magnetic field reduces atmospheric escape, because it deters stripping of the upper layer by the solar wind. It's only one factor among several, either way, though.

Yea i was trying to say rain but i didnt know if it would just eveaporate before it reached the surface. When you said earlier several billion years retining would that be with a magnetc field and the several million years without. I was just wondering cus billions vs millions is a huuuuge difference haha. I would think volcanic activity would help replenish water and other gases and if it had a longer bombardment with more icy based comets or asteroids but idk. Thinking about this stuff is really cool, cus we might observe it one day.

When you said earlier several billion years retining would that be with a magnetc field and the several million years without. I was just wondering cus billions vs millions is a huuuuge difference haha.
No, the model only covers ordinary kinetic escape driven by heat, nothing else. The difference results from the simplicity of the model, which gives only one hard figure - the watershed between immediate escape and short-term retention. Beyond that, everything is gradual and has to be either intricately modelled or roughly estimated, and I only have the means to do the latter - thus, large error margins. Sorry.

I would think volcanic activity would help replenish water and other gases and if it had a longer bombardment with more icy based comets or asteroids but idk.
As I said, my best guess is that the seepage would be insignificant even over billions of years, but it's no more than a guess. If so, you don't need to do anything. If you want to err on the side of caution, give the planet more water than Earth had to start with, so that you can let some portion of it escape and still have enough left to go on with.

Volcanic activity would help replenish Co2 levels and if there are plants that produce oxygen more oxygen in the atmosphere. The increased eccentricity is interesting. You would be closer and farther from the sun than earth is to its own which will have minimal effects. On the close side you will be warmer having more solar enerfy and further less energy. The 80% water would definatly help stay put the water especially if your oceans and seas are deep.

Yes the i was going for more eccentricity to vary the nvirnments more between hot and cold and i would think that the increase in eccentricity would heat the core a little more than if it were not.

So how about nirtogen and oxygen can they stay for billions of years also? I also gave the atmosphere 1.5 bars to be realistic lol. Also how would the eccentricity affect the planet?

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Yes oxygen and nitrogen can stay indefinetly. A 1.5 atmosphere on your planet would keep the oceans in a liquid state and it will rain and have weather systems due to the heating and cooling from the star.

Eccentricity of 0.08 means that between perihelion and aphelion, orbital distance varies by ~1/6, insolation varies by ~1/3, temperature theoretically varies by up to 30 K. Practically, I'd expect something between 10K and 20K from that source. Definitely noticable; the details depend on the magnitude of your axial tilt and how the equinoxes aligns with perihelion and aphelion.

Yea i should have been more precise with the orbit. It orbits at 1.06 au. So at its nearest it orbits at 0.971 au and at the furthest it orbits at 1.14 au. The only reason the temperature isnt colder is because of the abundance of Co2 and water in the atmosphere. The axis tilt varies from 23-28 degrees because of the moon but its at 25 degrees right now.

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