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I have a planet with a surface gravity of 0.9 times that of Earth, and an escape velocity of 11.3 km/s, and a temperature like Earth's. My question is if it could retain a breathable atmosphere (for humans) but with more surface pressure than on earth (maybe around 1.5 atm). If so, what would be its composition?

It is also necessary to take into account that the point is to have very massive flying creatures in the air, and tiny ballons filled with helium or hydrogen, so they can float in the air, also the surface pressure can be higher than 1.5 atm if necessesary.

The tiny ballons may contain spores, and may be delivered into the air in large quantities by various plants, so the spores can be seen from the distance and maybe change the color of the sky a bit?

Thanks!

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    $\begingroup$ Hi, welcome to world building. To provide a useful answer to your question, I think we need a few more specifics on your requirements. Breathable to whom? Humans as we are now? Breathable on the surface? Do you know what surface pressure you're after? (Simply saying "higher" includes an average air pressure only a few millibars above Earth's, not necessarily useful to you. You may want to figure out the mass of those floating creatures to help figure out the pressure required for them to be buoyant). $\endgroup$ Feb 2 at 22:05
  • $\begingroup$ Thank you, i already updated it, i need to know how much surface pressure is necessary for maybe ballons filled with helium or hydrogen and containing spores to float, but also maintaining it breatheable for humans, and also i need that atmosphere to be estable for millions of years. $\endgroup$ Feb 2 at 22:17
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    $\begingroup$ Venus has 91% earths surface gravity and an atmosphere of 95 bar, or 95 times denser than earths. you're fine. $\endgroup$
    – John
    Feb 3 at 1:23
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    $\begingroup$ @Darrel Hoffman But unless someone in the story tries to use a rocket ship to leave the planet, it doesn't matter how much harder it will be to leave the planet from the surface. What matters in this story is that the escape velocity will keep gases from escaping from the exopshere, at the top of the atmosphere, into outer space. $\endgroup$ Feb 3 at 17:45
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    $\begingroup$ @DarrelHoffman The atmosphere does not affect escape velocity, it affects how much fuel you need to reach escape velocity. $\endgroup$
    – John
    Feb 3 at 21:13

1 Answer 1

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The answer is yes, you can!

The question of whether a planet can retain an atmosphere depends on the ratio between the escape velocity and the average thermal speed of particles in the atmosphere. Very, very roughly, if $v_{\mathrm{esc}}/v_{\mathrm{therm}}\gtrsim6$, the planet should be able to retain its atmosphere. A quick calculation shows that for nitrogen molecules, the ratio is a bit over 22, consistent with the fact that Earth's atmosphere contains quite a lot of nitrogen. For molecular hydrogen, on the other hand, the ratio is under 6 (though not by much), which explains why Earth has lost the hydrogen envelope it may have initially formed.

As your planet has an escape velocity very similar to Earth's and a temperature the same as Earth's, we would expect an atmosphere with a composition quite similar to Earth's - with heavier gases like nitrogen and oxygen, but little hydrogen and helium. (Earth actually isn't exceedingly far from the threshold for being able to retain some amount of helium, but you do have to account for factors like the solar wind's effect on the upper atmosphere.)

It's certainly possible to attain whatever pressure you want; simply increase the mass of the atmosphere! It turns out that we can relate the mass of the atmosphere $M_{\text{atm}}$ to the surface pressure $p_0$ by $$M_{\text{atm}}=\frac{p_0}{g}4\pi R^2=\frac{4\pi R^4p_0}{GM}$$ with $M$ the mass of the planet and $R$ its radius. Given your values for escape velocity and surface gravity, we can calculate that it should have a radius 1.14 times that of Earth and a mass 1.16 times that of Earth$^{\dagger}$. We plug these values into the above equation, along with a pressure of 1.5 atm, and we find that your planet would need to have an atmosphere 2.26 times that of Earth. This holds regardless of atmospheric composition!

There's still the question of how realistic it is for a planet to accrete that much gas in the first place, and I don't have a good answer for that. It's possible that the conditions in the protoplanetary disk included higher concentrations of these heavier gases than you'd normally find.


$^{\dagger}$Since $$v_{\mathrm{esc}}=\sqrt{\frac{2GM}{R}},\quad g=\frac{GM}{R^2}$$ we can show that $v_{\mathrm{esc}}=\sqrt{2gR}$, allowing us to calculate $R$ by $$R=\frac{v_{\mathrm{esc}}^2}{2g}$$ once we have that, we can find $M$ by rearranging our equation for escape velocity: $$M=\frac{v_{\mathrm{esc}}^2R}{2G}$$

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  • $\begingroup$ Thanks!, I just have 1 question, could you explain me how to get the Mass of the atmosphere and the surface pressure based on the gravity and the physical characteristics of the planet? i didn´t totally understand that formula. $\endgroup$ Feb 3 at 2:08
  • $\begingroup$ @CarlosSamuelAriza I've made some edits! Let me know if anything's still unclear. $\endgroup$
    – HDE 226868
    Feb 3 at 13:48
  • $\begingroup$ IIRC, A geomagnetic field is usually also assumed in order to counter/blunt the stripping effect of the solar wind. $\endgroup$ Feb 3 at 16:46
  • $\begingroup$ @RBarryYoung Yeah, certainly, but there are still some (less severe) effects - figured it wouldn't hurt to mention it. $\endgroup$
    – HDE 226868
    Feb 3 at 20:57

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