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Can a super-Earth of approximately 1.5 Earth-radius and 3.0 Earth-mass be habitable? By habitable, I mean terrestrial with liquid water on its surface, a rocky ocean floor, and no thick hydrogen/helium envelope like that of a sub-Neptune. I keep getting mixed results from my research. I have seen suggestions that 2.0 Earth-mass may be the upper limit for ideal habitability and that more than that would have a thick primordial H/He atmosphere. On the other hand, I've found some suggestions that mass could reach up to 5.0 Earth-mass and still be terrestrial. I simply want to know if a 1.5 Earth-radius, 3.0 Earth-mass planet could possibly sustain the above listed habitability conditions.

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  • $\begingroup$ The short answer is 'yes'. The long, involved, science-based answer is 'yes'. Every 'can't be possible' calculation involving planets has eventually been destroyed by reality. On a regular basis, cosmologists and astronomers are discovering planets with conditions that are 'impossible'. There is always something that we haven't thought about, that makes impossible conditions possible. The conundrum is, we just do not know what those 'somethings' are. They are things that we don't know we don't know. $\endgroup$ Feb 17, 2021 at 17:14
  • $\begingroup$ @Xi-K When you say "habitable", do you mean "habitable for some carbon based liquid water using lifeforms in general", or do you mean "habitable for humans specifically"? Humans can survive in only a small subset of the environmental conditions were Earth likelifeforms can survive. $\endgroup$ Feb 17, 2021 at 18:04
  • $\begingroup$ A lot of the calculations depend on how long since inception. Some atmospheres at the beginning of the formation of some planets become less likely over billions of years, and more likely on other planets. Compare Venus to Earth to Mars. Over billions of years, the atmosphere has changed on each planet dramatically. $\endgroup$ Feb 17, 2021 at 19:39
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    $\begingroup$ @M.A.Golding I describe "habitable" in my post as "with liquid water on its surface, a rocky ocean floor, and no thick hydrogen/helium envelope like that of a sub-Neptune." $\endgroup$
    – Xi-K
    Feb 17, 2021 at 20:21
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    $\begingroup$ @Xi-k I added to my answer on 07-23-2022, including a discussion of a possible expanation of why your world doesn't have a dense hydrogen helium atmosphere. $\endgroup$ Jul 23, 2022 at 20:36

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My calculations for the properties of your super Earth type planet are:

  • Average density of 4.902 g/cm$^\sf{3}$, compared to 5.514 g/cm$^\sf{3}$ for Earth
  • Gravity of 13.094 m/s$^\sf2$, compared to 9.78 m/s$^\sf2$ for Earth
  • Escape velocity of 15.82 km/s, compared to 11.184 km/s for Earth

The average density of the planet if fine. The surface gravity is 33.3% higher than Earth's, which is an issue in that in increases the escape velocity, which affects the gases retained in the atmosphere. It will also affect how life forms might develop to overcome a much higher surface gravity.

This might result in the muscles of animals being stronger than on Earth and flying animals might be lighter, or have stronger muscles.

As L. Dutch states in the escape velocity will have repercussions regarding atmospheric gases and possibly the required temperature to avoid hydrogen and helium retention.

Even a temperature of 350 K is 77 $^\circ$C.

Increasing the diameter of the planet to 1.75 Earth radius and keeping the mass as 3 Earth masses would reduce the surface gravity to 9.6 m/s$^\sf2$ (98% of Earth's) and the escape velocity would be 14.64 km/s. The average density would be 3.089 g/cm$^\sf{3}$, which would be similar to the Jovian moon Europa.

Keeping the diameter to 1.5 earth radii and reducing the mass to 2.5 Earth masses would change the density to 4.085 g/cm$^\sf{3}$, the surface gravity to 10.912 m/s$^\sf2$ and the escape velocity to 14.44 km/s. This would be a better scenario.

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    $\begingroup$ Brilliant. This is exactly the kind of analysis I was looking for and the range of alternatives you provided at the end is the cherry on top. May I inquire which calculator you used or in which manner you determined the density for this planet you listed? I would find such a resource incredibly valuable. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 20:30
  • $\begingroup$ @Xi-K: I have my own spreadsheet populated with data for some Solar System objects. I calculate the density, gravity & escape velocity to compare with ones provided by sources such a NASA or Wikipedia. Density is mass (tonnes) divided by volume (in cubic meters) - t/m3 is the same as g/cm3, all metric units. Gravity on the surface is g = GM/r2. Escape velocity, v = sqrt(GM/r). (G ≈ 6.67×10−11 m3·kg−1·s−2) $\endgroup$
    – user81881
    Feb 17, 2021 at 20:51
  • $\begingroup$ I see. I understand how to calculate density, I was more wondering how you determined that this particular planet volume should have this particular density. It seems like you have to take what type of planet it is (say gas giant or super-Earth) then you have a rough idea of composition (like how much iron, silicate, gases, etc. for that type of planet) and based on the amounts and proportions of those materials, combined with volume and gravity, it allows you to figure density. However, I have no idea how to get that precise. So far I've just been correlating with observed densities. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 22:19
  • $\begingroup$ I suppose the root of my inquiry is that density is mass divided by volume and I have volume, but I wonder how you calculate mass. Mass is determined by how much of a certain composition of materials you have, so you must have come up with a mass that, when divided by my given volume based on a 1.5 times Earth radius, gave you the 4.902 g/cm^3 density. That mass is based on all of the complex factors, like type of planet based on size and composition, as well as the proportion of those materials. This is what seems very detailed and complicated for me to figure out. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 22:25
  • $\begingroup$ @Xi-K: The process for determining a planet's density is firstly find the volume by measuring the diameter of the planet. Using the equation for the volume of sphere getting the volume is easy. Secondly, determine the mass of the planet. For this, measure the distance between the planet & its star (or barycenter of a binary star system). Also measure the time it takes the planet to orbit it's star (system). With a little math the mass of the planet can be determined. Divide the two to get average density. ... cont. $\endgroup$
    – user81881
    Feb 18, 2021 at 9:29
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According to this calculator, with your parameters your planet will have an escape velocity of about 16 km/s.

According to this graph correlating the escape velocity and the temperature of a planet to the gases it can trap,

escape velocities

to not trap hydrogen and helium the planet would need to be at somewhere around 350 to 400 K.

With those temperatures it's far from being habitable according to our definition. It might still host some sort of extremophile life form. Having liquid water on the surface with those temperatures would require higher atmospheric pressures, somewhere above 10 bar.

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  • $\begingroup$ I understand. My proposed mass was based on the same density as Earth. Based on the graph you posted, a planet would need less than 15 km/s escape velocity to shed its H/He layer. With a 1.5 Earth-radius, the planet could attain a 13 km/s escape velocity with 2 Earth masses, resulting in a density around 3.5 g/cm^3. What would be the composition of this density of a planet? More volatiles? A weaker magnetic field, or maybe not due to its large size? I know Mars has a density of around 3.9 g/cm^3. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 7:00
  • $\begingroup$ Note that the scale on the left is logarithmic; I'm a bit more optimistic about the loss of a hydrogen/helium atmosphere than you. What seems more likely is a thick atmosphere with a lot of water vapour, which at 400K is going to resemble a pressure cooker. I might try and have a look at the maths behin Jeans escape later and have a think about what might happen. $\endgroup$ Feb 17, 2021 at 9:29
  • $\begingroup$ @Xi-K Your proposed mass is slightly off, then: your planet has a lower density than earth (to have the same density at that radius, it would have to weigh 3.375 times as much as earth). $\endgroup$ Feb 17, 2021 at 19:27
  • $\begingroup$ Interesting. Does this chart mean that some asteroids might have an atmosphere of radon gas? Certainly, it seems an atmosphere of xenon gas is likely. $\endgroup$ Feb 17, 2021 at 19:41
  • $\begingroup$ @user3482749 Looking back at my calculation, my original was exactly 3.128 times Earth-mass with a radius of 1.464 Earth-radii. That's probably where the slight inconsistency you are seeing arose. My question was more about the plausibility of this type of planet being terrestrial in the sense that I described in my post, so I rounded. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 20:19
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Short answer:

Any writer can depict a habitable planet with any mass, radius, density, surface gravity, or escape velocity that they want to, without worrying about being arrested by the science fiction police. But a writer who cares about scientific plausibility in their stories should note that some scientists calculated that the maximum mass limit for a habitable world should be about twice the mass of Earth. A writer who cares about their scientific plausibility should research those calculations.

Long Answer:

There is a big difference between a planet habitable for life forms that are carbon based and use liquid water and can survive in conditions that some Earth life forms can survive in, and a planet where humans and beings with similar environmental needs can survive.

Part One of Two: A Planet Habitable for Humans.

I note that native intelligent beings or large land animals would probably need an atmosphere rich in oxygen, like that of Earth. And also any Earth humans who visit the planet would need an oxygen rich atmosphere if they walk around without breathing apparatus, and would need a small enough surface gravity that it wouldn't endanger their health, unless they can use some sort of antigravity devices which can protect them from dengerously high surface gravity.

I'm sure that a number of science fiction stories have settings where no human beings were in contact with any of the characters in the story, and where humans are never mentioned. Several such stories are listed in answers to this question:

https://scifi.stackexchange.com/questions/94253/what-is-the-first-work-of-science-fiction-in-which-no-character-is-an-earthling/94337#94337[1]

The small number of early stories mentioned may indicate that such stories are very rare. Since the question was about the first such story, possibly that sub genre has become a lot more common in the decades since the latest one mentioned in an answer.

As far as I know, the first and only scientific discusssion of the planetary attributes, including mass, radius, density, surface gravity, and escape velocity, for a planet to be habitable for humans is Habitable Planets for Man, Stephen H. Dole, 1964, 2007.

Here is a link to a pdf of the 1964 edition:

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf[2]

Later research may have made some of Dole's calculations obsolete.

In the chapter "Introduction to General Planetology" Dole discusses the relationship between a terrrestrial planet's mass and its other characteristics.

In figure 7 on page 28 Dole graphs the mass/volume relationship between the masses and volumes of stars and planets. In figure 8 on page 30 Dole graphs the density-radius relationshp for the then known terrestrial planets.

Note that Dole's figures give strightforward relationships between the mass, density,and radius of terrestrial planets. However, more acurate measurements since then of the data of various solar system bodies and exoplanets may have modified that.

For example, Mercury is much denser that such a small planet should be. It is now speculated that Mercury was much larger and had a lower average density until it collided with a smaller planet billions of years ago, and all of the lighter material was ejected from Mercury, leaving it excessively dense.

And many of the large moons in the other solar system are known to have low densities because they are mixtures of rock and ices of water, ammonia, and other substances which are liquid at Earthly temperatures. It is also now believed that worlds can migrate from where they form outward from their star or inward toward their star.

So it is possible that a partially icy world with a lower density than a totally rocky terrestrial planet could migrate inward toward its star and enter the circumstellar habitable zone of the star, and thus have temperatures suitable for life.

But of course there are limits to how low the density of such a world could be without being totally covered by an ocean many miles deep.

Part two: A Habitable World for Life in General.

And if a writer is certain that no humans or oxygen breathing land animals will ever need to survive unprotected on his planet, for all of their lives or for short visits, he can make it habitable for some life forms but not for humans or for oxygen breathing land animals.

Most scientific discussions of the habitablity of exoplanets in other solar systems discuss habitablity for carbon based, liquid water lifeforms in general, and not the more specific case of humans in particular. Thus a planet can be considered habitable for life even if an unprotected human would die within seconds or minutes anywhere on that planet - after all, many lifeforms on Earth flourish in parts of the biosphere where unprotected humans would died in minutes or seconds.

So what are the limitations of mass for a planet habitable for life in general, and not specifically habitable for humans?

"Exomoon Habitabilty Constrained by Illumination and Tidal Heating", Rene Heller and Roy Barnes, Astrobiology, Volume 13,number 1, 2013, is a comparatively recent discussion of the possibile habitability of worlds in other solar systems, in this case as yet undiscovered exommons obiting exoplanets in other solar systems. Heller and Barnes do not mention any reason to suppose that exomoons could be habitable if they were outside the mass range for an exoplanet to be habitable. Therefore they summarize scientific opinons about the mass range for potentially habitable worlds.

https://faculty.washington.edu/rkb9/publications/hb13.pdf[3]

In section 2. Habitability of Exomoons, the last paragraph before section 2.1 2.1. Formation of Massive Eexomoons, on page 20, discusses the mass range for habitable worlds, including exoplanets and exomoons.

An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011).

Their source for the importance of plate tectonics for habitability is:

Williams D.M. Kasting J.F. Wade R.A. Habitable moons around extrasolar giant planets. Nature. 1997;385:234–236. [PubMed] [Google Scholar]

Their sources for that maximium mass limit of 2 times the mass of Earth are:

Gaidos, E., Conrad, C.P., Manga, M., and Hernlund, J. (2010) Thermodynamics limits on magnetodynamos in rocky exoplanets. Astrophys J 718:596–609.

Noack, L. and Breuer, D. (2011) Plate tectonics on Earth-like planets [EPSC-DPS2011-890]. In EPSC-DPS Joint Meeting 2011, European Planetary Science Congress and Division for Planetary Sciences of the American Astronomical Society. Available online at http://meetings.copernicus.org/epsc-dps2011.

Stamenkovic´, V., Breuer, D., and Spohn, T. (2011) Thermal and transport properties of mantle rock at high pressure: applications to super-Earths. Icarus 216:572–596.

So a writer who is careful to design only worlds which are possible according to current science should research the importance of magnetic fields and plate tectonics to the habitability of worlds, and also research whether those calculations that the maximum possible mass of a habitable world is only twice the mass of Earth are correct.

Added 07-23-2022

The question asked about a world with 1.5 Earth radis and 3.0 Earth radius. Other answers may have done the calculaitons, but such aworld would have 1.5 cubedthe volume of Earth or 3.375 the volume of Earth, with 3.0 times the mass of Earth.

Thus it would have a lesser average density than Earth, about 0.8888888 times that of Earth. That would be an average density of 4.9013328 grams per cubic centimeter.

So you might assume that the varius materials which your planet was made of would have an average density 0.8888888 that of Earth. And a writer might worry about whether there will be enough highly dense elements and compounds on the planet for the needs (whatever they may be) of his story.

It gets worse. All planets are much denser in their cores, where their matter is being crushed and compressed to higher density by the matter above it. Teh more massive the planet, the more the core matter will be compressed to higher density. With three times the mass of Earth, the weight of even more thousands of kilometers of rock above will compress the core material even more. Thus the materials would need to have, when under zero pressure, an average density much less than 0.8888888 that of Earth, to have an average density of 0.8888888 when being compressed inside a planet with 3 times the mass of Earth.

Fortunately some heavy elements form cmpounds with much ligher elements, and some of those compounds are light enough to be found in Earth's crust. So the planet's crust should have some heavy elmeents in various compounds and ores, though a smaller percentage than on Earth I guess.

With an average density of 4.9013328 grams per cubic centimeter, the planet would be less dense than Mercury, 5.427 grams per cubic centimeter, or Venus, 5.243 grams per cubic centimter, but more dense than Mars, 3.9335 grams per cubic centimeter, or the Moon, 3.334 grams per cubic centimeter. And the good news is that all four astronomical objects are not covered with hundreds of miles deep world wide oceans, but have exposed solid surfaces. So a world doesn't need to be largely liquid to have such an average density.

According to these calculators:

https://philip-p-ide.uk/doku.php/blog/articles/software/surface_gravity_calc

https://www.calctool.org/astrophysics/escape-velocity

Such a world would have a surface gravity of 1.34 g and an escape velocity of 15.82 kilometers per second, 1.414 times that of Earth.

A comment by Xi-K says:

Looking back at my calculation, my original was exactly 3.128 times Earth-mass with a radius of 1.464 Earth-radii.

Using those figures, the planet would have 3.128 times Earth's mass in 3.1377853 times Earth's volume, and thus a density 0.9968814that of Earth, or 5.496804 grams per cupic centimeter, a very small difference. It would have a surface gravity of 1.46 g, and an escape velocity of 16.35 kilometers per second.

I don'tknow if any human characters are desired to visit or colonize that planet. Dole, in Habitable Planets for Man, decided that humans wouldn't want to colonize a planet with a surface gravity higher than 1.25 o r1.5 g, and the world as imagined would have surface gravities in that range and should be rather uncomfortable and unhealthy for long range human habitation.

Escape velocities of 15.82 or 16.35 kilometers per second might be high enough for the world to retain dense atmospheres of hydrogen and helium and become some sort of mini Neptune.

Fortunately helium would probably be safe to breath at a considrable atmospheric pressure, though it would be hard to have large amounts of hydrogen and oxygen in an atmsopehre without it burning into water.

So possibly your planet accumulated a large, dense, unbreathable, atmosphere of hydrogen and helium and then migrated to the habitable zone of your star. It's escape velocity was still high enough to retain hydrogen and helium, but it might be unable to capture more of those gases, since they might not be found that close to the star anymore. And then it lost most of its atmosphere, retaining only heavier gases like nitrogen, oxygen, carbon dioxide, and water vapor, plus trace gases.

The impact of a large meteoroid can lead to the loss of atmosphere. If a collision is sufficiently energetic, it is possible for ejecta, including atmospheric molecules, to reach escape velocity.[9]

In order to have a significant effect on atmospheric escape, the radius of the impacting body must be larger than the scale height. The projectile can impart momentum, and thereby facilitate escape of the atmosphere, in three main ways: (a) the meteoroid heats and accelerates the gas it encounters as it travels through the atmosphere, (b) solid ejecta from the impact crater heat atmospheric particles through drag as they are ejected, and (c) the impact creates vapor which expands away from the surface. In the first case, the heated gas can escape in a manner similar to hydrodynamic escape, albeit on a more localized scale. Most of the escape from impact erosion occurs due to the third case.[9] The maximum atmosphere that can be ejected is above a plane tangent to the impact site.

https://en.wikipedia.org/wiki/Atmospheric_escape#Impact_erosion

So possibly your planet suffered a few impacts after migrating to the habitable zone, and those impacts removed the hydrogena and helium from its atmosphere, while perhaps adding some heavier gases like nitrogen, oxygen, water vapor, and carbon dioxide.

Cometary impacts are one possible reason why Titan has an atmospherer billions of times as dense as those of the similar moons Ganymede and callisto.

An alternative explanation is that cometary impacts release more energy on Callisto and Ganymede than they do at Titan due to the higher gravitational field of Jupiter. That could erode the atmospheres of Callisto and Ganymede, whereas the cometary material would actually build Titan's atmosphere.

https://en.wikipedia.org/wiki/Atmosphere_of_Titan#Atmospheric_evolution

The number of major impacts by comets, asteroids, and possibly by other planets, your world would suffer, and the impact that each would have had on its atmosphere, adding and/or subtracting gases, is something that would not be obvious from even the most detailed description of the present state of your ficitonal star system. So if you need to explain why your world has the atmospheric composition desired for the story instead of a dense atmosphere of hydrogen and helium, large impacts in the past would be a reasonable explaination.

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Blast those pesky little molecules off with the solar wind.

solar wind on mars

https://svs.gsfc.nasa.gov/4370

The graphs consider mass and temperature and that is that. But these planets do not exist in a vacuum! Ok, they do, but nearby your planet is its star, and the solar wind can strip away gas molecules too. A planet which lacks a protective magnetic field will lose atmosphere to the solar wind as is thought to have happened with Mars.

Your big planet can have a weak or weakening magnetosphere such that it has lost lighter molecules to the wind. You are not constrained by gas laws here - you can assert that your star is strong enough to do what you need and your planets magnetosphere not strong enough to save the hydrogen and helium.


I was wondering why Venus, with minimal magnetosphere, still has an atmosphere much thicker than that of Earth. The answer is that Earth had that thick atmosphere too, but did something different with it.
https://space.stackexchange.com/questions/13833/how-does-venus-thick-atmosphere-survive-against-the-solar-wind


OK, this post will need something more if it is going to garner any upvotes. Let us add something else to deal with the hydrogen, which is 90% of the hydrogen / helium envelope. Let us biology away that hydrogen! Venus has a boatload of CO2 and Earth once did as well, but now a lot of that C is locked up in carbonate rocks and biology, and the O is loose as O2 or locked in water.

So too your super earth. Life forms take CO2 and hydrogen and make sugars or other reduced carbon forms. Oxygen is released and it also gets cozy with hydrogen, making water.

That will leave a fair bit of helium in the atmosphere. I think that will be ok.

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    $\begingroup$ Your last point emphasizes that a timeline since inception of the system is needed. Atmospheres that are possible in the very beginning become less so as billions of years pass. $\endgroup$ Feb 17, 2021 at 19:36
  • $\begingroup$ This is an interesting proposal, but there are a few problems. Firstly, to have liquid water (as my post lists as a requirement for my definition of habitability) it would need to be in its stars habitable zone. For this to be true and for the solar wind to be strong enough to strip its atmosphere down, the star would need to be very small. For stars more like our own, the reason super-Earths are considered to not be able to rid themselves of their H/He envelopes is because it would take longer than the entire age of such a solar system for the solar wind to do the job. $\endgroup$
    – Xi-K
    Feb 17, 2021 at 20:26

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