# How un-dense could a super-duper-Earth be if that super-duper Earth was bigger than Neptune?

Long story short, I have an Earth-like planet, which is orbiting a mega-Earth (think a super-duper-sized version of a super-Earth), which is orbiting a K-type star, which is orbiting UY Scuti.

I want this mega-Earth to be as massive as possible while still exhibiting a surface gravity less than or equal to twice that of Earth. This means increasing the radius of the mega-Earth; however, increasing the radius of the mega-Earth means that either the density decreases or the mass increases. I don't want the mass to increase - or, at least, I want to keep it within manageable limits, such that the gravity stays equal to or less than 2 G - so I decreased the density instead.

As of currently, the relevant parameters for the mega-Earth are approximately as follows:

• 24.5 M🜨 (note that this is approximately 25.75% of Saturn's mass, and at least 150% of Neptune or Uranus's mass)

• 3.5 R🜨 (you could fit three and a half Earths side-by-side inside this planet)

• 42.9 times the volume of Earth (still ~¾ or ~⅔ that of Neptune or Uranus, respectively)

• Average density of 3 grams per cubic centimeter/3000 kilograms per cubic meter

My question: is this density realistic for a terrestrial planet of this radius and mass? The Moon is known to have a density of approximately 3.344 grams per cubic centimeter/3344 kilograms per cubic meter, but I don't know if it's possible for that density to scale up; I'm currently of the impression that a larger planet would "compact" its matter to a greater density, enough such that the radius would decrease, thereby increasing the surface gravity.

Please ignore the fact that this planetary system is orbiting UY Scuti - a star that may only exist for a few million years, therefore not existing long enough to form a planetary system. Moreover, please ignore the fact that a habitable moon orbiting a habitable mega-Earth orbiting a sun which is itself orbiting another sun is a rather unplausible situation. These are both part of the story.

Moreover, I don't want a mini-Neptune; I want a planet which has an oxygen-nitrogen atmosphere, rather than a hydrogen-based, volatile-based, or steam-based atmosphere. This means that this reduced density cannot be due to a massive but un-dense atmosphere; I'm asking whether a 3 gram/cubic centimeter density is possible for a the crust, mantle, and core of a massive terrestrial planet.

Note that this planet does not need to have a magnetic field, but it should have enough silicates for an Earth-like surface.

• Jan 6 at 1:55
• @Willk That's a similar question, but it's incapable of answering this question; a planet with a surface gravity of 2G is going to have entirely different possible compositions and densities than one with a surface gravity of 1G. Moreover - and this is the important point - this is a reality-check question, meaning that I'm asking for assessments of how realistic my concept - in this case, a 3 g/cm^3 density - is, rather than answers to a "what would this look like" question. Jan 6 at 2:15
• @KEY_ABRADE Actually in terms of maximising size at a given surface gravity composition is going to be a fixed variable regardless of the gravity you're talking about.
– Ash
Jan 6 at 6:23
• @KEY_ABRADE Humans can survive 2 g surface for short times. Minutes or hours should be alright. But I don't know how long humans could survive in 2 g. If humans were seeded on a planet with 2 g. they might die off quickly. Jan 6 at 18:28
• @M.A.Golding A bit of genetic engineering can fix that problem. Really, the issue is getting blood to the brain, and I have a couple of ways around that. Jan 6 at 18:47

To get such a large, low-density planet, it would need to have a very small iron core. The challenge would be in how this might be achieved during planet formation. In theory, it might be possible for collisions between planetary bodies in the same system to strip off the light crust of one or more terrestrial-type planets, and for the light materials to form the large, light planet, while the heavy iron cores remain as one or more seperate planets in nearby different orbits if they are not entirely ejected from the solar system.

It is therefore unlikely, but not impossible for such a light, large planet to form.

However, I don't know how 'terrestrial' it would be. While surface gravity may be 2g, it would have an escape velocity much higher than Earth's, and due to lack of sufficient low molecular weight Jeans escape, it might accumulate Helium or even Hydrogen in its atmosphere, which could push it from being a terrestrial planet to a gas giant.

• Provided that it's a big, rocky core that doesn't have a massive gas envelope on it, it works. In-story, it got terraformed into something habitable and a bunch of species - including humans - got dumped on it to turn it into a sort of zoo. Jan 6 at 4:16

To answer the question of average density of a low density super-earth at 2 surface gravities 3 is not a completely unreasonable number, to get there we have to do some fairly radical things though:

• The core can't be metallic, in fact nowhere in the planet are there going to be what we would consider normal abundances of high weight elements. The core is going to be a massive chunk of high density amorphous carbon averaging somewhat less than 3.5gcm-3. We're going to say amorphous carbon rather than a single solid diamond to turn it into a giant spinning conductor so we have a magnetic field, it's also less dense than true diamond.

• The "outer core" is going to be a slush zone of giant diamonds floating in the lower mantle.

• The mantle will be a relatively thin layer of Carbonatite with a very thin, fragile, crust.

That will get you down to around the 3gcm-3 mark.

BUT

There are three major problems with this:

1. any world that big simply isn't going to have much relative relief. As a result if it has a reasonable [read life sustaining] percentage of water in it's total chemical make up it will be covered in fairly deep oceans with the possible exception of a few, short-lived (geologically speaking) island chains. It simply won't be a terrestrial world in terms of having a lot of continental landmasses to live on.

2. any world with this sort of composition will be as geologically dead as Mars in short order, it only has formation heat, and possibly some tidal heating, zero radioactive heating will occur later in it's life.

3. it's a once in a cosmic blue moon event, strange concentrations and differentiations of elements and chemicals do happen in the wider universe, there are several vast clouds of almost pure alcohol floating around after all but to peel this world out of a protostellar cloud of far more average composition is going to require some really unique circumstances.

Having said that if you're willing to have a world that is young enough, dry enough, and weird enough then by all means it is workable idea.

• Oh, I forgot to specify that it having a magnetic field isn't necessary. Jan 6 at 7:43
• @KEY_ABRADE That's cool the amorphous carbon is lower density, as well as potentially conductive, compared to a diamond of the same size so it's preferable unless you specifically don't want a magnetic field for some reason.
– Ash
Jan 6 at 7:47

According to the OP:

I want this mega-Earth to be as massive as possible while still exhibiting a surface gravity less than or equal to twice that of Earth.

But they also want the planet to be inhabited by seeded lifeforms including humans.

And it seems doubtful to me that humans from Earth could flourish 24 hours a day, year after year, in 2 g surface Gravity. It is quite possible that such high surface gravity would kill off the humans faster than they could reproduce.

See the discussion of surface gravity on a habitable planet in Habitable Planets for Man, Stephen H. Dole, 1964. On page 12 Dole says:

On the Basis of the available date, one might conclude that few people would choose to live on a planet where the surface gravty was greater than 1.25 or 1.50 g.

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

I suspect that any humans introduced to a planet with a surface gravity as high as 2 g would have to be bred for it over many generations, centuries, and millennia living on planets with successively slightly higher surface gravity. Or elese have their genes artifically modified all at once to transform them in to beings similar to humans but redesigned to withstand high gravity much better.

Thus the past history of the humans who were seeded on the planet needs to be considered if its surface gravity is anywhere near to 2 g.

The parameters of the planet are described as:

As of currently, the relevant parameters for the mega-Earth are approximately as follows:

24.5 M🜨 (note that this is approximately 25.75% of Saturn's mass, and at least 150% of Neptune or Uranus's mass)

3.5 R🜨 (you could fit three and a half Earths side-by-side inside this planet)

42.9 times the volume of Earth (still ~¾ or ~⅔ that of Neptune or Uranus, respectively)

Average density of 3 grams per cubic centimeter/3000 kilograms per cubic meter

So it has 3.5 times the radius of Earth, and thus 42.875 time the volume of Earth. With 24.5 times the mass of Earth it has a density of 0.5714285 Earth's density of 5.514 grams per cubic centimeter or 3.1508567 grams per cubic centimenter, which is close to your figure of 3 grams per cubic centimeter.

Since the matter of a planet is denser at the core than at the surface, it might turn out that your planet's outer layers would be a world wide ocean many miles deep.

According to this online calculator, the surface gravity of a planet with radius 3.5 times the radius of earth and 24.5 times the mass of Earth would be 2 g.

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

According to this escape velocity calculator, the escape velocity of a planet with radius 3.5 times the radius of earth and 24.5 times the mass of Earth would be 29.595 kilometers per second, or 2.6457 that of Earth.

https://www.omnicalculator.com/physics/escape-velocity

That would be a bit higher than the escape velocity of Uranus, which is 21.3 kilometers per second.

Uranus has a lot more hydrogen and helium in its atmosphere than Earth. And of course a habitable planet could not have a lot of hydrogen and oxygen for breathing in its atmosphere, since hydrogen and oxygen burn to form water vapor.

The ability of a planet to retain a gas in its atmosphere depends on the ratio between the heat and speed of particles of that gas in the exosphere of the planet and the planet's surface gravity.

Uranus is about 19 times as far from the Sun as Earth is. If Uranus was close enough to the Sun to have Earth like temperatures, it would receive about 19 X 19, or 361, times as much radiation as it does, and its exosphere would be much hotter, perhaps hot enough to lose its hydrogen and helium.

I suspect that you might want to change the parameters of your planet, to be at least as dense as before (if possible), but with a smaller mass and radius to get the surface gravity and escape velocity lower.

# Pave Saturn.

Saturn has just 1.07 g of gravity. All you need is a solid surface.

Go the artificial route and pave it over. Or give it an ecosystem that has generated aerial rafts that join together to reduce the rate at which they fall ... until the entire planet is surrounded ... and then they specialized into a more robust membrane of ecosystem from there. Doubtless they have a plant-like metabolism and have extracted an oxygen atmosphere that they vent above them, from the warm rain clouds that are found around 10 atm deep in our Saturn. Now there is a Saturn-sized world with Earthlike gravity, water (from oxygen reacting with remaining hydrogen), and an oxygen atmosphere ... with a peculiar basement waiting for those who like to dig into things.