Is a bigger planet than Earth with the same density possible?

Question

Let's say there's a planet with 18 times the radius of Earth, but has the same density as Earth. If so, how would it be possible for a big planet to such a density of Earth? Would it have the same gravity as Earth?

Answer 1

That's no planet!

Let's say that the radius is $18R_{\oplus}$, where $R_{\oplus}$ is Earth's radius. The volume will then be $$\frac{4}{3}\pi(18R_{\oplus})^3\bar{\rho}=5832\left(\frac{4}{3}\pi R_{\oplus}^3\bar{\rho}\right)=5832M_{\oplus}$$ where $M_{\oplus}$ is the mass of Earth and we assume the same mean density $\bar{\rho}$ for both bodies. That's roughly $18.4$ times the mass of Jupiter. Something this massive isn't a rocky planet, and it isn't even a gas giant. It's like a decent-sized brown dwarf.

Brown dwarfs generally have higher densities than gas giants; their central densities can reach anywhere from $\sim10$ to $10^3\text{ g/cm}^3$, much greater than Earth's density of about $5.5\text{ g/cm}^3$. The brown dwarf is less dense towards its surface, and there's not really a clear boundary (as is the case with stars, as they're gaseous), so some parts will be more dense than Earth (on average), while others will be less dense.

I see that Mormacil's answer mentioned a question I answered two years ago and have, I think, cited a couple of times since. An important takeaway is that you can't simply add more and more mass to rocky planets and expect them to stay rocky. One group (Lammer et al. (2014)) found that at around $2M_{\oplus}$, rocky bodies will retain hydrogen/helium envelopes, entering a class of objects that are more like gas planets than rocky planets. Your $18M_{\oplus}$ "planet" certainly won't be terrestrial in nature. Based on Seager et al. 2008, the maximum achievable radius for a terrestrial planet is, optimistically, $4\text{-}5R_{\oplus}$, assuming a pure ocean world (which should be less dense than a silicate Earth-like planet of the same mass).

Surface gravity

The surface gravity $g$ is related to the radius $R$ by $$g\propto\bar{\rho}R$$ Given that $R=18R_{\oplus}$, the surface gravity will be 18 times that of Earth. Again, though, it's not clear where the surface of a brown dwarf actually is, so take this figure with a grain of salt.

Life

Life on brown dwarfs has been discussed in Can life arise on a brown dwarf?, among other places. Essentially, there are some big problems you'd need to overcome, including high temperatures and possible radiation.

Answer 2

• If the planet is $n$ times bigger, then it has $n^3$ times bigger volume.
• But it has the same density as the Earth, thus it has $n^3$ times bigger mass.
• Its $n^3$ times more mass would produce $n^3$ times stronger gravity, but...
• Its surface is $n$ times more far away from its center, thus this gravity feels $n^2$ times lesser.

The result is that the surface gravity is $\frac{n^3}{n^2} = n$ times stronger!

Thus, on a planet having 18 times bigger size, but the same density as Earth, it would have $18g$ surface gravity.

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If somehow it has similar surface parameters as the current Earth, then life is possible, although it would be highly different as ours. We would be most probably some "turtle-like" lifeforms.

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About the physics: in general,

• if you make the density $n$ times bigger, the surface gravity will be $n$ times bigger
• if you make the planet $n$ times bigger, the surface gravity will be also $n$ times bigger
• but the mass of the planet will be $n^3$ times bigger and its surface area will be $n^2$ times bigger.
• also the escape speed will be $n$ times bigger, but note: to get anything to this $n$ times bigger escape speed, it requires $n^2$ times bigger kinetical energy.

Typically, in the atmospheric evolution of the planets, there are two effects:

1. The star heats the planet and blows it with stellar wind, and these try to evaporate its atmosphere
2. The planet's gravity tries to get the atmosphere on the planet.

The overall result — now, after knowing some hundreds of exoplanets, too — is that around Jupiter-sized planets can keep their atmosphere even if they are near to the star. Maybe even the lighter gases. This is why the large planets are mainly gas giants (≈ the atmosphere is so dense that the majority of the planet mass is built up from it).

If you want this planet not be a gas giant, instead to have a planet-like atmosphere, then the star have to be able to blow the the hydrogen and helium away. If the planet is in the near of the star (or it is a very big one), then it is possible, but it causes such a heating that the surface temperature will make it impossible for the life.

For example, large exoplanets, close to their star were found, with around 2000°K surface temperature. Their atmosphere is from gaseous sodium, and they may have liquid iron rains. Even oxygen couldn't remain on them, despite their high surface gravity.

Answer 3

According to the answers on this question that size won't be possible for an Earth like planet. They say about twice the radius/10 times the mass is the theoretical max.

Density is based on composition. If it's similar to Earth so should its composition. It will not however have the same gravity. If you scale up the liquid core the same amount as the rest of the planet it stands to reason its gravitational pull would similarly increase.

Higher gravity would dictate life that's shorter, closer to the ground and more dense in general. Things like grass would be rare but moss and short bushes would not. Animals likely have four or six limbs, very few bipedals. Flying would be much harder and birds would likely be smaller.

Life will probably favor the oceans that much more. As the water would nullify some of the crushing gravity. Regardless it will be impossible for humans to visit I think.

Answer 4

Some good answers.

Another consideration: Atmosphere: With 18 times the surface gravity and a much slower taper off of gravity. (Will go down by a factor of 4 at 2 R from the center. But your big planet is now 18 R, so you hve to get out to 36 R from the center to get that same lower gravity. This makes for a much much thicker atmosphere. Thousands of times more atmosphere.

Light is not going to reach the surface.

Escape velocity is $v=\sqrt{2GM/r)}$

But with $18^3$ times as much mass, and only 18 times as much r, escape velocity will be 324 times as great as earth's or about 3500 km/s. Not counting what you lose to atmospheric drag.

Answer 5

Yes it is, kind of, a planet that big with the same average density as Earth may be possible but it won't be a rocky, terrestrial world and it won't fit well in our existing planetary catalog. As HDE 226868 mentioned such a celestial object is heavy enough to be a Brown Dwarf Star but it won't be, the composition can't be right.

It's 1.65 times the radius of Jupiter which is too big to be a Brown Dwarf (measured Brown Dwarfs are in the 0.63-1.13 Jovian Radius range) and only 4.1 times the average density (Brown Dwarfs are normally twice that dense, or more), so it's got to have a big, but relatively low density, rocky/metallic core (probably composed primarily of high pressure Carbon allotropes) with a thick atmosphere of light gases (Hydrogen, Helium and Hydrocarbons). It's a weird elemental mix for "modern" stars but you might find such a world in a younger universe where the heavier elements were much rarer, possibly such worlds might still exist around the very oldest Red Dwarfs but I don't think one could form in the modern universe.