What's the largest rocky planet with 1g gravity in theory?

[greswd]

Based on our current understanding of astrophysics, what's the largest possible rocky planet, theoretically speaking, with a surface gravity of 1g?

The larger the planet, the lower the average density, and there's a structural lower limit to the density.

 

[Buzz Bloom]

Hi greswd:

If you knew the average density of "rock", you could calculate the mass of a sphere of a specified radius. Then you could calculate the surface gravitation for that radius. You could then calculate the radius for a 1 g gravity.

Can you do this?

Regards,
Buzz

 

[snorkack]

If you knew the average density of "rock", you could calculate the mass of a sphere of a specified radius. Then you could calculate the surface gravitation for that radius. You could then calculate the radius for a 1 g gravity.

Can you do this?

You cannot.
You cannot do that because density of rock depends on pressure.
What you need to do is to fit distribution of pressure from surface to centre:
g(r)=G/r²)(∫₀^r(4πρ(r)r²dr)
P(r)=∫_R^rg(r)ρ(r)dr
and then ρ(r) must be consistent with P(r) according to an empirical function which you need to know all the way to whatever P(0) turns out to be.

 

[phyzguy]

Look at the attached graph, from a presentation by Sarah Seager. Rocky planets follow the red lines. As they get more massive, they get denser because of the higher pressure. So any rocky planet more massive than the Earth will have a higher surface gravity than the Earth. So the answer to the question in the OP is "1 Earth mass". Unless the planet has different composition than the Earth (water rich for example, or without an iron core), in which case the answer can be different.

 

[greswd]

Hi greswd:

If you knew the average density of "rock", you could calculate the mass of a sphere of a specified radius. Then you could calculate the surface gravitation for that radius. You could then calculate the radius for a 1 g gravity.

Can you do this?

Regards,
Buzz

well, I'm wondering about the actually possibilities of such planets, hence I require real empirical data.

 

[phyzguy]

well, I'm wondering about the actually possibilities of such planets, hence I require real empirical data.

The graph I sent you is real empirical data, including solar system planets and exoplanets.

Starting from the lower left and looking only at the solar system planets, you can see Mars - Venus - Earth - Uranus - Neptune - Saturn - Jupiter

 

[greswd]

Look at the attached graph, from a presentation by Sarah Seager. Rocky planets follow the red lines. As they get more massive, they get denser because of the higher pressure. So any rocky planet more massive than the Earth will have a higher surface gravity than the Earth. So the answer to the question in the OP is "1 Earth mass". Unless the planet has different composition than the Earth (water rich for example, or without an iron core), in which case the answer can be different.View attachment 240648

thanks, though by "large" I was referring to the size.

could there exist an exoplanet somewhere out there with a composition light enough to be larger than the Earth, solid enough to walk on, yet have a gravity not exceeding 1g?

 

[phyzguy]

could there exist an exoplanet somewhere out there with a composition light enough to be larger than the Earth, solid enough to walk on, yet have a gravity not exceeding 1g?

Uranus has a surface gravity of 0.89 g. But it's not "rocky". Still, the answer is yes if you build it out of light elements. The question is whether planets like that really exist. I don't think we know.

 

[greswd]

Uranus has a surface gravity of 0.89 g. But it's not "rocky". Still, the answer is yes if you build it out of light elements. The question is whether planets like that really exist. I don't think we know.

and if they do exist, how large they could get.

they'd be a plus for human colonization. wide, open expanses of land, without a cripplingly strong gravity.

 

[snorkack]

Look at the attached graph, from a presentation by Sarah Seager. Rocky planets follow the red lines. As they get more massive, they get denser because of the higher pressure. So any rocky planet more massive than the Earth will have a higher surface gravity than the Earth. So the answer to the question in the OP is "1 Earth mass". Unless the planet has different composition than the Earth (water rich for example, or without an iron core), in which case the answer can be different.View attachment 240648

Precisely.
"Rocky planet" would be one lacking an iron core.
Not unlikely. Moon does lack iron core.
In the attached plot, the exercise I referred to - numerical solving of compressibility for integrated mass, gravity, pressure - has been done for us.
It is a log-log plot. Therefore any power dependence falls on a straight line.
Find the upper right of the two triangles near mass 1, radius 1. It has mass and radius exactly 1, because it is Earth. The lower left triangle nearby is Venus.
Mark location at mass 100, radius 10. Near but not exactly at triangle which is Saturn.
Draw straight line between Earth, and mass 100/radius 10. All points on that line have exactly 1 g.
Then identify its intersection with the continuous red line, and read the mass there. You may need to enlarge the plot.

 

[Nik_2213]

If you allow '1g At The Equator', then you could have a much more massive planet with a rapid spin...

 

[greswd]

If you allow '1g At The Equator', then you could have a much more massive planet with a rapid spin...

Not sure if a planet could handle the centrifugal stresses.

they'd be a plus for human colonization. wide, open expanses of land, without a cripplingly strong gravity.

also, we wouldn't be able to enjoy wide open lands.

 

[MikeeMiracle]

Whats the reasoning behind this question? To create more space for humanity? If we are talking about wide open lands then we only currently live on only 20% of the land mass on earth...

 

[greswd]

Whats the reasoning behind this question? To create more space for humanity? If we are talking about wide open lands then we only currently live on only 20% of the land mass on earth...

I'm kinda Malthusian, thinking of the future exponential expansion of the population.

Anyway, reasonings aside, I'm just wondering how large 1g planets can get.

 

[MikeeMiracle]

Any planet formed the normal way will almost certainly have an iron core.

I think we are looking more at a moon here. If we take the same process that formed our moon except have that process happen to a super-earth, It's concievable that we could have a moon larger than the Earth without an iron core and so could achieve that 1g we are looking for. Without an iron core though I'm not sure how it could generate a magnetic field to protect us though so not sure how habitable it would be. Maybe the super-earth's magnetic core could be large enough to encompass the moon also.

In any case, I am not sure there is a simple way to answer the question.

 

[davenn]

Moon does lack iron core.

incorrect

"Core[edit]

​

Schematic illustration of the internal structure of the Moon​

​

Several lines of evidence imply that the lunar core is small, with a radius of about 350 km or less.[3] The size of the lunar core is only about 20% the size of the Moon itself, in contrast to about 50% as is the case for most other terrestrial bodies. The composition of the lunar core is not well constrained, but most believe that it is composed of metallic iron alloyed with a small amount of sulfur and nickel. Analyses of the Moon's time-variable rotations indicate that the core is at least partly molten.[4]
In 2010, a reanalysis of the old Apollo seismic data on the deep moonquakes using modern processing methods confirmed that the Moon has an iron rich core with a radius of 330 ± 20 km. The same reanalysis established that the solid inner core made of pure iron has the radius of 240 ± 10 km. The core is surrounded by the partially (10 to 30%) melted layer of the lower mantle with a radius of 480 ± 20 km (thickness ~150 km). These results imply that 40% of the core by volume has solidified. The density of the liquid outer core is about 5 g/cm3 and it could contain as much 6% sulfur by weight. The temperature in the "