# I 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.

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#### Buzz Bloom

Gold Member
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)(∫0r(4πρ(r)r2dr)
P(r)=∫Rrg(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.

• Buzz Bloom

#### phyzguy

Science Advisor
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. #### Attachments

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• greswd

#### 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

Science Advisor
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

Science Advisor
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.

• Buzz Bloom

#### Nik_2213

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

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