Rocky planets size

[Moontanman]

How large could a rocky planet be? It seems that at some point the planet would hold onto too much gas to be a rocky planet. Even figuring lower average density than the Earth I would think there is a point of no return from being a mini Neptune at least...

[pavelcherepan]

From what I read in the Earth's upper atmosphere move at around 5 km/s with some more energetic particles peaking at ~16 km/s which is well above Earth's escape velocity. So then if you have similar upper atmosphere conditions and a planet with an escape velocity of 16+ km/s hydrogen will not escape very readily and you'll have a gas giant.

 

http://faculty.washington.edu/dcatling/Catling2009_SciAm.pdf

http://www.teachastronomy.com/astropedia/article/Velocity-of-Gas-Particles

 

Then we can use the escape velocity formula:

 

[latex]v_e=\sqrt{\frac{2GM}{r}}[/latex], but if we approximate the shape with a sphere then [latex]M=4/3*r^3*\pi*\rho[/latex], hence

 

[latex]v_e=\sqrt{8/3*G*r^2*\pi*\rho}[/latex]

 

Then if we say that our largest possible rocky planet has a average density a bit higher than Earth, say 6000 kg/m³ and has an escape velocity ~15 km/s so that hydrogen can still escape through both Jeans and hydrodynamic escape, then:

 

[latex]15000 = \sqrt{8/3*6.67*10^{-11}*3.14*6000*r^2}[/latex]

 

[latex]\frac{15000}{0.001832}=r[/latex]

 

[latex]r = 8187772.92\, m[/latex]

 

Probably can be slightly bigger depending on how close it's to the star, what the atmosphere thickness is and so on, but probably not by much.

 

EDIT: Also thinking about it a bit more and potentially you can have an extremely large rocky planet (it's just a guess) if it forms close to the parent star and most of the hydrogen gets blown away to the outer regions while the protoplanet is still small.

Edited January 11, 2016 by pavelcherepan

[Ophiolite]

In order to become a gas giant you need two things:

 

1. A rocky core

2. Gas

 

If the core forms in the inner part of the system, no gas.

If the core forms in the outer part of the system, after the gas has been dissipated, then no gas.

[Moontanman]

Would a planet of 8 Earth masses and 20,000 miles in diameter loose hydrogen? Could a planet hang on to helium and still loose it's hydrogen?

[Robittybob1]

Would a planet of 8 Earth masses and 20,000 miles in diameter loose hydrogen? Could a planet hang on to helium and still loose it's hydrogen?

Is that "8 Earth masses" all rock?

[Moontanman]

Is that "8 Earth masses" all rock?

 

 

No, at least some of it would be a metal core like the earth but the silicate Mantle would be thicker than Earths in relationship to the core.

[Robittybob1]

 

 

No, at least some of it would be a metal core like the earth but the silicate Mantle would be thicker than Earths in relationship to the core.

Have you tried the formulas given above, for that is what I'd do? You would also have to adjust the velocity of the atoms based on their kinetic energy. Then see if the escape velocity can be reached or exceeded for that more massive planet.

[Moontanman]

Have you tried the formulas given above, for that is what I'd do? You would also have to adjust the velocity of the atoms based on their kinetic energy. Then see if the escape velocity can be reached or exceeded for that more massive planet.

 

 

My math chops are somewhat less than that required to do those calculations. I used to have a site where it would do those calculations for me but in recent years it started to give nonsense answers and hasn't been fixed.

 

I am trying to figure out how to get a relatively thick atmosphere without hydrogen, possibly 10 bar but it has to be breathable by humans. I had figured that an atmosphere of maybe 85% helium and the N2, O2 and others would make up about 15% and a surface gravity of about 2G. I can't get the mountain heights or cut off time for plate tectonics because the alien planet site has died more or less...

Edited January 12, 2016 by Moontanman

[Robittybob1]

That seems a massive proportion to Helium. I looked at a problem like this once before and there end up being too many variables.

[Moontanman]

That seems a massive proportion to Helium. I looked at a problem like this once before and there end up being too many variables.

 

 

My concern is that helium is so close to the atomic weight of a hydrogen molecule that you can't get one without the other...