What Causes the Earth's Crust-Atmosphere Phase Transition?

[flicflex]

What you could say about the Earth's radius is that the radius at any point on the surface along a line extending from the center of gravity to outer space is the point of greatest gravitational potential along that line. The acceleration due to gravity on a test object falls as you move toward the center of mass from the surface and also falls as you move toward space from the solid or liquid surface.

This is an interesting element of answer. But why does the materia doesn't accumulate anymore (isn't solid anymore) beyond that greatest gravitational potential field (6400km)?

That said, I'm still not sure I have properly understood what it is you are trying to ask.

Calculate Earth's radius with the help of some chosen parameters (something like internal energy, temperature and quantity of materia, magnetic field, i don't know something like that)

As Borek had said, and I will try to reformulate, there is no special significance behind the numerical value (here 6400) of any physical quantity (here the radius of the Earth) when expressed in particular units (here km). Coming back to our example, one may say that it is so, because the kilometer had been initially defined as 1/10000 part of the distance from the North Pole to the Equator along the meridian passing through Paris.

Assuming the Earth resembles as a sphere, it means that 1/4 of a great circle has a length of 10000 km. But, a quarter of a circlular arc with radius R has a length R \pi/2. Then, solving for the radius, we have:
<br /> \frac{R \pi}{2} = 1.0000 \times 10^4 \, \mathrm{km}<br />
<br /> R = \frac{2 \times 1.0000 \times 10^4 \, \mathrm{km}}{3.14159} = 6.3662 \times 10^3 \, \mathrm{km}<br />
There is your magic number!

Dickfore, you just said that <br /> <br /> \frac{2 \times \frac{R\pi}{2}}{\pi}= R <br /> <br />

I may argue that the above number represents, at least to an order of a magnitude estimate, the number of atoms of which the solid portion of the Earth is made out of. Indeed, if you assign 1 a.m.u. of mass to each of these "atoms" (look up the atomic mass unit), then their combined mass would be 2.89 \times 10^{24} \, \mathrm{kg}. Compare this to the mass of the Earth, 5.97 \times 10^{24} \, \mathrm{kg}, and you are in the right order of magnitude range. But, by no means should you ask why the first result is nearly half of the second! It just turned out that way (we know that the Earth is not made out of hydrogen, nor can we pack spheres to occupy the whole space). But, what it should show you is that the Earth is made up of atoms, and that it is not a white dwarf or a neutron star.

Your comparison is interesting, but I'm looking for a more precise calculus (something close at least of 20% of the real radius). We obviously can't add the size of all the different atoms of earth, that's why I'm rather looking for a thermodynamic related calculus.

 

[Borek]

i don't know something like that

I am afraid that summarizes whole thread.

 

[flicflex]

I am afraid that summarizes whole thread.

Exactly. Which parameters can determinate Earth radius and how.

 

[Ophiolite]

Exactly. Which parameters can determinate Earth radius and how.

I have answered that in a general way in post #29. If you wish to get a more precise answer then an extensive study into geochemistry, geophysics and planetology over a five to ten year period should provide the answer you seek. The question is not, in my view, interesting enough to warrant anyone yet having considered it. You could become famous.

 

[flicflex]

Your answer was interesting, but I'm indeed looking for a thermal answer rather than a (geo)chemical answer.

Do you think Earth can be considered as some kind of solid gaz, or at least as complex system, in order to study it trough a thermal/energetical point of view? Is it what you call an extensive study?

Why would'nt it be interesting? Such a method would save obviously a lot of calculus and measures in order to describe few characterisics of any planet.

 

[Borek]

Such a method would save obviously a lot of calculus and measures in order to describe few characterisics of any planet.

No.

Mass & radius of a planet are in a way random and depend on the initial conditions in the system from which the planet emerged. They are easy to measure and they are the basic input data used to build the planet model. You can't use other data to predict mass & radius, as you don't have the other data.

 

[Dickfore]

solid gaz,

This is an oxymoron.

 

[AlephZero]

But why does the materia doesn't accumulate anymore (isn't solid anymore) beyond that greatest gravitational potential field (6400km)?

Mateiral is still accumulating, at a rate of about 10,000 to 20,000 tons per year. http://en.wikipedia.org/wiki/Micrometeoroid

 

[snorkack]

No.

Mass & radius of a planet are in a way random and depend on the initial conditions in the system from which the planet emerged. They are easy to measure and they are the basic input data used to build the planet model. You can't use other data to predict mass & radius, as you don't have the other data.

They are not independent.

You cannot predict mass from radius without knowing composition. With mass and composition you can predict radius - reasonably easy at intermediate masses, gets harder at low and high masses. The radius does depend on internal heat (slightly).

Now, as for "phase change"...

The surface of ground is NOT generally at 0 altitude. The surface of water is.

When you look at water surface, you commonly see two, and even three transitions, depending on weather.

Counting from up to down, you will find mostly gaseous air, then mostly solid water, then mostly liquid water, then mostly solid rock.

The smallest composition contrast is the one between mostly solid water and mostly liquid water.

But before you single that out as a phase transition in contrast to the other two transitions, note that the liquid water contains significant amounts of liquid (dissolved) rock, which is missing in solid water, and smaller but also significant amounts of liquid (likewise dissolved) air.

The mostly gaseous air above contains significant amounts of gaseous water. And the mostly solid rock contains significant amounts of liquid water, as well as liquid (dissolved) rock and liquid (dissolved) air.

 

[Borek]

You cannot predict mass from radius without knowing composition. With mass and composition you can predict radius - reasonably easy at intermediate masses, gets harder at low and high masses. The radius does depend on internal heat (slightly).

I never stated you can predict them. And the way I see it composition is a function of the initial conditions.