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Curious phase transition 
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#19
Nov2712, 06:04 AM

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P: 22,313

http://en.wikipedia.org/wiki/History...stem_formation 


#20
Nov2712, 06:08 AM

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#21
Nov2712, 08:31 AM

P: 13

Let me rephrase... which parameters determine the radius (in our case 6371km) of a planet and how (which function) ?



#22
Nov2712, 02:17 PM

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P: 22,313

Depends on how specific you want to get, but I'd start with mass and density:
V=m/d 


#24
Nov2712, 03:02 PM

P: 13

well let's admit the mass, but the density has to be explained !
does earth internal inergy alone can parametrize earth density? In such a case, how do we determine earth internal energy? earth initial internal energy + energy lost in the external system (cooling within the universe) + energy brought by the external system (sun and asteroid crashes) ? 


#26
Nov2712, 04:55 PM

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P: 22,313

I'll translate, and I was initially going to include this:
Temperature (internal energy), heat generation, heat dissipation, thermal conductivity, heat capacity and.....coefficient of thermal expansion. http://en.wikipedia.org/wiki/Thermal...sion_in_solids In other words, as the earth cools, it shrinks. How much? Probably not enough to be more significant than the effect of its oblateness or plate tectonics. 


#27
Nov2812, 04:09 AM

P: 13

Yes indeed the evolution of earth internal energy determines the evolution of its diameter.
But my question is rather how does earth internal energy determines its diameter (statically talking)? borek (numerology salad blabla), i apologize for my lack of vocabulary but I beg you to try to understand the topic behing my babblings rather than despise them 


#28
Nov2812, 06:11 AM

P: 2,504

However, as pointed out, the solid and liquid surfaces of the Earth consist of different substances than the atmosphere, so there is no phase transition per se. Where the surface is water or water ice, the atmosphere is still mostly nitrogen and oxygen with proportionately very little water vapor. http://www.syvum.com/physics/gravita...vitation2.html 


#29
Nov2912, 01:40 AM

P: 288

flicflex, phase transitions in geophysics refer to structural changes in minerals, generally associated with changes in pressure, or temperature. So, phase transitions do play a role in determining the Earth's radius, in as much as they have profound effects on the interior stucture and behaviour of the Earth's interior.
The original composition of the planetesimals forming the Earth, the siderophile, lithophile or chalcophile tendencies of the elements, the resultant differentiation into crust, mantle and core, the subsequent phase changes within mantle and core, the consequent initiation and evolution of convection, all of these things in combination have determined the particular radius of the Earth. (Other items could be added.) That said, I'm still not sure I have properly understood what it is you are trying to ask. 


#30
Nov2912, 02:45 AM

P: 3,014

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 [itex]R \pi/2[/itex]. Then, solving for the radius, we have: [tex] \frac{R \pi}{2} = 1.0000 \times 10^4 \, \mathrm{km} [/tex] [tex] R = \frac{2 \times 1.0000 \times 10^4 \, \mathrm{km}}{3.14159} = 6.3662 \times 10^3 \, \mathrm{km} [/tex] There is your magic number! Similar examples to your question would be to ask why is the radius of the Earth 3400 nautical miles (look up the definition of a nautical mile), or why is the triple point of water at an absolute temperature of 273.16 kelvin (look up a triple point, and the definition of a kelvin as a unit of thermodynamic temperature). What would make sense to ask is why does the ratio of two physical quantities of the same kind (eg. lengths) that are related to eachother, have a particular numerical value (but no units or dimensions). I emphasize the phrase "related", because, for example, you may take the Bohr radius (colloquially known as the radius of the hydrogen atom), which has a value [itex]a_0 = 5.29 \times 10^{11} \, \mathrm{m}[/itex], and calculate the ratio [tex] \frac{R}{a_0} = 1.20 \times 10^{17} [/tex] You may take the cube of the above ratio to find the ratio of the volume of the Earth to the volume of a single hydrogen atom [tex] x = \left( \frac{R}{a_0} \right)^3 = 1.74 \times 10^{51} [/tex] Is there any significance to this astronomical number? Not unless you show a reason behind your choice of the Bohr radius as a length of comparison. 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 [itex]2.89 \times 10^{24} \, \mathrm{kg}[/itex]. Compare this to the mass of the Earth, [itex]5.97 \times 10^{24} \, \mathrm{kg}[/itex], 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. Well, anyway, that was my long winded digression that I hope someone will read through. 


#31
Dec1412, 06:14 AM

P: 13

\frac{2 \times \frac{R\pi}{2}}{\pi}= R [/tex] 


#33
Dec1412, 07:05 AM

P: 13




#34
Dec1612, 03:35 AM

P: 288




#35
Dec1612, 11:34 AM

P: 13

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. 


#36
Dec1612, 11:57 AM

Admin
P: 23,711

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. 


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