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Really small "solar systems" (Read 6429 times)
frankuitaalst
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Really small "solar systems"
10/24/07 at 12:39:43
 
Off topic ...but interesting ...
Solar systems can be described by Newtons law GmM/r² where r is of order 10E+12 m.  
But how about the building blocks of matter , protons and electrons ?  
Their motion can be described ( omitting magnetic fields ) by the differential equation  
md²r/d²t= -GMm/r²+kQq/r² ,  
where k is Coulombs constant and Q and q are the electrical charges in Coulomb .  
There's a strong analogy between the gravitational force and the electrical force as both vary with 1/r².  
This means the methodology of GravSim may be used also to simulate the behaviour of electrons around their nucleus , if also charges are taken into account .  
 
The analogy with gravitiotional fields holds , but things become interesting while charges can repell each other and while the electrical force is much stronger  than the gravitational force .
Distances are very small . The radius of a hydrogen atom is about 31 * 10E-12 meters ! .    
This gives velocities of the electron around its nucleus in the range of 2000km/sec !  
I ran some simulations of such a system , using the Picard Integrator.  
Typical timesteps of such systems are about 10E-15 s ! .  
 
Herunder is a simulation of a Helium nucleus consisting of (2p+2n) + 2  electrons .  
It is assumed that both electrons evolve in the same plane and both were originally positionned  opposite to each other . Distance from the nucleus is 31E-12 meters.  
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frankuitaalst
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Re: Really small "solar systems"
Reply #1 - 10/24/07 at 12:43:13
 
Assuming however that the electrons have an opposite direction and still rotate in the same plane gives the following picture ....
Coming close the electrons repell each other .
The resulting pattern cannot be created in pure gravitational systems.
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EDG
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Re: Really small "solar systems"
Reply #2 - 10/24/07 at 17:39:34
 
Wait, are you using the normal version of GravSim for that, or have you somehow tweaked its code first? Cos that's pretty darn cool if you can do it with the default version...
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frankuitaalst
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Re: Really small "solar systems"
Reply #3 - 10/24/07 at 22:11:49
 
Quote from Mal on 10/24/07 at 17:39:34:
Wait, are you using the normal version of GravSim for that, or have you somehow tweaked its code first? Cos that's pretty darn cool if you can do it with the default version...

I wrote some code to do this . But I think the GravSim may be able to do so as well if it also deals wit charges .  
However theres a lot of nerviousity in this systems as the electrons have mutually repulsive forces .
For instance having a second or third electron in another orbit causes a lot of interaction ... I'll try to post such system .  
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frankuitaalst
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Re: Really small "solar systems"
Reply #4 - 10/25/07 at 04:09:51
 
As mentionned above electrons in different orbits have a lot of interference . Hereunder a sim of two electrons in different orbits around a nucleus.  
It can be seen that the electrons rather have an orbit "shell" than an orbit as we expect if it were electrical neutral bodies.
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Re: Really small "solar systems"
Reply #5 - 10/28/07 at 11:24:36
 
I guess you could use it as evidence that electrons are not really point charges (and masses) as you would never find a stable configuration. Well not one that reflects proper atomic structure. Its one of those really mind bending bits of quantum theory. The electrons are not really in one place or the other and neither particle or wave. That is of course untill you try and find them!
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frankuitaalst
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Re: Really small "solar systems"
Reply #6 - 10/28/07 at 12:35:44
 
Quote from shellandtube on 10/28/07 at 11:24:36:
I guess you could use it as evidence that electrons are not really point charges (and masses) as you would never find a stable configuration. Well not one that reflects proper atomic structure. Its one of those really mind bending bits of quantum theory. The electrons are not really in one place or the other and neither particle or wave. That is of course untill you try and find them!

One if the differences to normal gravity problems is that it is a lot more difficult to find initial conditions to create stable orbits as charges repell . In the case above the orbits are dynamically stable . Dynamic stabilty is also found in gravity problems . I remember a sentence in the work of Murray&Dermot saying also our solar system is "chaotic" .  
If you say electrons are neither in one place or another you're probably right ...as in the model above they orbit that quickly that it seems they are everywhere at once ( typical orbit periods are much smaller than 10E-15 seconds !) . I don't know of any device being capable to measure this tiny timeunit .
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« Last Edit: 10/28/07 at 15:42:51 by frankuitaalst »  
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Re: Really small "solar systems"
Reply #7 - 10/29/07 at 16:30:28
 
When you start looking at subatomic particles the physics totally changes. You can not really apply newtonian mechanics or simple electrostatics to the problem. Electrons are best modelled as energy waves and schrodingers equation gives a probability of position in relation to the nucleus. Everything on this scale becomes probablistic. They exist in neither one state or another untill the act of observation forces them to assume a particular state. Do a search on schrodingers cat its an interesting thought experiment about probability and quantum superposition. I had to do some of this quantumn theory as part of my chemistry degree and its hard concept to grasp.
 
With reference to time measurement I think oscilloscopes are as close as you can get and the best they can do is 100GHz or 1E-11 second time intervals. Although 1E-15s is tiny for us its a long time for an electron!
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frankuitaalst
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Re: Really small "solar systems"
Reply #8 - 10/29/07 at 23:50:58
 
Thanks for the comments ,shellandtube. With this model I only wanted to show the Bohrs model of the electrons and draw some analogies to gravity ( it turns out that the particles mass is really of second or even third...order ) .  
The Schrödinger Wave equation which explains a lot more of the weird behaviour of the electron cloud is much harder to visualise isn't it ?  
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Re: Really small "solar systems"
Reply #9 - 10/30/07 at 12:03:25
 
Yes very. The shapes of the electron orbitals are derived from the wave function (schrodinger) and they are anything but simple in shape. The link below gives a nice picture of the orbitals for single atoms. Molecular orbitals are also briefly mentioned.
 
http://en.wikipedia.org/wiki/Atomic_orbital
 
Its a nice sim and clearly illustrates the relative size of the electromagnetic and gravatational field strengths. Also it might be worth noting at velocities of 2000 km/sec relativistic effects might start coming into play.
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frankuitaalst
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Re: Really small "solar systems"
Reply #10 - 10/31/07 at 10:26:42
 
Thanks for the link . I found a sublink which is quite interesting ....
http://winter.group.shef.ac.uk/orbitron/
In the meantime I have been playing with de H-atom and tried to let collide two of them in order to see if they would form H2.  
Nopes ... Sad
One of the electrons always , no matter what the energy of approach is , escapes ...leaving one empty nucleus .  
Seems as the Bohr model cannot explain the dynamical bouding .
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