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Tier 4 revisions

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@DontTalk

Thank you for responding.

@All

I think that we should preferably wait with any revisions until DontTalk has the time to evaluate this problem more thoroughly after a few weeks. I definitely don't want us to make any mistakes due to lack of advanced physics knowledge or impatience.
 
I agree with Ant. Nothing would be worse than spending a bunch of time and work into a site wide revision that's wrong.
 
I looked around a bit and found a value for the suns GBE in a book.

See here .

Sadly... it's in german.

To quickly translate it for those of us that don't understand german:

German text: "Fūr die Sonne ist die gravitations Bindungsenergie ungefähr EG = 3,8*1041 Ws; der Inhalt der Sonne an thermischer Energie ist von derselben Größenordnung,"

Translation: "For the sun the gravitational binding energy is approximately EG = 3.8*1041 Ws; the content of thermal energy of the sun is of the same magnitude."

The author is a theoretical physicist, so the information is likely reliable.

(Ws are equal to Joule)
 
So now we have 3 values, with two bearing citations, and one bearing a formula. Seems like our current number is most certainly wrong, and this new number is far closer to our found result than the other.
 
http://www.ucolick.org/~woosley/hw1_soln.pdf

Found this.

"6. a) The gravitational binding energy for a sphere of constant density is Ôäª = 3GM┬▓/5r

and substituting the mass of the Sun (1.99 ├ù 10^33 g) for M and the radius of the Sun (6.96 ├ù 10^10 cm) for R, we find that Ôäª = 2.3 ├ù 10^48 erg"

2.3x10^48 erg = 2.299984e+41 joules.

Which is literally almost 100% identical to our value. In fact, pretty sure it IS our value, but whoever wrote the paper rounded 2.277164e+48 ergs to 2.3e+48 ergs.

So, there is an actual paper supporting what Assalt and I got.
 
Lovely. More citations and evidence. So I think our current value is undoubtedly proven false.

So we have two educational papers that cite similar, yet different results. I support our the one we calced, since it is supported by a formula, as well as sources.
 
And then, we have this paper which states (I think) the Sun's average thermal energy is 1.2x10^48 ergs, and since thermal energy is 50% of the GBE, you multiply that by 2 and then convert it to joules, and you get 2.4e+41 joules which is far more in line with our result.

I don't know what to make of this overall.
 
@Kepekley23: Differentiate between those papers that assume a constant density (simpler but worse approximation) and those that don't.

My source doesn't have the restriction of assuming constant density and this source you mentioned goes over it and then corrects it with a more accurate value for the sun, which results in the 3.8x10^48 erg result.


On the other hand this paper as well as this homework sheet explicitely state they assume a constant average density for the sake of simplicity.


Basically the 3.8 value is more accurate, since the sun does not have a constant density.
 
If want to known, there's at least three different equations for GBE:

  • (0.6*G)*M^2/r (mass-radius relationship)
  • (0.6/G)*r^3*g^2 (radius-gravity, or volume-gravity relationship)
  • (16/15*pi^2)*G*r^5*¤ü^2 (radius-density relationship)
In theory, everything will lead to the same result, but most likely will have different results cuz any value, gravity, density and radius is an approximation. Calculated the value of the sun's GBE several times, is always around 10^41 J, but considering that, according to several sources, the sun's radius vary from 695000 to 696000 km, and density from 1400 to 1410, you will have a variation (from low to high end) of 2.17% in only one of the equations from above.

That would explain the times that my results differed from others when talking in chat, no one bodered in calculate this before? I also would expect to look for at least three sources to get a value. If we going with details the baseline for planet level would change since we are using the higher value (~2.5*10^32) rather than the lower (~2.24*10^32), but the difference here is not so big, so it can be easily ignored.
 
Antoniofer said:
If we going with details the baseline for planet level would change since we are using the higher value (~2.5*10^32) rather than the lower (~2.24*10^32), but the difference here is not so big, so it can be easily ignored.
Click to expand...
If the values mentioned here are what you are going by than the 2.487 value is simply more accurate than the 2.24 value. (Due to planets not having constant density either, meaning none of your 3 formulas really give an accurate result for them, but instead broad approximations)
 
Nah, that is not the formula that I usually use. Earth density vary from 5.5 to 5.52 g/cc, and radius from 6371 to 6378 km, that the difference between the low and high end GBE is around 2.8%. Other factor is the value of G, I generally use 6.67*10^(-11), but it seems it can vary too. However, is still far from the 11.6%, guess is used an integral or something to get the 2.5*10^32 J, in whose case it would be more accurate.
 
Given the uneven mass distributions, I would much prefer if we use GBE values found in official sources and calculated by professional physicists via computer models.

Also, as I mentioned earlier, we definitely shouldn't rush into this until everything is thoroughly evaluated and figured out.
 
DontTalk found a good value that accounts for pretty much all we need, I agree with it so far.
 
Yes, but we preferably need reliable values for the other borders/types of stars as well.
 
Is there a way to determine the non-uniform density of other stars and apply it so a more accurate formula? If there isn't we'll have to live with the 50%~ variance using uniform density.
 
I'm not staff, but the TLDR from that is this the GBE of a star = q*GM^2/r where q=3/(5-n).

Where n is 0 for constant density and for a sun like star is >=3.
 
It seems using the formula with q=1.5 is the closest we are going to get to state of arts for now. (Unless someone wants to go to his local library and read a book about the state of art models.)


I should probably at least read that article in its entirety, instead of just skimming through it, before we implement something, though. (and all results of this should be summarized in a later thread to have them reviewed by all calc group members and whoever else is available)


But for now we should probably get to the next topic that needs to be debated:

Baseline stars.

I would say for multi-solar system level using the sun is definitely fine.


The question is if we want to use the sun also as baseline for galaxies and multi-galaxies or if we want to choose some other star for that.

Using the sun would keep the changes small.
 
I mean using the Sun is probably inaccurate, since most stars are red dwarves, which are Low 4-C (approx.), and you probably won't destroy many white and blue-white main sequence or carbon white dwarves to compensate. If anything they would hit some brown dwarves.
 
Maybe we can use the main sequence chart to get the percentages of the stars, calc the mean GBE for each classification, weight them all accordingly, then get the average for all stars?

That may be too complicated though.
 
Percentage and average actually doesn't matter, because the calculation runs over the inverse square law, not over adding up the energy to destroy the separate stars.
 
Well I know that. I figured we use invers square but instead of basing it in our own Sun we get the average star in the galaxy and use that instead.

Destroying individual stars even on a galactic level wouldn't break 4-B.
 
Blademan9999 wrote the following post in the blog:

It changes things a lot.

Note that .34^2/.2=0.578, compare to .34^(5/3)=.1656

So even assuming that everything neare then .2 radii to the center has uniform density. Then everything more then .2 radii from the core has a different density which is uniform from .201 radii to the surface increases the GBE by more then 40%

And of course .5^2/.25=1, compared to .315

Then there is this.

https://ia800602.us.archive.org/26/...oductionToTheStudyOfStellarStructure_text.pdf

Note pages 96 and 101.

On table 4 (page 96) the 4th column is core density / average density. The sun has a density at the center of 150g/cm^3. Which is reach for a value of n between 3.25 and 3.5

And by equation 90 page 101, ╬® which is used to represent potential energy

= 3GM^2/r(5-n)

Plugging this is gives a value close to our original one.
 
Looks like the omega formula is identical to the original formula, save the addition of n. Man, so should we use 2.24x10^41 or the 3.8x10^41 number? 2.24 sets a precedent for getting our GBE from that formula accurately in the future. 3.8 is harder.

Edit: Wait, do you mean close to our original as in the one we are currently using, or the one that I proposed? There are so many values floating around right now it is hard to keep track.
 
Also how sure are we that the book is still accurate? That thing is coming up on 80 years old. I'm pretty sure we have made a fair bit of progress in astrophysics since WW2.
 
Yikes. A citation for the original value. Now three values all have merit. Maybe we should use the most recent source if we can't determine which is more valid than another?
 
Pretty sure that'd be an ad novitatem.

I think we should use 3.8x10^41 due to it accounting for non-uniform density.
 
You can ask DontTalk to comment here again if you wish, but I do not think that he has unsubscribed to the thread, just that he is busy IRL.
 
question, does this affect the Kingdom Hearts 4-B ranking as it derives from a feat that involves moving multiple starts?
 
I just calculated the GBE for the sun using the q*GM^2/r using q=1.5, like this source suggested and was a bit suprised over the result not being 3.8*10^41.

Checking it again I just now see that in the 3.8 result said there, there is still standing the q in the formula, meaning it actually suggests a 3.8*1.5 result.

Antvasima said:
Blademan9999 wrote the following post in the blog:

[...]

On table 4 (page 96) the 4th column is core density / average density. The sun has a density at the center of 150g/cm^3. Which is reach for a value of n between 3.25 and 3.5

And by equation 90 page 101, ╬® which is used to represent potential energy

= 3GM^2/r(5-n)

Plugging this is gives a value close to our original one.
Click to expand...
That result and this one is more or less the same. q=1.5 in the source mentioned before means as much as n=3 in this one. so n=3.25 to 3.5 is resonably close.


Thing is given this the result actually doesn't match the german source on the gbe. (For the GBE of the german source q=1 or n=2 would have to be the case)

So this is getting difficult again.

Assaltwaffle said:
Also how sure are we that the book is still accurate? That thing is coming up on 80 years old. I'm pretty sure we have made a fair bit of progress in astrophysics since WW2.
Click to expand...
This article writes in regards to the model:

"Before astronomers learned to make "real" stellar models, polytropes were quite impottant. As shown in the next figure, where I have plotted the actual density distribution of the Sun compared with an n = 3 polytrope, there is a real similarity. While polytropes are only of historical interest for the study of main sequence and giant stars, they still have their use."

So it definitely isn't up to date, albeit not completely bad either.


Which brings us to the debate if taking the german source wouldn't still be the correct course of action. While the GBE is only a fleeting mention there without more being explained the source is very credible and from 1997, meaning reasonably modern.


Aside from that we could still use the model this or this model (basically the same) as a good approximation when calculating other stars, unless someone finds out what the modern star model suggests. (I could see if my library in my university offers something, but I probably won't find time to study a bunch of books on astrophysics during this or the next month)

Assaltwaffle said:
Honestly we should probably calculate the "average star." Because the Sun is way above average.
Click to expand...
For star level? No. 99% of all stars destroyed in fiction are our sun or at least similar to it. It makes most sense to use that as baseline for star and solar system stuff.

Assaltwaffle said:
Well I know that. I figured we use invers square but instead of basing it in our own Sun we get the average star in the galaxy and use that instead.
Click to expand...
Thing is: Why the average star? You would also need to destroy above average stars and for the actual result of the calculation with inverse square law basically only one star, that is very far away and has high gbe, matters. To that comes that, if we simply calculate some average from a bunch of examples, we risk that needing to be changed in the future again, once someone makes an average over a large sample or finds some professional average star, or something.

I think there are mainly two options for choosing the baseline star for galaxies that would have arguments going for them:

1. Sun:


Pro

-the most common star in fiction and often other stars in fiction are somewhat similar

-only slight change to the current value (few revision necessary)

-low end

-star we use as standard for star level


contra

-other stars would give higher results, meaning it is a low end


2. Star with high GBE/frontal area ratio

pro
-Makes sense, as those stars also need to be destroyed when the galaxy is destroyed (less of a low end)


contra

-which star to take? -> better choices could come up later causing yet another revision

-Technically no clear upper end (the closer a star is to a black hole the higher its GBE gets, with the upper end being the infinite/undefined GBE of a black hole)

-Our star formula don't really apply to exotic stars making that a source of possible revision as well if we take more extreme cases


All in all I believe choosing the sun would result in the least trouble, to be honest.
 
Making a star other than the sun the baseline is a terrible idea. Most fiction tend to base standards for Planets, Stars and Galaxies on our own since it is the most common for us.

Even though neither match the average planet / star / galaxy size for our universe.

It should still be what we use as baseline.

Hell, if we were to use the "Average star rating" in real life for our Baseline, our Baseline Planet level would be Jupiter, since last I checked that's the actual average planet size in the universe.
 
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