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"Just a change of name" is pretty big. It's a change spanning the names of 3 subtiers that would change hundreds of characters. As much as I want to implement less of a misnomer name, we can't rush into this.
The problem is also that we need the GBE values of other types of stars than the Sun. Othervise we will likely have to merge High 5-A, Low 4-C, 4-C, and High 4-C into one.
Do we need to change them? Were they using an erroneous calculation method like the Sun? What stars are chosen to make up the baselines for the other tiers?
I obviously agree that it wouldn't be good to merge the tiers, and I think that there are explanations for the GBEs in the Attack Potency page, possibly via a link to a blog post.
They estimate, based on the density model in Landolt-Börnstein (1981), that the gravitational potential energy of the sun is 6.13*10^41 J.
However, it also mentions that the density model seems to assume a too strong concentration of mass towards the center, because under the given conditions the sun doesn't reach hydrostatic equlilibrum (or something like that).
So we now have a value we pretty much all agree on. Can we organize the revisions now? I would prefer to get this overwith so we can move on to other topics.
Supposedly it already has been, although I can calc the result they got within a couple decimals.
Honestly my question of "does average density cover the increase for density approaching the center" wasn't answered to my knowledge, and I am not sure what the specific formula used to get 3.8x10^41 is, but it has many sources acknowledging it as correct.
As of now I don't think so. I'm going to read through some of the articles again and wait for DontTalk and Kep to weigh in here, since they are two other big players in this.
I am starting to get more confused reading back over our sources... seems Stellar Structure indicates that U = 2x10^41, which is total thermal energy, which our German guy attests is equal to GBE.
OK, going through the sources, here is what I'm seeing. This source actually kinda supports 2.27, not 3.8. Why? Because their formula is identical to ours, yet they treat Omega not as GBE, but rather U as total thermal energy. As stated by our German source, total thermal energy equals GBE. However, according to Virial Theorem, total thermal energy doesn't EQUAL GBE, it is half of it. This would lean to 4x10^41, which is closer to 3.8x10^41.
Next, an astrophysics lecture cites the GBE of the Sun to be 2.4x10^41, which is very close to our calculated 2.27.
But Bladema brought up a different formula, using a new variable, n, which is used to get a different result. However from what I can see this is calculating Gravitational Potential Energy, not Gravitational Binding Energy.
So, do you have concrete plans for how to move the borders for Low 4-C and High 4-C as well, and what will those border be based on in that case?
Perhaps it would be best if you ask all calc group members (including Executor N0) to help out with this by commenting here? It is a very important topic to get right after all.
In lack of better options, I also think that we should probably use Low Star level and High Star level as substitute titles.
I'm going to make another thread, since this is already getting long, exclusively about the bounds of the tiers. I have submitted a question to a physics forum, so maybe I can get some answers concerning the value in question.
Either way I will bring them in given time.
As for names, I'll forgo that right now, as getting our values right is far more important than naming.
I figured getting as much info and clarification as possible is a good idea. I am reposting the question to both the Physics and Astronomy subreddits as well.
Heh... I just imagined Neil Degrasse Tyso tweeting out how much energy it would take to destroy celestial bodies and how he's glad to be your personal astrophysicist
Okay. Thank you for the dedication to get this properly done. However, please remember that we need the GBE for a few other types of stars as well, so we can set up different borders for the tiers.
I figured the Sun's GBE question can snowball into finding values for all the other stars. Once we have a hard-and-fast way to get proper GBE, we can go from there.
If the other bounds (not just baseline 4-C) need to be adjusted, I'll wait until Naruto and Bleach wrap up, since that kind of change would be massive.
Okay. Thanks again. And I agree that a complete revision of tier 4-C would be massive and requires us to wait until we are able to commit to the project.
Great news, guys! This has been much more fully fleshed out by a staff member of the astrophysics branch of the Physics Forum. Here is his response. It is basically what Blademan originally brought up, and this user even brought up the specific value, as being Polytrope. Now we have a direct formula to calculate GBE of stars!
This new formula would be U = (3*G*M^2)/(r(5-n)), in which U is GBE in joules, G is the gravitational constant of 6.67408x10^-11, M is mass in kilograms, r is radius in meters, and n is the polytropic value attributed to the type of star. For example, for giants and brown dwarves would be 1.5, while n for main-sequence and degenerative core (white dwarves, for example) is 3, and extremely dense stars, such as the neutron pulsars, have an value of 1.
Using this new formula, we get a value of 5.6928564x10^41 joules for our Sun's GBE. This is closer to the original value, and actually has a new, cited, and hard-and-fast formula behind it. I believe this should be the number, and we should update our GBE page with this new polytrope-compensated formula, as well as the polytrope values for the different types of stars.
That's excellent!... if I'm reading this right, Star level will generally remain in about the same place its in right now, using this value? (Current low-end for Star level being 6.276x1041 Joules)
Which would be what, 136.06 Tenatons of TNT, about?