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Impossibly Massive Celestial Body Destruction Calcs are just Faster Than Light Kinetic Energy Calcs

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Alright so this exists for the purpose of pointing out a double-standard in the rules for Kinetic Energy feats.

So, Faster Than Light Kinetic Energy is not allowed given how the Relativistic KE Formula goes to infinity energy at light speed, and using the Regular Kinetic Energy Formula which ignores relativistic mass isn't allowed because that's not how you [physics].

Despite this, calculating Gravitational Binding Energy for celestial bodies which, by all natural laws should absolutely be Black Holes (Solar System sized planets and the like), is allowed. This is a double standard.

Now, why is this a double standard? Because the formula for Gravitational Binding Energy is based on the formula for Regular Kinetic Energy, plus 3 layers of trench-coats for the variables.


The simplified Gravitational Binding Energy Formula is based on having a uniform sphere, and "imagining that it is pulled apart by successively moving spherical shells to infinity, the outermost first, and finding the total energy needed for that." The energy to pull apart the spherical shell from the gravitational body is the negative of the Gravitational Potential Energy.

Gravitational Potential Energy (acceleration * mass * height) is just Kinetic Energy you'd have when hitting the ground from a certain height.
Let's say a 1 kg object falls from a height of 10 meters, and experiences 9.8m/s^2 of acceleration.
Energy Via GPE (height*mass*acceleration)- 1 * 10 * 9.8 = 98 joules
Energy Via Kinetic Energy right before you hit the ground- Displacement = initial velocity*time + 0.5*acceleration*time^2
The ball is 10 meters off the ground, is unmoving before it falls, and falls at 9.8m/s2 so-
10 = 0*time + 0.5*9.8*time^2
10 = 4.9*time^2
sqrt(10/4.9) = time, time = 1.428571429 seconds
Accelerating 9.8 meters per second every second, after falling for 1.428571429 seconds, means the speed before hitting the ground is 9.8*1.428571429 = 14 meters per second
Kinetic Energy = 0.5*mass*velocity^2, so 0.5*1 kg*14 m/s^2 = 98 joules
In other words, Gravitational Binding Energy is just the kinetic energy required to send apart the mass of a body fast enough that it won't come back together again. This can best be seen with how GBE can be roughly approximated by multiplying a celestial body's Mass by its surface Escape Velocity.

Earth GBE: ~2.487*10^32 joules (from AP Chart)
Earth Mass * Escape Velocity KE: 0.5* 5.9722*10^24 kg * 11186m/s^2 = ~3.7364*10^32 joules
Difference: 2.487*10^32 vs. 3.7364*10^32 joules

Jupiter GBE: ~1.775*10^36 joules
Jupiter Mass * Escape Velocity KE: 1.898 * 10^27 kg * 60200m/s^2 = ~3.439*10^36 joules
Difference: 1.775*10^36 vs. 3.439*10^36 joules

Sun GBE: ~5.693*10^41 joules (from AP Chart)
Sun Mass * Escape Velocity KE: 0.5 * 1.98847*10^30 kg * 617500m/s^2 = 3.791*10^41 joules
Difference: 5.693*10^41 vs. 3.791*10^41 joules
Not a perfect estimate of GBE, but still consistently within a factor of 2.

So when a body is so massive that it should become a Black Hole, it means that its surface escape velocity has exceeded the speed of light. Which means that it should be impossible to blast it apart due to Relativity- even if the celestial body still retained its shape and didn't collapse into a singularity somehow, the mass still has to move faster than light in order for the Celestial Body to be destroyed.

Impossibly Massive Celestial Body Calcs are basically doing the equivalent of using the Regular Kinetic Energy formula for FTL Speeds. Such as the calc of Godzilla Earth shattering Black Holes, Ergenverse's destruction of a Cultivator Planet, this Sage Monarch Calc, or (sigh...) the Asura's Wrath Moon Calc. (I'm so sorry Zamasu_Chan...)

As proof- I'm going to do the same GBE vs. Mass * Escape Velocity KE comparison for the Giga-Moon Calc-
  • Galaxy Sized Moon GBE: 1.9811372*10^93 joules
  • Mass * Escape Velocity KE, with the Moon's Escape Velocity gotten from plugging the Radius and Mass into this Escape Velocity calculator- 0.5 * 2.4396811*10^61 kg * 16452333899637669m/s^2 = 3.30185575*10^93 joules
  • 1.9811372*10^93 vs. 3.30185575*10^93 joules (BASICALLY THE SAME ENERGY VALUE, STILL WITHIN A FACTOR OF 2)

TLDR: Here is the problem.
1. Planet/Star GBE is essentially the Kinetic Energy of its Mass times its Escape Velocity, plus a couple other factors
2. Black Holes are created when a star core is so crushed, that its escape velocity exceeds the Speed of Light
3. Impossibly Massive Celestial Bodies in fiction have Escape Velocities waaaay higher than Lightspeed, and should be Black Holes
4. Energy yields via FTL KE by using the regular KE formula isn't allowed, yet [Should Be A Black Hole By IRL Physics] Celestial Body GBE is usable for energy yield, despite the two being the same thing
5. That is a Double Standard.

Either we allow FTL KE, or we don't allow Impossibly Massive Celestial Body GBE.


(If you wanna know if a fictional planet/star should be a blackhole, just plug its mass and diameter into a Schwarzschild radius calculator. If the Schwarzschild radius is smaller than the Planet's radius, then it's not a black hole)
 
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Thank you for helping out, DontTalk. So is there anything that we need to do based on this thread, or should we close it?
 
Probably a note should be added to the Creation Feats page that, if the GBE of an object is infinite/unquantifiable due to relativism, it should be quantified similar to black hole creation.
 
Okay. That seems fine.

Would you be willing to handle it please?
 
That's a really roundabout way of saying "we shouldn't do GBE of impossibly large bodies, because by proper physics the GBE would be infinite."
Admittedly I probably didn't need to go into that much detail...
(and can you please use normal formatting....)
What would be normal formatting?
Probably a note should be added to the Creation Feats page that, if the GBE of an object is infinite/unquantifiable due to relativism, it should be quantified similar to black hole creation.
But they aren't creating the Celestial Bodies- every calc linked is about destroying them
 
I tend to agree more on accepting Newtonian FTL KE. Since this is more likely how most ACGN works are demonstrating FTL KE.

Sometimes they have to specifically show specific scenes to counter their arguments (like showing far less target / collateral destruction as a result damage) or they specifically tell they are applying relativism at a point (like how white dwarf star punch by the DC Flashes).

Probably a note should be added to the Creation Feats page that, if the GBE of an object is infinite/unquantifiable due to relativism, it should be quantified similar to black hole creation.
This can serve as an alternative for the matter of discussion which is celestial object creation.
 
I tend to agree more on accepting Newtonian FTL KE. Since this is more likely how most ACGN works are demonstrating FTL KE.

Sometimes they have to specifically show specific scenes to counter their arguments (like showing far less target / collateral destruction as a result damage) or they specifically tell they are applying relativism at a point (like how white dwarf star punch by the DC Flashes).
Already been conclusively rejected.
 
Yes, that is not up for debate again. My apologies.
 
So uh, how do we know that the GBE is infinite? Will it be when the Schwarzchild radius is bigger than the object's diameter? Is that when we'll use the Black Hole formula?
 
So uh, how do we know that the GBE is infinite? Will it be when the Schwarzchild radius is bigger than the object's diameter? Is that when we'll use the Black Hole formula?
Correct- although it'd be the object's radius not diameter but you get the idea
 
So what should we do here exactly?
 
Okay. Thank you for the reply. That is not my area though, so we should probably wait for input from knowledgeable staff members.
 
Been thinking. I think if one calculates mass via surface gravity instead of simpler density calcs some cases where the Schwarzschild Radius would get problematic might still be calculatable as usual.
That should probably also be noted as well... (this stuff is getting complicated)
 
Thank you for helping out as usual. 🙏
 
Been thinking. I think if one calculates mass via surface gravity instead of simpler density calcs some cases where the Schwarzschild Radius would get problematic might still be calculatable as usual.
That should probably also be noted as well... (this stuff is getting complicated)
Instead of assuming the planet has Earth density, we assume the planet has Earth gravity? Interesting...

That... probably would make more sense, since stuff on most absurdly large planets doesn't fall like it's experiencing a bajillion times earth gravity, so Earth Gravity is a more backed up assumption than Earth Density.

Granted, it'll probably result in giga-planets less dense than cotton candy on average, despite having solid surfaces, but that still makes more sense than the planets having obscene gravity which nobody notices.
 
Instead of assuming the planet has Earth density, we assume the planet has Earth gravity? Interesting...

That... probably would make more sense, since stuff on most absurdly large planets doesn't fall like it's experiencing a bajillion times earth gravity, so Earth Gravity is a more backed up assumption than Earth Density.

Granted, it'll probably result in giga-planets less dense than cotton candy on average, despite having solid surfaces, but that still makes more sense than the planets having obscene gravity which nobody notices.
https://emandpplabs.nscee.edu/cool/temporary/doors/space/planets/find/findFg.htm

There is also this website that has a formula for gravitational force. Gonna have to look for other sources to ensure this is also backed up fully
 
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https://emandpplabs.nscee.edu/cool/temporary/doors/space/planets/find/findFg.htm

There is also this website that has a formula for gravity. Gonna have to look for other sources to ensure this is also backed up fully
I'd just use the planet-maker equation from Artifexian, which has everything in Earth Units
(Earth Gravity = (Earth Masses/Earth Radii^2) = Earth Radii * Earth Density.
(It's for the purposes of scientifically accurate World Building for Sci Fi planets, but it'll work fine for here as well)

Since Earth Gravity would be 1G, and we're solving for mass so we can get GBE later, the formula would be rearranged like-
  • 1 Earth Gravity = Earth Mass /Earth Radii^2
  • 1 * r^2 = M/r^2 * r^2
  • r^2 = M
 
I'd just use the planet-maker equation from Artifexian, which has everything in Earth Units

(It's for the purposes of scientifically accurate World Building for Sci Fi planets, but it'll work fine for here as well)

Since Earth Gravity would be 1G, and we're solving for mass so we can get GBE later, the formula would be rearranged like-
  • 1 Earth Gravity = Earth Mass /Earth Radii^2
  • 1 * r^2 = M/r^2 * r^2
  • r^2 = M
https://pages.uoregon.edu/jimbrau/astr121/Notes/Jupiter/jupitergrav.html

There is also this.
 
Been thinking. I think if one calculates mass via surface gravity instead of simpler density calcs some cases where the Schwarzschild Radius would get problematic might still be calculatable as usual.
That should probably also be noted as well... (this stuff is getting complicated)
I'd just use the planet-maker equation from Artifexian, which has everything in Earth Units

(It's for the purposes of scientifically accurate World Building for Sci Fi planets, but it'll work fine for here as well)

Since Earth Gravity would be 1G, and we're solving for mass so we can get GBE later, the formula would be rearranged like-
  • 1 Earth Gravity = Earth Mass /Earth Radii^2
  • 1 * r^2 = M/r^2 * r^2
  • r^2 = M
Using Planet Suzaku to see how using Earth Gravity would change the GBE-

Planet Suzaku Radius: 2.36E+12 metres
Earth Radius: ~6371000 meters
Suzaku in Earth Radii: 370428.5042

Suzaku Mass: 370428.5042^2 = 137217277000 Earth Masses, or 137217277000 * 5.9722*10^24 = 8.19489022*10^35 kg

The Schwarzschild Radius of ~819 decillion kilograms is 1.217*10^9 meters
2.36E+12 metres > 1.217*10^9 meters
Suzaku is not a Black Hole by this method.

GBE: 3GM^2/5R, where M is in Kg, R is in meters, and G is the Gravitational Constant-

(3 * 6.674×10^(-11) * (8.19489022*10^(35))^2) / (5 * 2.36*10^12) = 1.13949318*10^49 joules

Still pretty damn high, but about 100 billion times lower than the Earth-Density GBE value of 1.928E+60 Joules

(This also results in Planet Suzaku being 370428.5042 times less dense than the Earth on average, or 14.875 g/m3- only a dozen or so times denser than the water vapor content of a cloud, but oh well.)
 
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So what should we do here exactly?
 
Why not just use the Planetary Parameters calculators for these kinds of feats instead of having to punch in all of these equations?

I guess deciding which surface gravity value to use can be problematic as that influences the mass of the planet, but a massive spherical object is guaranteed to be self-gravitating (unless otherwise stated or demonstrated). So at bare minimum, one could say that the object has a surface gravity equivalent to that of a 600km spherical asteroid (which according to this is the bare minimum a celestial body has to be to become circular and self-gravitating).

Using the same calculator I find out that the surface gravity of an asteroid with a density of 2700 kg/m3 is around 0.02309g. This value could be used if the celestial body in question has been shown to have a surface gravity far less than the Earth.

If it does have a comparable gravity to Earth, just keep the surface gravity value to 1.
 
Thank you extremely much for helping out so much. You are awesome. 🙏 🙂
 
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