Introduction[]
This is a re-calculation of the Eclipse Cannon's feat of being able to pierce through stars with its full power. The original calc was done by Mephistus
Despite some controversy regarding what the Eclispe Cannon was described to pierce whether it would planet or star, we do get an answer in the game. In the original Japanese version, Black Doom claims that the Eclipse Cannon can pierce through stars. The Japanese version uses the kanji "hoshi" (星), which can mean either planet or star. However, in the game, it is translated into star by Windii, who is japanese can has the most accurate translations from Japanese to English for the Sonic franchise.
The English version further supports this by directly saying the word "star" rather than planet
Furthermore, in Sonic Adventure 2, which originally came in Japanese, the kanji "hoshi" is used once again, and is also translated as star by Windii.
With these examples, it's pretty clear that the kanji "hoshi" meant star instead of planet in this case
In the original calc, the method used was that the blast basically expanded the sun as it went through, and thus used difference in GBE to get the result for the attack.
However, it would be far more accurate to calculate the materials of the sun being destroyed as the laser passes through it, and since the Sun is made of plasma, regular methods of destruction are not enough, as plasma is beyond even vaporization.
As such, the only way to destroy the materials of the sun even further would be to break them atomically, which means that for this calc, atomization would have to be used
Once again, I'm using the Sun for this calc as it is the closest star to Earth and is basically our default star for calculations regarding stars
The Calculation[]
Assuming the hole the ARK makes in the sun would need to be visible to really consider it piercing the sun it would need to be at least 10 pixels wide based on this calculation
Another point would be, that since the Space Colony ARK would fire at the sun from Earth, the hole it creates in the sun would also need to be seen from that far away from the sun, so the size used in the calc would be a safe low-ball
Teal line = The Sun's Diameter = 672px = 2 * 695,700 = 1,391,400 km
Hole's diameter = 10px = (1,391,400 / 672) * 10 = 20,705.357142857 km
Using the volume of a cylinder for approximation: V = π * r^2 * h
V = π * ((20,705.357142857/2)^2) * 1,391,400 = 4.684975588774168822856122303579e+14 km^3 = 4.684975588774168822856122303579e+23 m^3
Using the average density of the sun of 1,408 kg/m^3, we get:
M = 4.684975588774168822856122303579e+23 * 1,408 = 6.5964456289940297025814202034392e+26 kg
The sun is made out of 71% hydrogen and 27.1% helium, 0.97% oxygen, 0.4% carbon, 0.1% nitrogen, 0.1% silicon, with the rest being other heavy elements, though their mass by comparison to the rest is neglible
Below are listed the binding energy of the different elements per nucleon:
Atomic mass is measured in daltons, which is: u = 1.6605390666e-27 kg
Hydrogen: 0 (as it doesn't have any other nucleons attached to its single proton)
Helium: 7.073915MeV
Oxygen: 7.976206MeV
Carbon: 7.680144MeV
Nitrogen: 7.475614MeV
Silicon: 8.447744MeV
Now, to calculate their respective yields:
E = (Binding Energy per nucleon) * (eV in joules) * (Number of nucleon in an atom) * (6.02214076e+23 atoms per mol) * (molar mass per kg) * (Percentage of Total Mass * Material's Mass)
Eh = 7.073915e+6 * 1.602176634e-19 * 4 * 6.02214076e+23 * (1 / (4.002602 * 1.6605390666e-27 * 6.02214076e+23)) * (0.271 * 6.5964456289940297025814202034392e+26) = 1.2193208343743468377211743988996e+41 joules
Eo = 7.976206e+6 * 1.602176634e-19 * 16 * 6.02214076e+23 * (1 / (15.999 * 1.6605390666e-27 * 6.02214076e+23)) * (0.0097 * 6.5964456289940297025814202034392e+26) = 4.924549688397149385322107515121e+39 joules
Ec = 7.680144e+6 * 1.602176634e-19 * 12 * 6.02214076e+23 * (1 / (12 * 1.6605390666e-27 * 6.02214076e+23)) * (0.004 * 6.5964456289940297025814202034392e+26) = 1.955242540635446763180025976803e+39 joules
En = 7.475614e+6 * 1.602176634e-19 * 14 * 6.02214076e+23 * (1 / (14.00643 * 1.6605390666e-27 * 6.02214076e+23)) * (0.001 * 6.5964456289940297025814202034392e+26) = 4.7557468905461942407302837811054e+38 joules
Es = 8.447744e+6 * 1.602176634e-19 * 28 * 6.02214076e+23 * (1 / (28.085 * 1.6605390666e-27 * 6.02214076e+23)) * (0.001 * 6.5964456289940297025814202034392e+26) = 5.3603806534942080739462930567014e+38 joules
Total Energy: 1.2193208343743468377211743988996e+41 + 4.924549688397149385322107515121e+39 + 1.955242540635446763180025976803e+39 + 4.7557468905461942407302837811054e+38 + 5.3603806534942080739462930567014e+38 = 1.2982348842087132015208723106566e+41 joules = 31.028558417990277283003640312061 Quettatons of TNT, or Small Star level
Quite an upgrade I would say
EDIT:[]
I was told by Jasonith to use the composition of the Sun from here, and assume the rest of the heavy elements to be nickel, as shown here
According to the page, the sun's composition is about 70.6% hydrogen, 27.4% helium, and the rest are other heavy elements
Below are listed the binding energy of the different elements per nucleon:
Atomic mass is measured in daltons, which is: u = 1.6605390666e-27 kg
Hydrogen: 0 (as it doesn't have any other nucleons attached to its single proton)
Helium: 7.073915 MeV
Nickel: 8.732041 MeV
E = (Binding Energy per nucleon) * (eV in joules) * (Number of nucleon in an atom) * (6.02214076e+23 atoms per mol) * (molar mass per kg) * (Percentage of Total Mass * Material's Mass)
E (Helium) = 7.073915e+6 * 1.602176634e-19 * 4 * 6.02214076e+23 * (1 / (4.002602 * 1.6605390666e-27 * 6.02214076e+23)) * (0.274 * 6.5964456289940297025814202034392e+26) = 1.232818850991037024116611753868982392883e+41 joules
E (Nickel) = 8.732041e+6 * 1.602176634e-19 * 58 * 6.02214076e+23 * (1 / (57.935342907 * 1.6605390666e-27 * 6.02214076e+23)) * (0.02 * 6.5964456289940297025814202034392e+26) = 1.112759874957811423492498725812665884055e+40 joules
E = E = (1.232818850991037024116611753868982392883e+41) + (1.112759874957811423492498725812665884055e+40) = 1.344094838486818166465861626450248981288e+41 joules = 32.12463763113810149296992415034055882619 Quettatons or Small Star level
Still Quite the upgrade
Tally[]
The Eclipse Cannon Pierces the Sun: 31.028558417990277283003640312061 Quettatons of TNT, or Small Star level\- EDIT: The Eclipse Cannon Pierces the Sun: 32.12463763113810149296992415034055882619 Quettatons, or Small Star level