This is going to be a lot of math and walls of text. We now have a new GBE formula for stars to use, and as such any value at or above High 5-A will need to be recalculated. The following is a thorough explanation of how the results are reached, the math itself, and the new chart. Here we go.
1. GBE: Gravitational binding energy is the energy needed to completely disperse a celestial body. If GBE is broken, the particles of the body will not reform or be bound to each other's gravity, but instead drift off infinitely in the direction they were moved towards. For our purposes, we can find GBE of a star with the following formula.
This formula is 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. While this blog is not perfectly accurate, it is widely applicable, and is still within the acceptable margin for error.
2. Inverse Square Law: In short, inverse square states that the farther away from an omnidirectional (or even spreading attack) the target is, the more energy would be required by the attack to destroy the target. For example, a planet 100 meters away from a blast will be damaged far more than one that is 1000 meters away from the same blast. In order to compensate for the extra distance, the blast would need to be more powerful to accommodate the increased distance. The formula needed to calculate the destruction of celestial bodies at range, as per inverse square, is at follows.
The formula can be simplified as follows: E = 4*U*(Er/Tr)^2, which E is energy in joules, U is GBE in joules, Er is explosion radius in meters, and Tr is target radius in meters.
Bodies Used for Tiers
The following shows all the stars used for the baseline calculation for the corresponding tier. If the star itself is all that is required, the energy will be just GBE. If the star needs to be put through inverse square, the energy will be GBE of the star put through the inverse square formula given the proper radius.
- High 5-A: OTS 44
- Low 4-C: VB 10
- 4-C: Sol, the Sun
- High 4-C: Rigel A
NOTE!: Despite Rigel A being a giant, it is not fully convective, and thus will receive a polytrope value of 3, rather than 1.5 for the standard giant and dwarf.
- 4-B: Neptune through Inverse Square Law at 4.498x10^12 meter radius (Distance from the Sun to Neptune)
- 4-A: Sun through Inverse Square Law at 2.06575x10^16 meter radius (Halfway to Alpha Centauri A)
- 3-C: Sun through Inverse Square Law at 4.73037x10^20 meter radius (Milky Way Galaxy radius)
- 3-B: Sun through Inverse Square Law at 1.3514653x10^22 meter radius (Halfway between the distance from the outer edge of the Milky Way Galaxy and the outer edge of the Andromeda Galaxy)
- 3-A: PSR J0348+0432 through Inverse Square Law at 4.4087x10^26 meter radius (Observable Universe radius)
Note!: PSR J0348+0432 was chosen as the body for this rating, as it is the most conventionally durable body currently known. For one to truly destroy the entire observable universe, all bodies, including one as durable as PSR J0348+0432, must be destroyed, even if their location is at the edge of the observable universe.
Requirements to Hit these Tiers
Below you will find worded descriptions of what the above statements mean, in terms of destructive power.
- High 5-A: Energy equal to or above what it needed to overcome the GBE of OTS 44.
- Low 4-C: Energy equal to or above what is needed to overcome the GBE of VB 10.
- 4-C: Energy equal to or above what is needed to overcome the GBE of Sol, our Sun.
- High 4-C: Energy equal to or above what is needed to overcome the GBE of Rigel A.
- 4-B: Energy equal to or above what is needed to overcome the GBE of Neptune with an omnidirectional blast with the point of origin of the blast beginning at the Sun and the target Neptune being located at Neptune's orbital distance.
- 4-A: Energy equal to or above what is needed to overcome the GBE of the Sun with an omnidirectional blast with the point of origin of the blast beginning halfway between the Sun and Alpha Centauri A with the target Sun being located at it's original position, 4.367 light years away from Alpha Centauri A.
- 3-C: Energy equal to or above what is needed to overcome the GBE of the Sun with an omnidirectional blast with the point of origin of the blast beginning at the core of the Milky Way Galaxy and the Sun being located at the edge of the Galaxy.
- 3-B: Energy equal to or above what is needed to overcome the GBE of the Sun with an omnidirectional blast with the point of original of the blast beginning half way between the outer edge of the Milky Way and Andromeda Galaxies and the Sun being located at the outer edge of either Galaxy.
- 3-A: Energy equal to or above what is needed to overcome the GBE of the Neutron Pulsar PSR J0348+0432 with an omnidirectional blast with the point of origin of the blast beginning at the Earth and PSR J0348+0432 being located at the edge of the observable universe.
All values found will be in joules. All values found will be the baseline for the tier. All values rounded up from the forth decimal place to the third, if applicable.
High 5-A: (3*(6.67408×10^-11)*((1.989×10^30)*0.011)^2)/(((6.957×10^8)*0.57)*(5-1.5)) = 6.906x10^37
Low 4-C: (3*(6.67408×10^-11)*((1.989×10^30)*0.075)^2)/(((6.957×10^8)*0.102)*(5-3)) = 3.139x10^40
4-C: (3*(6.67408×10^-11)*(1.989×10^30)^2)/((6.957×10^8)*(5-3)) = 5.693x10^41
High 4-C: (3*(6.67408×10^-11)*((1.989×10^30)*23)^2)/(((6.957×10^8)*78.9)*(5 - 3)) = 3.817x10^42
4-B: 4*(3*(6.67408×10^-11)*(1.024×10^26)^2)/(5*24622000)*((4.498×10^12)/(24622000))^2 = 2.277x10^45
4-A: 4*(5.693×10^41)*((2.06575×10^16)/(6.957×10^8))^2 = 2.008x10^57
3-C: 4*(5.693×10^41)*((4.73037×10^20)/(6.957×10^8))^2 = 1.053x10^66
3-B: 4*(5.693×10^41)*((1.3514653×10^22)/(6.957×10^8))^2 = 8.593x10^68
3-A: 4*(3*(6.67408×10^-11)*((1.989×10^30)*2.01)^2)/(13009.59*(5-1))*((4.4087×10^26)/13009.59)^2 = 2.825x10^92
|Energy in Tonnes
of TNT Equivalent
|Energy in Joules||High End to Low End ratio|
|5-A||Large Planet||2.7 Yottatons
to 16.512 Ninatons
|2.7x1024 to 1.651x1028||1.13x1034 to 6.906x1037||~6111.5x|
|High 5-A||Dwarf Star||16.512 Ninatons
to 7.505 Tenatons
|1.651x1028 to 7.505x1030||6.906x1037 to 3.139x1040||~454.53x|
|Low 4-C||Small Star||7.505 Tenatons
to 136.066 Tenatons
|7.505x1030 to 1.36x1032||3.139x1040 to 5.693x1041||~18.14x|
to 912.295 Tenatons
|1.36x1032 to 9.12x1032||5.693x1041 to 3.817x1042||~6.71x|
|High 4-C||Large Star||912.295 Tenatons
to 22.77 Foe
|9.12x1032 to 5.442x1035||3.817x1042 to 2.277x1045||~596.54x|
|4-B||Solar System||22.77 Foe
to 20.08 TeraFoe
|5.442x1035 to 4.799x1047||2.277x1045 to 2.008x1057||~881.86 billion x|
|4-A||Multi-Solar System||20.08 TeraFoe
to 10.53 ZettaFoe
|4.799x1047 to 2.517x1056||2.008x1057 to 1.053x1066||~198.37 million x|
to 8.593 YottaFoe
|2.517x1056 to 2.054x1059||1.053x1066 to 8.593x1068||~816.05x|
to 2.825 TenaexaFoe
|2.054x1059 to 6.752x1082||8.593x1068 to 2.825x1092||~1.04x1023x|
|3-A||Universe||2.825 TenaexaFoe to any higher finite number||6.752x1082 to any higher finite number||2.825x1092 to any higher finite number||Not available|
Tier Value Shifts
Depending on the previous value compared to the new value, the tiers may have shrunken or grown, with the baseline or cap of the tier rising or falling. Below are all the changes that occurred.
Large Planet level: Baseline unchanged, Cap lowered
Dwarf Star level: Baseline lowered, Cap raised
Small Star level: Baseline raised, Cap lowered
Star level: Baseline lowered, Cap raised
Large Star level: Baseline raised, Cap raised
Solar System level: Baseline raised, Cap lowered
Multi-Solar System level: Baseline lowered, Cap lowered
Galaxy level: Baseline lowered, Cap raised
Multi-Galaxy level: Baseline raised, Cap lowered
Universe level: Baseline lowered, Cap unchanged
Tier Arithmetic Means
The arithmetic mean between the tier's baseline and cap determines the starting point for the "+" at the end of a tier, as stated here. As such, changes to the tier values may move calculation values into or out of the "+" level of the tier, in addition to lowering or raising the tier itself. The calculations below determine the starting point of the upper half of the tier.
Large Planet level+: ((6.906×10^37)+(1.13x10^34))/2 = 3.454x10^37
Dwarf Star level+: ((3.139×10^40)+(6.906×10^37))/2 = 1.573x10^40
Small Star level+: ((5.693×10^41)+(3.139×10^40))/2 = 3.003x10^41
Star level+: ((3.817×10^42)+(5.693×10^41))/2 = 2.193x10^42
Large Star level+: ((2.277×10^45)+(3.817×10^42))/2 = 1.14x10^45
Solar System level+: ((5.308×10^57)+(2.277×10^45))/2 = 1.004x10^57
Multi-Solar System level+: ((1.053×10^66)+(5.308×10^57))/2 = 5.265x10^65
Galaxy level+: ((8.593×10^68)+(1.053×10^66))/2 = 4.302x10^68
Multi-Galaxy level+: ((2.825×10^92)+(2.771×10^69))/2 = 1.413x10^92
The previous tiers didn't account for non-uniform density or stars, and or did not use the widely applicable and still generally accurate formula for GBE, listed above. This caused the results of the tiers to be different, and in need of adjustment for consistency, applicability, and transparency.
The new values have been calculated using the agreed upon, and already used, figures of calculation (Sun GBE through inverse square, GBE of VP 10, etc.) while using the new formula, causing a new baseline for all tiers above 5-A to arise.
Significant Modifications Thus far (1-21-18):
Below will be the changes I do to math and assumptions. Additions to the blog that are made for ease of reading or clarification shall not be recorded here.
1. 4-B's rating recalculated using a corrected distance.
2. 4-B's rating recalculated with Neptune's values, rather than the Sun's.
3. 4-A's rating recalculated with a corrected distance.
4. 4-A's rating recalculated with Alpha Centauri A's values, rather than the Sun's.
5. 4-A's rating recalculated with the Sun's values rather than Alpha Centauri A's values and half the distance from Alpha Centauri A to the Sun.
6. 3-B's rating recalculated with the half of the distance between the outer edges of the Andromeda and Milky Way Galaxies.