Tier High 5-A & above Calculations

# **GBE Formula: Attack Potency & Destructive Capacity**

## Introduction

This is going to be a lot of math and walls of text. The following is a thorough explanation of how the results are reached, the math itself, and the new chart. Here we go.

#### **Fundamental Principles:**

The two principles needed to be understood here are GBE, Gravitational Binding Energy, and Inverse Square Law.

### 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.

* Tier High 5-A: OTS 44

* Tier Low 4-C: VB 10

* Tier 4-C: Sol, the Sun

* Tier 4-B: Rigel A

**NOTE:** Despite Rigel A being a giant, it is , and thus will receive a polytrope value of 3, rather than 1.5 for the standard giant and dwarf.

* Tier 4-A: Neptune through Inverse Square Law at 4.498x10^12 meter radius (Distance from the Sun to Neptune)

* Tier High 4-A: Sun through Inverse Square Law at 2.06575x10^16 meter radius (Halfway to Alpha Centauri A)

* Tier 3-C: Sun through Inverse Square Law at 4.73037x10^20 meter radius (Milky Way Galaxy radius)

* Tier High 3-C: 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)

* Tier 3-B: 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.

* Tier High 5-A: Energy equal to or above what it needed to overcome the GBE of OTS 44.

* Tier Low 4-C: Energy equal to or above what is needed to overcome the GBE of VB 10.

* Tier 4-C: Energy equal to or above what is needed to overcome the GBE of Sol, our Sun.

* Tier 4-B: Energy equal to or above what is needed to overcome the GBE of Rigel A.

* Tier 4-A: 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.

* Tier High 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.

* Tier 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.

* Tier High 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 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.

* Tier 3-B: 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.

## The Math

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.

Tier 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

Tier 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

Tier 4-C: (3\*(6.67408×10^-11)\*(1.989×10^30)^2)/((6.957×10^8)\*(5-3)) = 5.693x10^41

Tier 4-B: (3\*(6.67408×10^-11)\*((1.989×10^30)\*23)^2)/(((6.957×10^8)\*78.9)\*(5 - 3)) = 3.817x10^42

Tier 4-A: 4\*(3\*(6.67408×10^-11)\*(1.024×10^26)^2)/(5\*24622000)\*((4.498×10^12)/(24622000))^2 = 2.277x10^45

Tier High 4-A: 4\*(5.693×10^41)\*((2.06575×10^16)/(6.957×10^8))^2 = 2.008x10^57

Tier 3-C: 4\*(5.693×10^41)\*((4.73037×10^20)/(6.957×10^8))^2 = 1.053x10^66

Tier High 3-C: 4\*(5.693×10^41)\*((1.3514653×10^22)/(6.957×10^8))^2 = 8.593x10^68

Tier 3-B: 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