User:MrWarnerTheGreat/Standard Calculation for Destroying a Planetoid

Introduction

This is a general calculation for destroying celestial bodies large enough to have a self-gravitating sphere we associate with planets like Earth.

The Calculation

References and Sources

It's agreed upon that most rocky planetoids with a shape akin to a planet's have a diameter of at least six-hundred kilometers. This will be a good reference point.

It should be made clear that the radius of the core of rocky planets typically are about nineteen percent of the whole planet's radius, which will be factored into our first result. The core of planets are made of nickel and iron, with the former having a fracture toughness of 67.5 J/cm³.

Igneous rock, which will be our basis for the planet's primary body, has a fracture toughness of 50 MPa, which translates to 50 J/cm³. With all this, now we need to get the destructive value for destroying a planetoid such as this.

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Fracture Toughness

9.0477868423386E+23 cm³*0.19 = 1.7190795e+23 for the core.

((1.7190795e+23)*(70%))*(67.5) = 8.1226506e+24 Joules.

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9.0477868423386E+23 cm³*0.81 = 7.3287073e+23 for the rest of the planet ((7.3287073e+23)*(70%))*(50) = 2.5650476e+25 Joules.

2.5650476e+25 + 8.1226506e+24 = 3.3773127e+25 Joules, which translates to 8.07197108030602 petatons of TNT, which is a bit into Continent level.

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Gravitational Binding Energy

Based on our previous source, a planetoid must have a diameter of six-hundred kilometers to be a self-gravitating sphere. Using a calculator made by SD.net here, we get a value for a standatd planetoid's GBE.

• Gravitational Binding Energy: 2.335E+28 Joules, which translates to 5.58078393881 exatons of TNT which is Multi-Continent level+.

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Standard Explosion

The full-sphere explosion formula will be used here. As established prior, our planetoid diameter is six-hundred kilometers.

((600/0.28)^3)/1000/2 = 2.0584548104972e+22 joules, which is about 4.9198250728900569939 teratons of TNT, or Small Country level.

Final Results

• Planetoid Fracture Toughness: 8.07197108030602 petatons of TNT (6-A)

• Planetoid GBE: 5.58078393881 exatons of TNT (High 6-A)

• Planetoid-sized Explosion: 4.9198250728900569939 Teratons of TNT (Low 6-B)