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Destroying half a planet?

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Is the AP for destroying half of a planet just half of the AP needed to destroy the whole planet, or are the destruction of half a planet and the destruction of a whole planet different matters entirely?
 
I think a good example would be Beerus tapping that random planet in half, we can assume its Earth.
 
There are two ways to go about this. We will use Earth as an example here. 1. Find the energy required to pulverize (or any other method of destruction) half of that planet.

  • Find the volume of half of a planet or half of said sphere in question.
  • Multiply said volume of hemisphere (convert it to cc first), and multiply that by destruction value of said material (rock is 214J/cc for pulverization)
2. Find the GBE of half of the planet, and compare it to the GBE of the full planet. The difference between the two is the energy required to completely obliterate half a planet (assuming the other half remains intact while the one half is completely gone).
 
Half the volume of earth is 5.41673684E+26 (214) = 1.15918168376e+29

GBE of earth is 2e32, half is 1e32.

1e32 + 1.159e29 = 1.001159e32, small planet.
 
Just a thought: Keep in mind that if you only manage to bust half of the Earth, said pieces of the destroyed Earth will eventually come back together if the attack in question does not exceed said planet's GBE.

However, I will make an exception that half of said planet has been completely destroyed, and the pieces do not exist anymore. What would actually happen here is that instead of said planet remaining in the shape of a hemisphere, the planet will rearrange itself to form an evenly shaped sphere instead.

  • Assuming density of Earth is the same, or 5503kg/m^3
  • 1/2 the volume of Earth = 5.43e20 m^3 (as the volume of full Earth = 1.085e21 m^3)
  • U (or GBE) = 3*(Gravitational Constant)*(Mass^2)/(5*radius in meters)
Since the volume of Earth is now halves, and said hemisphere eventually returns to a full (albeit smaller) sphere, we find the radius of said sphere that has a volume of 5.43e20 m^3.

  • Volume of sphere = 5.43e20 m^3 = (4/3)*(Pi)*(radius^3)
  • Radius = 5061008m, or ~5061km (radius of newly formed sphere)
  • 1/2 Mass of Earth = 2.986e24 kg (Google Mass of Earth, and divide that value by 1/2)
  • GBE (half of Earth) = 3*(6.67e-11)*((2.986e24)^2)/(5*5061008) = 7.05e31 Joules.
  • GBE (full Earth) = 2.24e32 Joules
  • Total energy expended to bust 1/2 of Earth = 2.24e32 - 7.05e31 = 1.535e32 Joules.
 
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