| “ |
He used the macro as a way of moving the micro. By adding a large tree to the cosmos and thoroughly shaking the world out to the ends of the galaxy, he was applying a physical blow to a single person’s flesh and blood. |
„ |
| ~ To Aru Majutsu No Index NT Volume 22 |
So Accelerator has a galaxy shaking feat now.
I will use this occasion in order to calculate general purpose "shaking the galaxy" feats via differing methods.
Method 1: Global Earthquakes[]
So for our first method we are going to assume that the shaking caused a global earthquake on a earth-like planet at the edge of the galaxy. The reason it has to be earth-like is, because that's the only thing our earthquake formulas work for.
I will use DMUA's global earthquake block, to get the energy to cause the earthquakes on this planet.
As per inverse square law the energy to cause such earthquake throughout the whole galaxy, spreading energy equally, is given by
(earthquake energy on planet)* (4*pi*(radius of galaxy)^2 / pi*(radius of planet)^2)
radius of the milkyway is about 52 850 ly = 5e+20 m, radius of planet = 6 371 000 m
Setting that in we simply the above to
(earthquake energy on planet)*2.46368279039472164831e28
With that we get a handy way to calculated it for a few magnitudes:
Magnitude 1: 1.410253747010E17 * 2.46368279039472164831e28 = 3.4744178865982086e45 J (4-B)
Magnitude 2: 4.459613919340E18 * 2.46368279039472164831e28 = 1.0987074064882712e47 J (4-B)
Magnitude 3: 1.410253747010E20 * 2.46368279039472164831e28 = 3.4744178865982086e48 J (4-B)
Magnitude 4: 4.459613919339E21 * 2.46368279039472164831e28 = 1.0987074064880249e50 J (4-B)
Magnitude 5: 1.410253747010E23 * 2.46368279039472164831e28 = 3.4744178865982086e51 J (4-B)
Magnitude 6: 4.459613919340E24 * 2.46368279039472164831e28 = 1.0987074064882712e53 J (4-B)
Method 2: Shaking the planet[]
In this and the following method we will make use of a little something I found recently. Here is a table, that correlates peak ground velocity with strength of shaking.
This way we can do earthquakes with a simple KE calc. What's the advantage of that? Well, instead of using the earth we can apply this to other celestial bodies.
As before we will use the inverse square law, but this time our base formula is
(kinetic energy of planet shaking)* (4*pi*(radius of galaxy)^2 / pi*(radius of sun)^2)
radius of galaxy is 5e+20 m again and the radius of the sun is 6.96342*10^8 m.
The suns mass is 1.989*10^30 kg, meaning the shaking energy is given by 0.5*1.989*10^30 * (shaking velocity)^2.
So we get the shortened formula 2.050971409814989305330414505058589e54 * (shaking velocity)^2
With that we get the following bottom ends:
Weak: 2.050971409814989305330414505058589e54 * (0.001)^2 = 2.0509714098149893e48 J (4-B)
Light: 2.050971409814989305330414505058589e54 * (0.011)^2 = 2.4816754058761371e50 J (4-B)
Moderate: 2.050971409814989305330414505058589e54 * (0.034)^2 = 2.3709229497461276e51 J (4-B)
Strong: 2.050971409814989305330414505058589e54 * (0.081)^2 = 1.3456423419796145e52 J (4-B)
Very Strong: 2.050971409814989305330414505058589e54 * (0.16)^2 = 5.2504868091263726e52 J (4-B)
Method 3: No Inverse Square Law[]
Since we can with the above velocities quantify things without a specific reference body we can also quantify what shaking the galaxy without inverse square law results in.
The mass of the milkyway should be at least 1*10^12 solar mass. One solar mass is approximately 2*10^30 kg, so mass of the milky way should be about 2e42 kg.
With that it's just simple kinetic energy:
Weak: 0.5*2e42*(0.001)^2 = 1e36 J (5-A)
Light: 0.5*2e42*(0.011)^2 = 1.21e38 J (High 5-A)
Moderate: 0.5*2e42*(0.034)^2 = 1.156e39 J (High 5-A)
Strong: 0.5*2e42*(0.081)^2 = 6.561e39 J (High 5-A)
Very Strong: 0.5*2e42*(0.16)^2 = 2.56e40 J (High 5-A +)
Results[]
Almost everything is 4-B. So unless we are not talking inverse square law Solar System level it is.