What Does the Science Say?

Game Theorist Austin has dissected the the physics of Legion’s finale. Originally, I was skeptical of whether he would understand the gravity of Blizzard’s story. But very early on, he makes a joke on orbital mechanics. I concluded his words–and more importantly his math–deserved my attention.

His Preliminary Jokes

Before I begin, I want to dissect his jokes, as they hold some insight. For instance, take his joke on orbital mechanics:

“I wish I could get into orbital mechanics, but there’s no time.”

He is absolutely right. Azeroth is a many-bodied gravitational problem and likely impossible to analytically solve.

He also makes a quip concerning the tides, stating what the effect Argus would have on the tides. In laymen’s terms, you probably wouldn’t want beachfront real estate. Moreover, monsoon season would become linked to the orbital period of Argus.

Force on the Planet

He first uses the known height of the night elf- 7 feet- to measure certain quantities of the sword. He then figures out the terminal velocity to be 53.9 meters per second. He uses a pixel conversion to do this. This is roughly equivalent to the terminal velocity on humans from Earth. Cool. He finds the gravitational constant, small g, to be over triple that of Earths, however.

This calculation is important because it means Azeroth is much more massive than Earth. Up to this point, his calculations and simplifying assumptions are intuitive and true.

From here, he measures his falling time to be 22.5 seconds. With this calculation, he finds the exposed blade to be over a kilometer. Using a calculator to input his values into the equations for kinematics here, I arrive at an exposure height of around 7 kilometers.

Now to Figure out the Damage

Ignoring the above discrepancy, the theorist then looks at the cinematic of the stabbing. This way, he can figure out just how deep the sword is embedded and arrive at a total length. The blade is 2674.74 m long by his calculations. This is the height of a small mountain, and as such–within reason.

He concludes the sword is 13 and half football fields deep.

He takes the distance between a first and second point on the blade over time to find the velocity to be roughly 900 m/s. My own calculation of his numbers gives the same result.

Following this measurement, the mathematics becomes more based on trigonometry. His known values are thickness, wideness, total length, and buried length. The law of sines and law of cosines is used to great effect by simplifying the buried sword as two triangles. One triangle’s angle is similar to the other by a proportionality constant. He then does the following:

  1. Find the Hypotenuse of the blade using the Pythagorean Theorem.
  2.  The inverse of a trig function can give the angle, and this is exactly what he does for the corner of the blade. The value is approaches a right angle at 85 degrees.
  3. The embedded portion of the sword is merely a smaller triangle of the entire sword, and so he applies similarity to dissect each angle. However, he has to apply the use of trig to each cross-section as the structure is not uniform in its dimensions.

Essentially, the Sword Creates a Crater with the Volume of the Hoover Dam.

He then shows Azeroth- at least from the perspective of the cinematic- is ridiculously small. However, if this is scaled to Earth’s dimensions the sword is over a 1000 miles deep. Using equations for gravity, we find Azeroth also has an extremely small size. It is essentially an asteroid in mass. Yet, because of this and the relationship between volume and mass–the density of Azeroth is three orders of magnitude larger than Earth’s.

The Juicy Calculations in Words:

In the time it takes for the sword to fall, the theorist finds the force of the stabbing to equal 14 nuclear bombs. Moreover, the theorist finds this to be 1.1 million times more farts than all the farts ever released by humanity.

“This I cannot tolerate. “

The average energy of farts has varied over humanity’s existence. Our wisdom teeth are relics of this fact, as are our spleens. We used to eat more fibrous and hard to digest foods, leading to a more complex relationship with our butts. Indeed, one cannot divide humanity into an average because evolution of traits is gradual and there was never actually a first human. This is essentially Zeno’s paradox. Granted, up to this point the author has been using many simplifying assumptions, but…

The Fart is Sacred. Respect the Fart.

The math however, is justified (ignoring the one discrepancy through kinematics). Perhaps he used a different equation to find the displacement while his character fell. In conclusion, the theorist is correct in stating the stabbing would be cataclysmic.

Yet no zone revamp?

Writer’s Conclusion:

This blast would cause extinction events and plunge the Earth’s ecosystems into darkness. And while calculations like this are great fun, they are approximations. Once one considers spaghettification due to the non-homogeneous gravitational field Sargeras’ body will create–all simplifications the theorist make break down. Also, the differential density of the core was not taken into account. Perhaps Azeroth has a metal-rich core which holds most of its mass, and subsequently would not be touched?

Eventually, all theories break down. That is just how physics and science works, in the end.

Einstein and the Ether, Ludwik Kostro