To calculate the energy required for the Queen Beast to knock the tilt out of Earth’s rotational axis, causing the Earth's rotation to slow down over 1200 years and eventually stop moving, we need to consider the following:
1.
Earth's Angular Momentum:
- The Earth has significant angular momentum due to its rotation.
- The formula for angular momentum (\(L\)) of a rotating sphere is:
\[ L = I \omega \]
- Where:
- \(I\) is the moment of inertia of the Earth.
- \(\omega\) is the angular velocity of the Earth.
2.
Moment of Inertia (\(I\)):
- For a solid sphere:
\[ I = \frac{2}{5} M R^2 \]
- Where:
- \(M\) is the mass of the Earth (\(5.972 \times 10^{24} \text{ kg}\)).
- \(R\) is the radius of the Earth (\(6.371 \times 10^6 \text{ m}\)).
3.
Angular Velocity (\(\omega\)):
- The Earth rotates once every 24 hours (86400 seconds):
\[ \omega = \frac{2\pi}{T} \]
- Where \(T\) is the period of rotation.
\[ \omega = \frac{2\pi}{86400 \text{ s}} \approx 7.272 \times 10^{-5} \text{ rad/s} \]
### Step-by-Step Calculation:
1.
Calculate the Moment of Inertia (\(I\)):
\[ I = \frac{2}{5} \times 5.972 \times 10^{24} \text{ kg} \times (6.371 \times 10^6 \text{ m})^2 \]
\[ I \approx 9.72 \times 10^{37} \text{ kg} \cdot \text{m}^2 \]
2.
Calculate the Angular Momentum (\(L\)):
\[ L = I \omega \]
\[ L = 9.72 \times 10^{37} \text{ kg} \cdot \text{m}^2 \times 7.272 \times 10^{-5} \text{ rad/s} \]
\[ L \approx 7.07 \times 10^{33} \text{ kg} \cdot \text{m}^2 \text{/s} \]
3.
Energy to Stop Earth's Rotation:
- The rotational kinetic energy (\(E\)) is given by:
\[ E = \frac{1}{2} I \omega^2 \]
\[ E = \frac{1}{2} \times 9.72 \times 10^{37} \text{ kg} \cdot \text{m}^2 \times (7.272 \times 10^{-5} \text{ rad/s})^2 \]
\[ E \approx 2.57 \times 10^{29} \text{ joules} \]
### Energy Comparison:
- 1 megaton of TNT is approximately \(4.184 \times 10^{15} \text{ joules}\).
- Therefore, the energy required to stop Earth's rotation:
\[ \text{Megatons of TNT} = \frac{2.57 \times 10^{29} \text{ joules}}{4.184 \times 10^{15} \text{ joules/megaton}} \]
\[ \text{Megatons of TNT} \approx 6.14 \times 10^{13} \text{ megatons of TNT} \]
### Conclusion:
The energy required for the Queen Beast to knock the tilt out of Earth’s rotational axis and cause the Earth's rotation to eventually stop is approximately
61.4 trillion megatons of TNT. This immense amount of energy underscores the sheer power of the Queen Beast within the Drakengard/NieR universe.