More Happy Tree Friends calcs. Once more, be aware of gore.
1. Splendid flies into the Moon
0:25
Splendid flies away to escape the Kryptonuts aura and flies straight into the Moon. The Moon looks small, but as we see the Moon directly in comparison to the Earth when Splendont drops it on Splendid, it's just some wonky cartoon visuals. This will be more or less straightforward. The distance from the Earth to the Moon is 384,400km.
Timeframe is 4.67 seconds.
T = 384,400km/4.67s
= 82312633.8/299792458 X 100
= 27.4565392% C
2. Splendid passes wind
2:09
Splendid eats a cyclone, but then can't hold it in and farts it out, covering the entire planet in noxious fumes. The diameter of the Earth is 12,742km.
Timeframe is 0.72 seconds.
535 pixels = 12,742km
12,742km/2 = 6371km (6371000m)
1 pixel = 12,742km/535 = 23.8168224km
23.8168224km X 624 = 14861.6972km
14861.6972km/2 = 7430.8486km (7430848.6m)
To find the volume of the fumes, we'll find both the volume of it as a sphere and the volume of the Earth, then take away the volume of the Earth.
V = 4/3πr^3
= 4/3 X π X 6371000^3
= 1.08320692e21m^3
V = 4/3πr^3
= 4/3 X π X 7430848.6^3
= 1.71871492e21m^3
V = 1.71871492e21 - 1.08320692e21
= 6.35508e20m^3
Now for our mass of the...uh...cloud. Methane has a mass of 0.554kg/m^3.
M = 6.35508e20 X 0.554kg
= 3.52071432e20kg
With our mass, let's get our speed. The circumference of the Earth is 40075km, half of which is 20037.5km.
T = 20037.5km/0.72s
= 27829861.1m/s
Enter that through the relativistic kinetic energy calculator and we get a yield of 137227424204902609642918929412 megajoules, or 1.37227424204902605e+35 joules, or 32.798141540368689562 yottatons. Something about that feels kind of off. I don't know if I messed up the calculations somewhere, it seems fine, but let's be sure and add a low end of the volume of the Earths atmosphere times'd by methane (the volume of the Earth's atmosphere being estimated to be 5.18*10^19m^3, or 5.18e19m^3, as revealed by a quick search).
M = 5.18e19 X 0.554kg
= 2.86972e19kg
Entering that into the above relativistic kinetic energy calculator and we get a yield of 11185351834774629398061394260 megajoules, or 2.6733632492291179439 yottatons. Large planet no matter how you look at it.
3. Sniffles rocket
1:35
Sniffles makes a rocket to escape a deserted island. This succeeds, but the rocket flies into the Sun and explodes. Though he doesn't survive, this is a very impressive tech feat, especially given the rocket was constructed from the ruins of a school bus. The distance from the Earth to the Sun is 147720000km.
Timeframe is 19.68 seconds.
T = 147720000km/19.68s
= 7.50609756e9/299792458
= 25.0376464 C
There's also an explosion as the rocket hits the Su which is visible from Earth, but said explosion expands at FTL speeds, so unfortunately we can't calc it for energy.
Final Results
Splendid flies into the Moon = 27.457% C
Splendid poisons the world (low end) = 2.673 yottatons
Splendid poisons the world (high end) = 32.798 yottatons
Sniffles rocket speed = 25.038 C
1. Splendid flies into the Moon
0:25
Timeframe is 4.67 seconds.
T = 384,400km/4.67s
= 82312633.8/299792458 X 100
= 27.4565392% C
2. Splendid passes wind
2:09
535 pixels = 12,742km
12,742km/2 = 6371km (6371000m)
1 pixel = 12,742km/535 = 23.8168224km
23.8168224km X 624 = 14861.6972km
14861.6972km/2 = 7430.8486km (7430848.6m)
To find the volume of the fumes, we'll find both the volume of it as a sphere and the volume of the Earth, then take away the volume of the Earth.
V = 4/3πr^3
= 4/3 X π X 6371000^3
= 1.08320692e21m^3
V = 4/3πr^3
= 4/3 X π X 7430848.6^3
= 1.71871492e21m^3
V = 1.71871492e21 - 1.08320692e21
= 6.35508e20m^3
Now for our mass of the...uh...cloud. Methane has a mass of 0.554kg/m^3.
M = 6.35508e20 X 0.554kg
= 3.52071432e20kg
With our mass, let's get our speed. The circumference of the Earth is 40075km, half of which is 20037.5km.
T = 20037.5km/0.72s
= 27829861.1m/s
Enter that through the relativistic kinetic energy calculator and we get a yield of 137227424204902609642918929412 megajoules, or 1.37227424204902605e+35 joules, or 32.798141540368689562 yottatons. Something about that feels kind of off. I don't know if I messed up the calculations somewhere, it seems fine, but let's be sure and add a low end of the volume of the Earths atmosphere times'd by methane (the volume of the Earth's atmosphere being estimated to be 5.18*10^19m^3, or 5.18e19m^3, as revealed by a quick search).
M = 5.18e19 X 0.554kg
= 2.86972e19kg
Entering that into the above relativistic kinetic energy calculator and we get a yield of 11185351834774629398061394260 megajoules, or 2.6733632492291179439 yottatons. Large planet no matter how you look at it.
3. Sniffles rocket
1:35
T = 147720000km/19.68s
= 7.50609756e9/299792458
= 25.0376464 C
There's also an explosion as the rocket hits the Su which is visible from Earth, but said explosion expands at FTL speeds, so unfortunately we can't calc it for energy.
Final Results
Splendid flies into the Moon = 27.457% C
Splendid poisons the world (low end) = 2.673 yottatons
Splendid poisons the world (high end) = 32.798 yottatons
Sniffles rocket speed = 25.038 C
