Giant caterpillar brings some biggatons.
1. Size of Dead Leaves and the Giant Catepillar
The Moon was fucked up, so we'll need to find the proper dimensions of the remains of the Moon and the size of the Giant Caterpillar and Dead Leaves. To start, we'll need the radius of the Moon. The radius of the Moon is 1737.4km.
R = (h/2) + c^2/(8h)
= (278/2) + 670^2/(8 X 278)
= 340.843525 pixels
1737.4km = 340.843525 pixels
1 pixel = 1737.4km/340.843525 = 5.09735369km
5.09735369km X 86 = 438.372417km
533 pixels = 438.372417km
1 pixel = 438.372417km/533 = 0.822462321km
0.822462321km X 210 = 172.717087km
0.822462321km X 125 = 102.80779km
0.822462321km X 24 = 19.7390957km
0.822462321km X 66 = 54.2825132km
That's not including the parts of the caterpillar still underground.
2. Giant Caterpillar emerges
The Giant Caterpillar bursts out of the ground and starts firing lasers. As per above, the giant caterpillar is over 19.7390957km long
The timeframe is 2 seconds and 9 frames.
T = 1s/24
= 41.6666667ms X 9
= 0.375s + 2s
= 2.37500s
T = 19.7390957km/2.37500s
= 8311.19819/340.29
= Mach 24.4238684
We have the speed, so let's also go for the mass using square law. A caterpillar the same length as a silkworm weighs 3 grams (or 0.003kg), and a silkworm ranges from 40mm to 50mm in length (an average of 45mm). As per above, the length of the Giant Caterpillar is 19.7390957km (or 19739095700mm)
M2 = (H2/H1)^3*M1
= (19739.095700/0.045)^3 X 0.003
= 2.53201032e14kg
KE = (0.5)mv^2
= (0.5) X 2.53201032e14 X 8311.19819^2
= 8.74505919e21 joules
= 2.0901193092734224876 teratons
The Giant Caterpillar then fires off a series of laser beams, so let's get them too.
Timeframe is 1 frame.
207 pixels = 172.717087km
1 pixel = 172.717087km/207 = 0.834382063km
0.834382063km X 725 = 604.926996km
T = 604.926996km/41.6666667ms
= 14518247.9/340.29
= Mach 42664.3389
3. Giant Caterpillar destroys Dead Leaves
The Giant Caterpillars laser blows up Dead Leaves. Remember as per above; Dead Leaves is fucking huge.
174 pixels = 54.2825132km
1 pixel = 54.2825132km/174 = 0.311968467km
0.311968467km X 776 = 242.08753km (242087.53m)
0.311968467km X 769 = 239.903751km
239.903751km/2 = 119.951875km (119951.875m)
Volume as a conical frustrum.
R = 54.2825132km/2
= 27.1412566km (27141.2566m)
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π (27141.2566^2 + 27141.2566 X 119951.875 + 119951.875^2) X 242087.53
= 4.65976636e15m^3
The explosion looks super violent, so we'll go with violent fragmentation (69000000 joules/m^3).
E = 4.65976636e15 X 69000000
= 3.21523879e23 joules
= 76.846051386233270364 teratons
And incase there's any issues, we'll also go with a low end of fragmentation (8000000 joules/m^3).
E = 4.65976636e15 X 8000000
= 3.72781309e22 joules
= 8.909687117590822325 teratons
3. The Butterfly explodes
Pandy & Retro's newborn son becomes an old man and flies into the mouth of the Giant Caterpillar, causing it to turn into a butterfly and explode. Did I mention this movie makes no damn sense? It takes out a huge chunk of the Moon, so we'll be calcing it.
270 pixels = 438.372417km
1 pixel = 438.372417km/270 = 1.62360154km
Timeframe is 7 seconds and 22 frames.
T = 41.6666667ms X 22
= 0.916666667s + 7s
= 7.91666667s
1.62360154km X 532 = 863.756019km
To find the area blown out, we'll need to find the area destroyed. Thankfully, it's a pretty nice circle, but due to the wonkiness of the landscape, we'll be using the same tactic as per the start of this calc to help us find the radius.
R = (h/2) + c^2/(8h)
= (160/2) + 411^2/(8 X 160)
= 211.969531 pixels
1.62360154km X 211.969531 = 344.154057km (344154.057m, or 34415405.7cm)
Now, the distance the debris travelled in the timeframe.
863.756019km - 344.154057km = 519.601962km
T = 519.601962km/7.91666667s
= 65633.932m/s
Volume as a semi-sphere.
V = 4/3πr^3
= 4/3 X π X 34415405.7^3
= 1.70744723e23/2
= 8.53723615e22cm^3
The Moon on average has a mass of 3.34g/cm^3.
M = 8.53723615e22 X 3.34g
= 2.85143687e23g/1000
= 2.85143687e20kg
With all that, we can get our kinetic energy.
KE = (0.5)mv^2
= (0.5) X 2.85143687e20 X 65633.932^2
= 6.14172845e29 joules
= 146.79083293499043793 exatons
Final Results
Dead Leaves facility size = 102.808km
Giant Caterpillar length = >19.739km
Giant Caterpillar bursts out of the ground (speed) = Mach 24.424
Giant Caterpillar bursts out of the ground (energy) = 2.090 teratons
Giant Caterpillars laser beam = Mach 42664.339
Giant Caterpillar destroys Dead Leaves (low end) = 8.91 teratons
Giant Caterpillar destroys Dead Leaves (high end) = 76.846 teratons
Pandy & Retro's Son destroys the Giant Caterpillar = 146.791 exatons
1. Size of Dead Leaves and the Giant Catepillar
The Moon was fucked up, so we'll need to find the proper dimensions of the remains of the Moon and the size of the Giant Caterpillar and Dead Leaves. To start, we'll need the radius of the Moon. The radius of the Moon is 1737.4km.
R = (h/2) + c^2/(8h)
= (278/2) + 670^2/(8 X 278)
= 340.843525 pixels
1737.4km = 340.843525 pixels
1 pixel = 1737.4km/340.843525 = 5.09735369km
5.09735369km X 86 = 438.372417km
1 pixel = 438.372417km/533 = 0.822462321km
0.822462321km X 210 = 172.717087km
0.822462321km X 125 = 102.80779km
0.822462321km X 24 = 19.7390957km
0.822462321km X 66 = 54.2825132km
That's not including the parts of the caterpillar still underground.
2. Giant Caterpillar emerges
The Giant Caterpillar bursts out of the ground and starts firing lasers. As per above, the giant caterpillar is over 19.7390957km long
T = 1s/24
= 41.6666667ms X 9
= 0.375s + 2s
= 2.37500s
T = 19.7390957km/2.37500s
= 8311.19819/340.29
= Mach 24.4238684
We have the speed, so let's also go for the mass using square law. A caterpillar the same length as a silkworm weighs 3 grams (or 0.003kg), and a silkworm ranges from 40mm to 50mm in length (an average of 45mm). As per above, the length of the Giant Caterpillar is 19.7390957km (or 19739095700mm)
M2 = (H2/H1)^3*M1
= (19739.095700/0.045)^3 X 0.003
= 2.53201032e14kg
KE = (0.5)mv^2
= (0.5) X 2.53201032e14 X 8311.19819^2
= 8.74505919e21 joules
= 2.0901193092734224876 teratons
The Giant Caterpillar then fires off a series of laser beams, so let's get them too.
207 pixels = 172.717087km
1 pixel = 172.717087km/207 = 0.834382063km
0.834382063km X 725 = 604.926996km
T = 604.926996km/41.6666667ms
= 14518247.9/340.29
= Mach 42664.3389
3. Giant Caterpillar destroys Dead Leaves
The Giant Caterpillars laser blows up Dead Leaves. Remember as per above; Dead Leaves is fucking huge.
1 pixel = 54.2825132km/174 = 0.311968467km
0.311968467km X 776 = 242.08753km (242087.53m)
239.903751km/2 = 119.951875km (119951.875m)
Volume as a conical frustrum.
R = 54.2825132km/2
= 27.1412566km (27141.2566m)
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π (27141.2566^2 + 27141.2566 X 119951.875 + 119951.875^2) X 242087.53
= 4.65976636e15m^3
The explosion looks super violent, so we'll go with violent fragmentation (69000000 joules/m^3).
E = 4.65976636e15 X 69000000
= 3.21523879e23 joules
= 76.846051386233270364 teratons
And incase there's any issues, we'll also go with a low end of fragmentation (8000000 joules/m^3).
E = 4.65976636e15 X 8000000
= 3.72781309e22 joules
= 8.909687117590822325 teratons
3. The Butterfly explodes
Pandy & Retro's newborn son becomes an old man and flies into the mouth of the Giant Caterpillar, causing it to turn into a butterfly and explode. Did I mention this movie makes no damn sense? It takes out a huge chunk of the Moon, so we'll be calcing it.
1 pixel = 438.372417km/270 = 1.62360154km
T = 41.6666667ms X 22
= 0.916666667s + 7s
= 7.91666667s
1.62360154km X 532 = 863.756019km
To find the area blown out, we'll need to find the area destroyed. Thankfully, it's a pretty nice circle, but due to the wonkiness of the landscape, we'll be using the same tactic as per the start of this calc to help us find the radius.
R = (h/2) + c^2/(8h)
= (160/2) + 411^2/(8 X 160)
= 211.969531 pixels
1.62360154km X 211.969531 = 344.154057km (344154.057m, or 34415405.7cm)
Now, the distance the debris travelled in the timeframe.
863.756019km - 344.154057km = 519.601962km
T = 519.601962km/7.91666667s
= 65633.932m/s
Volume as a semi-sphere.
V = 4/3πr^3
= 4/3 X π X 34415405.7^3
= 1.70744723e23/2
= 8.53723615e22cm^3
The Moon on average has a mass of 3.34g/cm^3.
M = 8.53723615e22 X 3.34g
= 2.85143687e23g/1000
= 2.85143687e20kg
With all that, we can get our kinetic energy.
KE = (0.5)mv^2
= (0.5) X 2.85143687e20 X 65633.932^2
= 6.14172845e29 joules
= 146.79083293499043793 exatons
Final Results
Dead Leaves facility size = 102.808km
Giant Caterpillar length = >19.739km
Giant Caterpillar bursts out of the ground (speed) = Mach 24.424
Giant Caterpillar bursts out of the ground (energy) = 2.090 teratons
Giant Caterpillars laser beam = Mach 42664.339
Giant Caterpillar destroys Dead Leaves (low end) = 8.91 teratons
Giant Caterpillar destroys Dead Leaves (high end) = 76.846 teratons
Pandy & Retro's Son destroys the Giant Caterpillar = 146.791 exatons
