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Introduction[]

This calc is a re-calculation of this calc. This calc was originally calced by Mephistus

This is a calculation of this feat from Sonic Unleashed, where a single Chaos Emerald restore one of the segments of the broken planet back to its place

Feat is shown in this video:

The Calculation[]

Pink line (1st picture) = Earth Diameter = 543px = 12,756,200 m

Green line = 732px = (12,756,200 / 543) * 732 = 17,196,203.31491712707182320441989 m

Pink/Yellow line (2nd picture) = 900 px = Earth Diameter = 543px = 12,756,200 m

Rose line = 291px = Height of the Crust = (12,756,200 / 900) * 291 = 4,124,504.6667 m

1 Pixel = 12,756,200 / 543 = 23,492.081031307550644567219152855 m

Px ^ 2 = (23,492.081031307550644567219152855 m) ^ 2 = 5.5187787118152003228771337192936e+8 m^2

As the continent shown in the 1st scan is the exact same continent shown in the 3rd and 4th scans, the pixel scaling used in the 1st scan would apply to the other two scans as well.

Using Pixel coloring, represented in the 4th scan, the continent is 164,740 pixel squares big.

A = 5.5187787118152003228771337192936e+8 * 164,740 = 9.0916360498443610119077900891643e+13 m^2

Using the volume of a spherical sector:

Volume of the entire piece can be found here by converting the surface area to fit onto a spherical cap portion on the top of a spherical sector, solving for that thing's volume, and subtracting the volume of the spherical sector portion below it to obtain the section's volume that would be cut out.

Area of a Spherical Sector:

r here represents half of 12,756,200 meters, or radius of Earth, the sphere in question here.

h = 9.0916360498443610119077900891643e+13 /(2*π*(12,756,200/2)) = 2.2686674999219256255162858016724e+6 m

Volume of first spherical sector = (2*π*(r^2)*h)/3

Volume of first spherical sector = (2*π*(12,756,200/2)^2)* 2.2686674999219256255162858016724e+6)/3 = 1.9329121296504106323349691989233e+20 m^3  

The distance below our first spherical sector is the central "thickness" of the crust we found above; 4,124,504.6667 meters. Now to find the second spherical sector.

Volume of second spherical sector = (2*π*(r^2)*h)/3

Volume of second spherical sector = (2*π*(((12,756,200/2)- 4,124,504.6667)^2)*(2.2686674999219256255162858016724e+6)/3 = 2.4131334097899486945257182104105e+19 m^3

Volume of continent = 1.9329121296504106323349691989233e+20 - 2.4131334097899486945257182104105e+19 = 1.6915987886714157628823973778823e+20 m^3

As the crust segment reached through most of the radius of the Earth, leaving the core exposed, it should be safe to assume the density would be similar to Earth’s density of 5,515 kg / m^3

M = V * ρ = 1.6915987886714157628823973778823e+20 * 5,515 = 9.3291673195228579322964215390209e+23 kg

So each Emerald moves this much mass. Impressive

Using watch frame by frame, Feat starts at frame 41,975 and ends in frame 42,040 using 25FPS framerate

T = (42,040 – 41,975) / 25 = 65 / 25 = 2.6 seconds

As the crust was moved out to the extended Earth radius seen in the Green line of the 1st picture, the distance the crust traveled would be: [(12,756,200 / 543) * (732-543)] / 2 = 2.2200016574585635359116022099448e+6 m

V = D / T = 2.2200016574585635359116022099448e+6 / 2.6 = 8.5384679133021674458138546536337e+5 m/s

E = 0.5 * 9.3291673195228579322964215390209e+23 * (8.5384679133021674458138546536337e+5) ^ 2 = 3.4007349757386668475575204179437e+35 joules = 81.279516628553222933975153392535 Yottatons of TNT, or Large Planet level

RE-CALCULATION[]

The pixel scaling and idea for the recalc was made with the help of LaserPrecision. So credit goes to him too

Apperantly, Angel Island compared to the size of the planet is so small, that it cannot be seen from space despite being above the clouds

As it cannot be seen, I would assume the island has a size of half a pixel compared to the planet. In particular, Scan 1 shows the planet from the gameplay, and it allows you to rotate the Earth freely to access the different levels. Angel Island isn't seen no matter where you try to look at it. Also, this was directly confirmed by Tails

To calculate Angel Island's size, we can use Sandopolis Zone Act 2's size compared to Sonic, as the length of the act is the size of the pyramid that appears on the Island due to all of it being inside of the pyramid

So:

Sonic = 17px = 0.80576923076923076923 m

Pyramid (Sandopolis Act 2 scan) = 10,495px = (0.80576923076923076923/17) * 10,495 = 497.444 m

Pyramid (Angel Island scan) = 43px = 497.444 m

Angel Island = 1920px = (497.444/43) * 1920 = 22,211.453 m

From before we'll assume Angel Island is the size of half a pixel

Angel Island = 1/2px = 22,211.453 m

Earth Diameter = 543px = (22,211.453/(1/2)) * 543 = 24,121,637.958 m or 24,121.637958 km

That is almost twice the size of the Earth in the real world lol

Now the rest of the calc will be changed accordingly with the new distance (Used a Hide/Show button to not make it as long and for TLDR):

Hide/Show

Pink line (1st picture) = Earth Diameter = 543px = 24,121,637.958 m

Green line = 732px = (24,121,637.958 / 543) * 732 = 32,517,567.192 m

Pink/Yellow line (2nd picture) = 900 px = Earth Diameter = 543px = 24,121,637.958 m

Rose line = 291px = Height of the Crust = (24,121,637.958 / 900) * 291 = 7,799,329.60642 m

1 Pixel = 24,121,637.958 / 543 = 44,422.906 m

Px ^ 2 = (44,422.906 m) ^ 2 = 1.973394577484836e+9 m^2

As the continent shown in the 1st scan is the exact same continent shown in the 3rd and 4th scans, the pixel scaling used in the 1st scan would apply to the other two scans as well.

Using Pixel coloring, represented in the 4th scan, the continent is 164,740 pixel squares big.

A = 1.973394577484836e+9 * 164,740 = 3.250970227e+14 m^2

Using the volume of a spherical sector:

Volume of the entire piece can be found here by converting the surface area to fit onto a spherical cap portion on the top of a spherical sector, solving for that thing's volume, and subtracting the volume of the spherical sector portion below it to obtain the section's volume that would be cut out.

Area of a Spherical Sector:

r here represents half of 24,121,637.958 meters, aka half of the calculated Earth diameter, the sphere in question here.

h = 3.250970227e+14 /(2*π*(24,121,637.958/2)) = 4.28999e+6 m

Volume of first spherical sector = (2*π*(r^2)*h)/3

Volume of first spherical sector = (2*π*(24,121,637.958/2)^2)* 4.28999e+6)/3 = 1.30697878e+21 m^3  

The distance below our first spherical sector is the central "thickness" of the crust we found above; 7,799,329.60642 meters. Now to find the second spherical sector.

Volume of second spherical sector = (2*π*(r^2)*h)/3

Volume of second spherical sector = (2*π*(((24,121,637.958/2)- 7,799,329.60642)^2)*(4.28999e+6)/3 = 1.63169023e+20 m^3

Volume of continent = 1.30697878e+21 - 1.63169023e+20 = 1.143809757e+21 m^3

As the crust segment reached through most of the radius of the Earth, leaving the core exposed, it should be safe to assume the density would be similar to Earth’s density of 5,515 kg / m^3

M = V * ρ = 1.143809757e+21 * 5,515 = 6.308110809855e+24 kg

This is more than the mass of the Earth in real life. Very Impressive

Using watch frame by frame, Feat starts at frame 41,975 and ends in frame 42,040 using 25FPS framerate

T = (42,040 – 41,975) / 25 = 65 / 25 = 2.6 seconds

As the crust was moved out to the extended Earth radius seen in the Green line of the 1st picture, the distance the crust traveled would be: [(24,121,637.958 / 543) * (732-543)] / 2 = 4.197964617e+6 m

V = D / T = 4.197964617e+6 / 2.6 = 1.6146e+6 m/s

E = 0.5 * 6.308110809855e+24 * (1.6146e+6) ^ 2 = 8.22241162358e+36 joules = 1.9652035429213 Ronnatons of TNT, or Large Planet level


TLDR: It's now 1.9652035429213 Ronnatons of TNT, or Large Planet level

Recalc Additional Ends[]

Well thanks to LaserPrecision, Omegabronic and the other supporters, they brought into my knowledge two new possible values for the size of the planet. Let's tackle each individually:

End 1: Sonic Adventure 2[]

First we shall use a screen shot from Sonic Adventure 2, where the cast is on the Ark, and orbital space station that is close to the planet

Sonic adventure 2 Sonic's Earth pixel scaling




Using the result we found earlier for Angel Island:

Earth Diameter = 2204px = (22,211.453/(1/2)) * 2204 = 97,908,084.824 m or 97,908.084824 km

Plugging the diamter we'll go through the rest of this calc:


Hide/Show

Pink line (1st picture) = Earth Diameter = 543px = 97,908,084.824 m

Green line = 732px = (97,908,084.824 / 543) * 732 = 131,986,589.486497 m

Pink/Yellow line (2nd picture) = 900 px = Earth Diameter = 543px = 97,908,084.824 m

Rose line = 291px = Height of the Crust = (97,908,084.824 / 900) * 291 = 31,656,947.42642666 m

1 Pixel = 97,908,084.824 / 543 = 180,309.54848 m

Px ^ 2 = (44,422.906 m) ^ 2 = 3.2511533272e+10 m^2

As the continent shown in the 1st scan is the exact same continent shown in the 3rd and 4th scans, the pixel scaling used in the 1st scan would apply to the other two scans as well.

Using Pixel coloring, represented in the 4th scan, the continent is 164,740 pixel squares big.

A = 3.2511533272e+10 * 164,740 = 5.35595e+15 m^2

Using the volume of a spherical sector:

Volume of the entire piece can be found here by converting the surface area to fit onto a spherical cap portion on the top of a spherical sector, solving for that thing's volume, and subtracting the volume of the spherical sector portion below it to obtain the section's volume that would be cut out.

Area of a Spherical Sector:

r here represents half of 97,908,084.824 meters, aka half of the calculated Earth diameter, the sphere in question here.

h = 5.35595e+15 /(2*π*(97,908,084.824/2)) = 1.741278e+7 m

Volume of first spherical sector = (2*π*(r^2)*h)/3

Volume of first spherical sector = ((2*π*(97,908,084.824/2)^2)* 1.741278e+7)/3 = 8.739847e+22 m^3  

The distance below our first spherical sector is the central "thickness" of the crust we found above; 31,656,947.42642666 meters. Now to find the second spherical sector.

Volume of second spherical sector = (2*π*(r^2)*h)/3

Volume of second spherical sector = (2*π*(((97,908,084.824/2)- 31,656,947.42642666)^2)*(1.741278e+7)/3 = 1.091121384e+22 m^3

Volume of continent = 8.739847e+22 - 1.091121384e+22 = 7.6487256e+22 m^3

As the crust segment reached through most of the radius of the Earth, leaving the core exposed, it should be safe to assume the density would be similar to Earth’s density of 5,515 kg / m^3

M = V * ρ = 7.6487256e+22 * 5,515 = 4.218272177e+26 kg

This is about 3/4 the mass of Saturn. Very Impressive

Using watch frame by frame, Feat starts at frame 41,975 and ends in frame 42,040 using 25FPS framerate

T = (42,040 – 41,975) / 25 = 65 / 25 = 2.6 seconds

As the crust was moved out to the extended Earth radius seen in the Green line of the 1st picture, the distance the crust traveled would be: [(97,908,084.824 / 543) * (732-543)] / 2 = 1.703925e+7 m

V = D / T = 4.197964617e+6 / 2.6 = 6.5536e+6 m/s

This about 2% the speed of light so we use Relativistic KE here. Relativistic calaculator link:

E = 9.061918531525281e+39 joules = 2.16585051 Quettatons of TNT, or Brown Dwarf level


TLDR: It's now 2.16585051 Quettatons of TNT, or Brown Dwarf level


End 2: Sonic 3 & Knuckles[]

Now we will use a screen shot from the Death Egg Zone in Sonic 3 & Knuckles, where we see the Earth from even closer, but we are still in space as we later see on Doomsday Zone, a zone that happens immediately after Sonic destroys the Death Egg and in the same place as the Death Egg Zone, asteroid belts, which confirms that we are in space there as well

Sonic 3 and Kuckles Earth size









Using the result we found earlier for angel island:

Earth Diameter = 4158px = (22,211.453/(1/2)) * 4158 = 184,710,443.148 m or 184,710.443148 km


Hide/Show

Pink line (1st picture) = Earth Diameter = 543px = 184,710,443.148 m

Green line = 732px = (184,710,443.148 / 543) * 732 = 249,001,923.35973 m

Pink/Yellow line (2nd picture) = 900 px = Earth Diameter = 543px = 184,710,443.148 m

Rose line = 291px = Height of the Crust = (184,710,443.148 / 900) * 291 = 59,723,043.28452 m

1 Pixel = 184,710,443.148 / 543 = 340,166.56196685 m

Px ^ 2 = (44,422.906 m) ^ 2 = 1.1571328988e+11 m^2

As the continent shown in the 1st scan is the exact same continent shown in the 3rd and 4th scans, the pixel scaling used in the 1st scan would apply to the other two scans as well.

Using Pixel coloring, represented in the 4th scan, the continent is 164,740 pixel squares big.

A = 1.1571328988e+11 * 164,740 = 1.90626e+16 m^2

Using the volume of a spherical sector:

Volume of the entire piece can be found here by converting the surface area to fit onto a spherical cap portion on the top of a spherical sector, solving for that thing's volume, and subtracting the volume of the spherical sector portion below it to obtain the section's volume that would be cut out.

Area of a Spherical Sector:

r here represents half of 184,710,443.148 meters, aka half of the calculated Earth diameter, the sphere in question here.

h = 1.90626e+16 /(2*π*(184,710,443.148/2)) = 3.285041134e+7 m

Volume of first spherical sector = (2*π*(r^2)*h)/3

Volume of first spherical sector = ((2*π*(184,710,443.148/2)^2)* 3.285041134e+7)/3 = 5.868435e+23 m^3  

The distance below our first spherical sector is the central "thickness" of the crust we found above; 59,723,043.28452 meters. Now to find the second spherical sector.

Volume of second spherical sector = (2*π*(r^2)*h)/3

Volume of second spherical sector = (2*π*(((184,710,443.148/2)- 59,723,043.28452)^2)*(1.741278e+7)/3 = 3.88346e+22 m^3

Volume of continent = 5.868435e+23 - 3.88346e+22 = 5.480089e+23 m^3

As the crust segment reached through most of the radius of the Earth, leaving the core exposed, it should be safe to assume the density would be similar to Earth’s density of 5,515 kg / m^3

M = V * ρ = 5.480089e+23 * 5,515 = 3.0222690835e+27 kg

This is about 3 times the mass of Jupiter. Very Impressive

Using watch frame by frame, Feat starts at frame 41,975 and ends in frame 42,040 using 25FPS framerate

T = (42,040 – 41,975) / 25 = 65 / 25 = 2.6 seconds

As the crust was moved out to the extended Earth radius seen in the Green line of the 1st picture, the distance the crust traveled would be: [(184,710,443.148 / 543) * (732-543)] / 2 = 3.21457401e+7 m

V = D / T = 4.197964617e+6 / 2.6 = 1.2363746e+7 m/s

This about 4% the speed of light so we use Relativistic KE here. Relativistic calaculator link:

E = 2.312904531337e+41 joules= 55.279745 Quettatons of TNT, or Small Star level (ACCEPTED)


TLDR: It's now 55.279745 Quettatons of TNT, or Small Star level (ACCEPTED)

New Lifting Strength value edit:[]

I forgot about the formula of F = M * A for LS, so:

Average acceleration was calculated as: 9,510,574 m/s^2. So we get:

F = M * A = 3.0222690835e+27 * 9,510,574 = 2.8743514e+34 kg or Multi-Stellar. To give you idea how insane that is, this is about 10,000 solar masses.

Calculation through work (ACCEPTED)[]

Well it was brought to my attention that I could use work to get an even higher result by CloverDragon03, so I'll use that

Using force and mass calculated earlier using S3&K's accepted end:

Work = Force * Distance = F * D

F = 2.8743514e+34 * 9.80665 = 2.818776e+35 Newtons

D = 3.21457401e+7 meters

W = 2.818776e+35 * 3.21457401e+7 = 9.0611641e+42 joules = 2,165.67018872 Quettatons of TNT, or Large Star level

Honestly this is insane but it is what it is lol

Tally[]

Original:

  • Chaos Emerald shifts a continent: 81.279516628553222933975153392535 Yottatons of TNT, or Large Planet level
  • Lifting Strength: 9.3291673195228579322964215390209e+23 kg, or Class Z

Re-calculation:

  • Chaos Emerald shifts a continent: 1.9652035429213 Ronnatons of TNT, or Large Planet level
  • Lifting Strength: 6.308110809855e+24 kg, or Class Y

Additional Ends:

Sonic Aventure 2 end:

  • Chaos Emerald shifts a continent: 2.16585051 Quettatons of TNT, or Brown Dwarf level
  • Lifting Strength: 4.218272177e+26 kg, or Class Y

Sonic 3 & Knuckles end:

Calculation through work:

  • Chaos Emerald shifts a continent: 2,165.67018872 Quettatons of TNT, or Large Star level (ACCEPTED)
  • Lifting Strength: 2.8743514e+34 kg or Multi-Stellar (ACCEPTED)