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 Post subject: Angel Island calc
PostPosted: Mon Mar 04, 2019 6:44 am 
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Rocky Road
Rocky Road
Joined: Mon Apr 02, 2018 11:44 pm
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The size of the Little Planet
In Sonic 4 Episode Metal we see Metal Sonic flying from the Little Planet to Earth following his recovery from his defeat in Sonic CD.
https://i.imgur.com/WSajO9U.png
https://i.imgur.com/KNaknL3.png
In the cutscene we get a view of the Little Planet from space where we can see the distance between its surface and its clouds. We know the Little Planet has gravity and atmosphere similar to Earth since Sonic and Dr. Eggman walk around on it no differently than they do on Earth, so we can conclude that it's clouds form in the same way clouds do on Earth. This means we can use the clouds as a measuring stick to determine the size of the whole planet.
https://i.imgur.com/eQbdDa1.png
https://i.imgur.com/1DYDb7p.jpg
Distance from surface to cloud top: 45,000 ft
Diameter of Little Planet is around 92 times the distance between the surface and the clouds: 4,140,000 ft, or 784 miles
In other words the Little Planet is less than half the size of the Earth's Moon (2,159 miles) and a little bit larger than Pluto's moon Charon (753 miles). For some perspective, here's how big Charon is compared to Earth and it's Moon:
https://upload.wikimedia.org/wikipedia/ ... arison.jpg
It's surface area is roughly 1,930,896 square miles, about two thirds the size of Australia. That river winding around the planet's eastern hemisphere is about 8 miles wide, which sounds plausible enough; if the Little Planet were much larger it would have to have uniform land formations over improbably large distances.
Since it has Earth-like gravity despite being many orders of magnitude smaller than the Earth, it must be composed of some sort of exotic high density materials. Maybe Quartz Quadrant is an artificial gravity plant and the crystals have similar gravity altering properties as Chaos Emeralds.
It's atmosphere might also be artificial; perhaps the Wacky Workbench is an atmosphere generator.

The distance Metal Sonic flew
We can use the stars and planets around the Earth to estimate the angular size of the two planets, from which we can determine their distance from the viewer in the cutscene. Earth's diameter is 36 times that of the bright object to the right of it; I got various different numbers comparing the object to bright stars and planets, before settling on the Big Dipper as a measuring stick. I used this photo to judge the size of the stars in the cutscene and the distance between the stars of the Dipper to estimate the apparent diameter of the Earth, which I found to be just twice the distance between Merak and Phecda.
https://i.pinimg.com/originals/45/0f/5d ... e68a67.jpg
This gave the Earth an angular diameter of 16 degrees.
Knowing the actual diameter of Earth is 7,917.5 miles (or 40,075 km), the distance from the viewer in the image must be 85,697 miles (137,916 km)

In the image the Little Planet is twice the apparent size of the Earth, 32 degrees. Since we determined that its actual size is 784 miles (1,261.73 km), the Little Planet's distance from the viewer is 1,367 miles (2,200 km).

Metal Sonic flew in an arc from the surface of the Little Planet towards the viewer, then away from the viewer towards Earth, approximately 87,064 miles (140,116 km).
Metal Sonic seems to have flown the entire distance in fifteen seconds. His speed would clock in at 20,895,000 miles per hour or 33,628,000 kilometers per hour.

Sonic running up the Little Planet's chain
Naturally, Sonic's speed scales off of Metal Sonic's, so we can reasonably presume he's capable of matching the interplanetary velocity. We can compare Sonic scaling the Little Planet's chain in the Sonic CD intro animation using the distance we arrived at above. The Little Planet's distance from Earth most likely varies with its orbit, and frequently it looks much closer to Earth than as depicted at the beginning of Episode Metal. For simplicity's sake we will assume that it was at its maximum distance in the Sonic 4cutscene, and that the chain was long enough to cover that distance, however far away the planet was during Sonic CD.
https://i.imgur.com/RoFLYVsl.jpg
Sonic's height in Sonic CD: 76.5 cm
Size of the chain link: 230 cm
If the chain is 87,064 miles long, and each link is the same size, then the chain is made of 60,920,000 links. It's interesting that Metal Sonic flew between Earth and the Little Planet in 15 seconds, because Sonic historically can only hold his breath for around 18 to 23 seconds, meaning he would have had to clear the length of the chain outside of the two planets' atmospheres within a similar timespan to avoid suffocation. So his speed would be somewhere between 17,412,480 mph to 20,895,000 mph.

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 Post subject: Re: Little Planet calc
PostPosted: Fri Mar 08, 2019 7:18 am 
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Rocky Road
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Joined: Tue Mar 06, 2018 3:38 pm
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what can be done with this information now


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 Post subject: Re: Little Planet calc
PostPosted: Fri Mar 08, 2019 11:54 pm 
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Rocky Road
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Joined: Mon Apr 02, 2018 11:44 pm
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When someone tells you Sonic's top running speed is only a couple hundred miles per hour based on frame rate calculations, you now have scientific evidence that they are wrong.

Serious answer: I made this to post on SpaceBattles.com, which has a subforum specifically for Scifi Technical analysis like this, and since it was Sonic related I crossposted it on SC and CI. Over on SB it sparked a discussion on the validity of comparing data from different Sonic games and the internal consistency of the data (I pointed out to someone who objected that the Little Planet was smaller in it's original appearance that if it was the size they were suggesting it wouldn't be a sphere); on CI I got Jeffrey speculating about material densities to figure out how such a small object could have so much gravity. So that was interesting.

At minimum I hope to incorporate some of the details about the physical properties of the Little Planet into my Sonic fanfic/worldbuilding project.

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Quote NachoThePikachu :
I WILL BE AN ADMINISTRATOR, RULING OVER CHAO ISLAND
except it WON'T BE CHAO ISLAND ANYMORE
IT'LL BE BANANA ISLAnD


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 Post subject: Re: Little Planet calc
PostPosted: Sat Mar 09, 2019 6:43 am 
"Show me your power... Or I shall not obey."
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Rocky Road
Rocky Road
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https://www.youtube.com/watch?v=Cl_5UwS57X8

If I had to consider his top speed, Supermans World of Cardboard speech rings well here. If he really did go at top speed he'd likely burn his surroundings or others from the friction or heat.


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 Post subject: Re: Little Planet calc
PostPosted: Sat Mar 09, 2019 6:48 pm 
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Rocky Road
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I imagine all the characters hold back significantly to prevent collateral damage. I plan on re-doing the Sonic calcs I posted on CI a while back; some of those figures put their attack power on par with multi-ton bombs.

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Quote NachoThePikachu :
I WILL BE AN ADMINISTRATOR, RULING OVER CHAO ISLAND
except it WON'T BE CHAO ISLAND ANYMORE
IT'LL BE BANANA ISLAnD


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 Post subject: Re: Little Planet calc
PostPosted: Tue Mar 12, 2019 2:03 am 
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Rocky Road
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Size of Angel Island
Once again we will be using altitude to gauge the size of an object, this time the snow line of Angel Island's mountains.

First we need to figure out if snow forms naturally on the Floating Island. Since the Floating Island (obviously) floats in the air, it's mountains could potentially have snow no matter how tall they are, since the whole island is at a high altitude.

However, we've seen what Angel Island looked like before it rose into the air during Tikal's flashbacks, and it's mountains were indeed covered in ice at that time.
https://i.imgur.com/4fHV1Vwh.jpg
The Mystic Ruins are situated in a warm tropical jungle modeled on locations in real world Central America. At the equator snow begins to form on mountain tops at 15,000 ft; but Angel Island doesn't just have snow, it has an ice cap. The largest ice cap in Mexico is Gran Glacier Norte on the Citlalt├ępetl volcano. Citlalt├ępetl is 18,491 ft in elevation and 16,148 ft in prominence. The Mystic Ruins are located on a plateu at least a couple thousand feet above sea level, so the Angel Island Ice Cap probably has a similar difference in total elevation vs the height of the mountain's cone.
https://i.imgur.com/ZAQQFaL.png
https://i.imgur.com/02PUX1fh.jpg
https://i.imgur.com/ggoyGHB.png
Both in Sonic Adventure and S3&K the length of island appears to be around 3.5 times the height of its tallest mountain. If the mountain is approximately 16,000 ft tall then Angel Island would be 56,000 ft or 10.6 miles long. In Sonic Advneture its length is 1.09 times its width at its widest point, about 51,000 ft or 9.6 miles. This would give it an area somewhere around 100 square miles, similar in size to the Caribbean island nation of Antigua.
We've seen the Island lift off after the Master Emerald is restored. I'd estimate it's volume to be 78.8 trillion cubic feet given the size suggested above. Assuming it's mostly made of igneous rock like basalt (density of 2.7-3.0), its mass must be somewhere around 6,024,690,000,000 metric tons. In the cinematic it seems to cover the distance of it's own height in ten second or 3,200 ft/s. The amount of energy the Master Emerald would have to generate to lift the Island above the clouds is 2.9 zettajoules. In other words the Master Emerald by itself measurably produces more than five times the energy all of human civilization consumes in a year.
Size of the Death Egg
https://bastendorfgames.weebly.com/uplo ... 2_orig.png
In the intro to Sonic & Knuckles we see the Death Egg land in the caldera above the Lava Reef Zone. We can see the caldera is just above the Sandopolis pyramids in the intro, and there's a mountain with waterfalls in the same spot in the full length sprite of Angel Island. There's also what looks like a water filled basin in the shot of Angel Island from Sonic Adventure that also appears to represent the caldera. In both S3&K and Sonic Adventure the caldera is almost precisely one half the size of the tallest mountain on Angel Island, approximately 8,000 ft (around the size of Mt. St Helens). The Death Egg is twice the height of the caldera, making it 3 miles in diameter.
The Death Egg's launch
http://www.soniczone0.com/games/sonican ... ct2map.png
The Death Egg Zone is around 3,000 ft long (using Sonic's height as a measuring stick), 1/6th the diameter of the station as a whole. Judging from the amount of empty space seen in the Death Egg Zone the Death Egg's interior might be 14% empty space. The volume of the Death Egg is 14.14 cubic miles. It would weigh somewhere between 16,000,000 and 14,000,000 metric tons. For an object that heavy to launch from the planet's surface and reach space it would need an engine output of 875.886 petajoules. That is more than four times the yield of the Tsar Bomba. This is both a feat for Eggman's engineering capabilities and for the Master Emerald as an energy source.

_________________
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Quote NachoThePikachu :
I WILL BE AN ADMINISTRATOR, RULING OVER CHAO ISLAND
except it WON'T BE CHAO ISLAND ANYMORE
IT'LL BE BANANA ISLAnD


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