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One Piece Blue Planet Calc Revisions

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I think you misunderstood me. In the scene you linked we do have the Thousand Sunny and the Polar Tang sailing side by side... But what does that prove? That they are comparable to each other in that scene, and how fast were they going? Do we have any indication that the Polar Tang was sailing at Relativistic speed in that scene specifically?

To put it another way, it's like saying that the Flash ran at FTL speeds in one scene, and in an unrelated scene we see him walking side by side with Batman. The earlier FTL scene doesn't prove that he is always moving at that speed with no variation, and we shouldn't assume Batman is also FTL.
they were racing off the cliff, it was a scene showing their eagerness to speed to their deaths
 
I just wanted to add that the anime (16:37) seems to corroborate the fact that Alabasta/the middle path is the one that the Strawhats traveled. Luffy and Zoro are quite literally standing on either side of the middle path.
 
they were racing off the cliff, it was a scene showing their eagerness to speed to their deaths

I'm sorry, but what are you talking about?

Let's take the powerscaling goggles off for a second, and examine the scene objectively, shall we?

All three ships in this scene are travelling via their sails; they're harnessing the wind primarily to get to the edge of Wano where then the water flowing over the edge will also increase their speed as they're carried by it. Are there Relativistic winds blowing in Wano Country? Winds that only affect ships and aren't affecting anything else in the area with the ungodly wind pressure that would be created by winds at that velocity?

Furthermore, once they cross over the edge of Wano Country, their ships immediately begin falling; and not falling gradually but extremely quickly. What happened to all of that horizontal velocity they had? If they were travelling at baseline Relativistic speed (since you didn't specify how fast the Polar Tang is supposed to be), they'd have shot off the edge of the cliff like a cannonabll at 10% the speed of light. They'd begin accelerating down towards the ground thanks to gravity but their previous momentum should still carry them horizontally a fair distance if they were going that fast. If the cliffs of Wano Country were for example five kilometers above sea level, then at a speed of 10% the speed of light it would take them about 31.9 seconds to reach the sea, during which time they'd cover a horizontal distance of approximately 957,000 km. I don't see the three of them landing that far away from Wano; not when we see them plumetting straight down the waterfall.

Even ignoring the mathematical issues of this; you have to force an extremely unreliable interpretation on this scene to justify your claims. Firstly if we did accept the Polar Tang was "Relativistic" back during Marineford, it was only when it was submerged underwater and operating by motors to escape Kizaru, not when it was abovewater and driven by its sails. It's also extremely questionable in the first place whether the Polar Tang is "evading the lasers" as you claim; it was a widespread spray of lasers striking blindly across the depths of the sea; Kizaru wasn't aiming for the submarine specifically and he didn't know whether or not his lasers hit them. The Polar Tang erratically moving underwater with lasers falling all around them is not the same thing as the Polar Tang bobbing and weaving lasers at speeds close to light itself. Secondly, the edge of Wano was only hundreds of meters to a few kilometers away from these ships as they were sailing; if they were travelling at 10% of the speed of light then they would have zoomed off of Wano in about 67 microseconds. Yet there was a whole extended scene of the three ship captains conversing and having their competitive little argument before they all went off the edge; watch the entire scene in full and judge if it makes sense contextually to have all occured in a hundredth of an eye-blink from start to finish.

Lastly, think about how little narrative sense it would make. If the Thousand Sunny could sail at this kind of speed then it would be able to sail the seas and cross 30,000 kilometers in a single second of normal travel time. That would render the Coup de Burst feature of the Thousand Sunny (something that has a range of 1 km) as completely useless as it takes several seconds at least for the Sunny to travel that distance given that gravity has to pull the ship back down to the sea after it launches into the air. The Thousand Sunny regularly uses this feature to escape other sailing ships. I don't even want to get into the whole mess of other contradictions like the Thousand Sunny taking several hours to travel across Big Mom's territory, or being unable to escape a tsunami without the Coup de Burst until Jinbe harnessed the wind in order to navigate into the tsunami's wave. Even if every single thing you argued about the Polar Tang was true, it would still be an outlier and therefore still easily dismissable thanks to all of the contradictions that can be produced against travel speed being anywhere this high for any ship in the entirety of the series.

If the sole basis for your reasoning is "They were racing with each other for the edge, therefore Relativistic travel speed, therefore travel speed is too unreliable to use to evaluate One Piece" then I strongly urge you to reread the scene again.
 
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i do think marcos statement should not be disregarded as we know he's studied cartography when he was even younger then he was in the oden flashback
 
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Respectfully Damage you filled up an entire screen off of a subpoint of a subpoint of a subpoint that literally means nothing to the grand argument as a whole and I'm not gonna waste this long ass thread with arguing for relativistic ships when the entire damn point of the message was "Oda makes things as fast as they want" and you deadass only focused on the one highball speed instead of looking at the entire point.

It's clear you have your opinion and I have mine. I'm not going back and forth with arguments that mean nothing when the main person arguing is a person who doesn't think there's such thing as a "center of a map" and doesn't understand a "climate switch" just so that the staff who don't want to evaluate see "Big unanswered paragraph, must be right".

@Nierre @Godernet @Planck69 @whoeverthehellelse we need evaluations, and please thoroughly read it because half the people here disagree cause it's one piece and half the people here agree cause it's one piece which is a problem
 
Respectfully Damage you filled up an entire screen off of a subpoint of a subpoint of a subpoint that literally means nothing to the grand argument as a whole and I'm not gonna waste this long ass thread with arguing for relativistic ships when the entire damn point of the message was "Oda makes things as fast as they want" and you deadass only focused on the one highball speed instead of looking at the entire point.
It was the point that was most jarring to me and required a response. If part of the reason for our differences of opinions on the matter is you believing that the ships could be Relativistic, then I had to at least try and show you why I don't agree with that.

You may not want to continue the argument on that point which I respect, but does this mean any sort of acknowledgement that you could be mistaken about that part at least?


Also, Nierre, Godernet and Planck69 are not Calc Group members, so I'm not sure why you tagged them for a calc thread.
 
It was the point that was most jarring to me and required a response. If part of the reason for our differences of opinions on the matter is you believing that the ships could be Relativistic, then I had to at least try and show you why I don't agree with that.

You may not want to continue the argument on that point which I respect, but does this mean any sort of acknowledgement that you could be mistaken about that part at least?


Also, Nierre, Godernet and Planck69 are not Calc Group members, so I'm not sure why you tagged them for a calc thread.
We've gotten so far off track regarding math that this should honestly be a CRT, but fine, w/e

@Armorchompy @Dalesean027 @SunDaGamer
 
on the whole topic of the strawhats traveling the grand line using the center point, there is a moment in the live action where nami mentions as their leaving reverse mountain that their going straight ahead

i get that its the live action, but still
 
If we take the statement reliable but unknown for sizes, Assuming average island size for those unknowns, which wouldn't be higher than 100km^2 (Bigger islands carries the average here) then saying it'd only cover 1/4 of the surface with the rest being water, the radius of the planet would be: sqr((100x10000000*4)/(4*pi)) = 17841.2411615 km

so around 36k for diameter. (should be higher considering the known islands, or using not 10m but 15 or 20 etc.

Now that I think about it,1/8 of surface being land being land seems more reasonable here with the whole pirate and aquatic theme going on. With 2,5% of those 12,5% being reserved for the Red Line and some other unknown superstructures, this would leave one with the planet radius being 28 209,479 18 km (i.e. roughly 56km diameter). Which is roughly beyond the biggest Mega Earths but obviously not anywhere close to sun-sized.

Some other point.

If the picture of the triangle is accurate, one could deduce the distance between each of the three positions based on the fact that the time it takes to reach one of those places is known - the Tarai Current, which is supposed to be some super fast maritime express highway, supposedly allows for 3 days worth of regular (who knows if wiki makes sense)? travel in 30 minutes, and that the travel time supposedly is 1 week from Amazon Lily to Impel Down or 4 days if one goes to the Tarai Current first and then heads there? - moves things between places AND we got at least some understanding of what maximum speed the Going Marry can take and what standard speed is assumed could be deduced from other things, too.
 
us being 28 209,479 18 km (i.e. roughly 56km diameter). Which is roughly beyond the biggest Mega Earths

There is no solid confirmed upper size limits on Mega Earths. I think you meant Super Earths as those are confirmed between 2 times to 10 times bigger than the Earth itself.





That is all I have to say here
 
Are there seriously no cgms that want to look at this
They've been pinged, but I can understand them being uninterested or reluctant. They might also be waiting for that other planet thread to be resolved, if it hasn't been yet.
 
Can both sides make a summary of their arguments please?
 
Can both sides make a summary of their arguments please?
First point:
In One Piece, each island has a distinct climate zone that extends hundreds of kilometers beyond the landmass and into the surrounding ocean. These zones have stable, consistent weather, such as winter or spring depending on the island. Outside of these climate zones are the waters of the Grand Line that are highly turbulent and characterized by chaotic weather. This is a consistent part One Piece's world that Oda has made sure to include whenever the crew traverses between locations.

The reason this is brought up is because in the current calc of planet, the height of the top-left panel of this page is used as a lowball estimate for the width of the Grand Line. The main argument in the OP is that there is no way to determine whether other islands are present in that panel since Alabasta is extremely large with a diameter of 5000 kilometers, meaning smaller islands would not be visible in the birds-eye-view.

The counter to that point is that the closest confirmed island to Alabasta, Drum Island, has a large and visually distinct winter climate zone. Even if Drum Island’s landmass were too small to be directly visible at that scale, its surrounding climate zone would. The unstable weather patterns of the Grand Line between Alabasta and Drum Island should also be visible, as it's consistently depicted as having a stark contrast to stable climate zones.

*Related point: Alabasta is canonically toward the middle of the Grand Line, so the argument that it borders its edge are invalid

Second Point:
The next argument against the planet size has more to do with consistency. It claims that if the planet were truly as large as calcs suggest, circumnavigation would take an unreasonably long amount of time, especially since most travel is done by ship.

The counter to this is that travel speed in the series is almost never portrayed consistently or realistically to begin with. For example, when the Straw Hat crew travelled to an island where a character that has a 4000 kilometer clairvoyance range lives, they entered her range the night before arriving, even though they set sail a day earlier. This implies that they covered a distance of about 4000 kilometers overnight, which does not align with conventional ship travel speeds. The key takeaway from this being that Oda treats travel speed as flexible and dependent on narrative needs.

Third point:
Something else in the OP is that the current moon size comes from Boichi's Zoro vs Mihawk One Piece. The argument against using that panel is that even though it's accepted as tertiary canon, the primary canon should be prioritized.

Nobody has any real issue with prioritizing what comes from the original manga. However, the only scalable depiction of the moon seen in it is from a planetary model.

The counter to this is that the model comes from Ohara’s Tree of Knowledge, which is the world’s greatest hub of information and scholars and was created and maintained by the world’s leading historians and archaeologists. Given that context, there's basis to treat the model as a credible in-universe source as they would know better than most.
 
There is no solid confirmed upper size limits on Mega Earths. I think you meant Super Earths as those are confirmed between 2 times to 10 times bigger than the Earth itself.
From your source.
Biggest known Mega Earth
"PSR J1719−1438 b may be one of the most massive mega-Earths ever known, with a mass of about 330 M🜨 and a radius less than 4 R🜨, slightly more massive but smaller than Jupiter. It is a pulsar planet which is most likely composed largely of crystalline carbon but with a density far greater than diamond."
I highly doubt that solid planet greater than this one would resemble Earth that much(especially considering how exotic is origin of this big giant)
Biggest known rocky planet(thought some sources say that they are gas giants).
"Kepler-277b and Kepler-277c are a pair of planets orbiting the same star, both thought to be mega-Earths with masses of about 87.4 M🜨 and 64.2 M🜨, and radii of about 2.92 R🜨 and 3.36 R🜨, respectively".

4 earth radii is around 54000 km. 3.36 radii is around 45360 km
 
Can both sides make a summary of their arguments please?
Most of the summary of my arguments can be found in the OP.

KT and Kachon’s main point is that the weather conditions for each Island as well as the ocean would be visible in the panel, but I still don’t think that would be the case due to the massive zoom out, with again, each pixel being 227km by 227km with no accepted island calc getting to even a ninth of that area. And each climate zone extending hundreds of kilometers, something I don’t even know has been proven yet, doesn’t really matter when a single pixel also extends hundreds of kilometers. And this is what the climate around drum island looks like. Alabasta has not been agreed upon by both sides to be in the middle of the grand line

The thing about the strawhats entering the vision of a character with a range of 4000km is completely false, as we have no confrontation as to when they entered her range, and that range of vision is an ability that needs to be activated.

The Boichi problem is misrepresented. The Boichi panel is an adaptation that does both follow the canon rules for adaptations on our page at all, and also contradicts the main story. And the ohara globe has problems with being used to. It is not supported at all by the main story and the reason the Boichi panel was used in the first place was because it’s use was not agreed upon
 
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KT and Kachon’s main point is that the weather conditions for each Island as well as the ocean would be visible in the panel, but I still don’t think that would be the case due to the massive zoom out, with again, each pixel being 227km by 227km with no accepted island calc getting to even a ninth of that area. And each climate zone extending hundreds of kilometers, something I don’t even know has been proven yet, doesn’t really matter when a single pixel also extends hundreds of kilometers. And this is what the climate around drum island looks like. And alabasta has not been agreed upon by both sides to be in the middle of the grand line
Egghead island is 60 km in diameter with a climate zone extending so far that you can be within it without the island being visible. I'm not sure why you keep on saying that there's no island near 227 kilometers.
 
The overhead panel with Alabasta in it has giant clouds covering significant portions of the sea. We cannot say for certain whether Drum Island or its climate would even be visible from that perspective with big areas being blocked from view.
 
Just a few thoughts on the Dressrosa point; the Straw Hats left Punk Hazard while it was still daylight and sunny; let's estimate it at around 6 PM that they left, assuming they spent the majority of the day on Punk Hazard. They arrived at Dressrosa before 3 PM but after they had their breakfast. Let's spitball it in the middle and say they arrived at 12 PM, as they had plenty of time to wander around Dressrosa and make their way to Green Bitt before the drop-off time.

So roughly 18 hours to cross the assumed 4,000 kilometers. That would net the Thousand Sunny a travel speed of 222.2 km/hr.

But the OP's point was that even if the Thousand Sunny + Going Merry spent an entire year travelling in a straight line at 250 km/hr, that it still wouldn't be enough to cover the length of half the Grand Line. And we know that the Straw Hat's journey took a lot less than a whole year Pre-Timeskip, and they didn't spend all of that time travelling in a straight line.

So even if we granted based on the Dressrosa arc that the travel speed of One Piece ships could be far higher than normal ships... it still wouldn't support the calculated figure for the distance of the Grand Line.

I don't think that the apparent inconsistency of the ship's travel speed is enough to debunk the concerns over the calculation, especially with how I debunked the point about "Relativistic" ships at the top of this page.
 
From your source.
Biggest known Mega Earth
"PSR J1719−1438 b may be one of the most massive mega-Earths ever known, with a mass of about 330 M🜨 and a radius less than 4 R🜨, slightly more massive but smaller than Jupiter. It is a pulsar planet which is most likely composed largely of crystalline carbon but with a density far greater than diamond."
I highly doubt that solid planet greater than this one would resemble Earth that much(especially considering how exotic is origin of this big giant)
Biggest known rocky planet(thought some sources say that they are gas giants).
"Kepler-277b and Kepler-277c are a pair of planets orbiting the same star, both thought to be mega-Earths with masses of about 87.4 M🜨 and 64.2 M🜨, and radii of about 2.92 R🜨 and 3.36 R🜨, respectively".

4 earth radii is around 54000 km. 3.36 radii is around 45360 km
Not my point though it is reasonable plus I seriously doubt that the one piece planet was meant to resemble our Earth that much outside of Earthlike qualities for rocky planets as that was the point of the term MegaEarths.

Also upon double checking the math and all.



Also, as a note, I was looking to Diameter rather than the Earth Radius.

“The Earth's radius (represented as R🜨 or
{\displaystyle R_{E}}
) is the distance from the center of Earth to a point on or near its surface.” Also quoted from Wikipedia

This is a friendly reminder this is talking about the distance between Earth’s core and its surface



Here it is, but from a different site that also backs up what the Wikipedia has on it.


I was thinking of the full diameter of a planet rather than its radius
 
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One of the main supporting arguments for Blue being much, much bigger than Earth is distance to horizon. Results based on it are actually very close to current used size. In absense of other reliable methods for calculating size, this calc could probably cement status of Blue as being Sun-sized.


Could, if not for atmospheric refraction. Calculator that was used in calc calculates true horizon, not apparent horizon(which is influenced by this refraction).
So, what problems does it pose to this method?
1. Density at surface is greater than density at higher altitudes, which results in greater apparent horizon (usually by 8% for Earth). Correcting for this is pretty easy, it would just lower calced radius of Blue to around 690,000 km. Doesn't sounds too bad, isn't?
2. Noticed now I accentuated on "usually". Temperature and density gradients can vary considerably by time and location, which can result in apparent horizon being much further away(potentially up to 750 km under best conditions).
3. Noticed how I accentuated on "Earth". Exact value of atmospheric refraction depends on density profile of atmosphere (and associated with it temperature and pressure profile). We can't possibly know exact data for Blue, but we can speculate. We can be fairly sure that atmosphere of Blue is much bigger and thicker than Earth. And apparently, if we use current maps that are used for calculating size of the planet, atmosphere of the Blue can support airdrops at 114,000 km height. Indicating that Armstrong limit(which is defined by pressure) is massively higher than Earth one(19 km). What it does means?:
Thicker atmosphere means higher atmospheric refraction, and bigger apparent horizon. For example, Venus has true horizon of 3.5 km and would have been in pocession of apparent horizon much greater than 16 km(this link leads to pdf file), if not for funny atmospheric and temperature phenomena. But if we could see such a long horizon, and used it as method for calculating radius for Venus, we would get 128,000 km (compared to actual 6051 km for Venus), nuff said.

In short, this method would face two most important problems:
1. Size of apparent horizon(only thing we can see and directly measure) is greatly dependent on specific atmospheric phenomena, local temperature and density gradients, which can vary dramatically by time and location.
2. Using this method would greatly inflate size of planets with thicker atmosphere.

In conclusion, we shouldn't try to calculate Blue size via horizon measurements
 
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One of the main supporting arguments for Blue being much, much bigger than Earth is distance to horizon. Results based on it are actually very close to current used size. In absense of other reliable methods for calculating size, this calc could probably cement status of Blue as being Sun-sized.


Could, if not for atmospheric refraction. Calculator that was used in calc calculates true horizon, not apparent horizon(which is influenced by this refraction).
So, what problems does it pose to this method?
1. Density at surface is greater than density at higher altitudes, which results in greater apparent horizon (usually by 8% for Earth). Correcting for this is pretty easy, it would just lower calced radius of Blue to around 690,000 km. Doesn't sounds too bad, isn't?
2. Noticed now I accentuated on "usually". Temperature and density gradients can vary considerably by time and location, which can result in apparent horizon being much further away(potentially up to 750 km under best conditions).
3. Noticed how I accentuated on "Earth". Exact value of atmospheric refraction depends on density profile of atmosphere (and associated with it temperature and pressure profile). We can't possibly know exact data for Blue, but we can speculate. We can be fairly sure that atmosphere of Blue is much bigger and thicker than Earth. And apparently, if we use current maps that are used for calculating size of the planet, atmosphere of the Blue can support airdrops at 114,000 km height. Indicating that Armstrong limit(which is defined by pressure) is massively higher than Earth one(19 km). What it does means?:
Thicker atmosphere means higher atmospheric refraction, and bigger apparent horizon. For example, Venus has true horizon of 3.5 km and would have been in procession of apparent horizon much greater than 16 km(this link leads to pdf file), if not for funny atmospheric and temperature phenomena. But if we could see such a long horizon, and used it as method for calculating radius for Venus, we would get 128,000 km (compared to actual 6051 km for Venus), nuff said.

In short, this method would face two most important problems:
1. Size of apparent horizon(only thing we can see and directly measure) is greatly dependent on specific atmospheric phenomena, local temperature and density gradients, which can vary dramatically by time and location.
2. Using this method would greatly inflate size of planets with thicker atmosphere.

In conclusion, we shouldn't try to calculate Blue size via horizon measurements
Yeah I completely agree with this I already pointed out some other issues with the horizon calcs here, mainly this one:
3)Another major problem is that the objects we're looking at from the other side of the river are mountains which are elevated above sea level. These tall objects can be viewed from beyond our horizon distance. In this calculator we can put the height of the observation point and the height of the object beyond the horizon to find the maximal distance at which the top of this object will be visible using earth parameters. We can use this calculator to approximate the minimal height needed for an object to be visible from a certain distance, for example the minimal height needed for an object to be visible from 50km away at the height we have is 115.3m (137.9m for the height of Vivi's eyes), obviously a taller mountain even more visible from 50km away (what we'll be able to view is the difference between the mountain's height and the minimal height required that we calculated earlier from the top, if the mountain is a good amount larger than the minimal height then you'd see most of it and won't notice the missing part at the base). Considering Alabasta is a pretty mountainous kingdom it's not that ridiculous to assume that these mountains that we see in the other side of the Sandora River are much taller than these minimal values, so the fact that they are visible from 50km away doesn't really give us the info needed to find the diameter of the planet.

And to illustrate this even further since the previous calculator uses earth parameters this time let's use the parameters of a planet arbitrarily larger than earth and smaller than the one found in the blog for example one with a diameter of 40000km, to find the apparent radius of the planet due to atmospheric refraction we will use this formula/This formula, while the formula for the maximal distance between two points we can use This which is d = sqrt(2*R*h1) + sqrt(2*R*h2) we can then use this to find the formula for the minimum height of an object to be visible from a certain distance to find h2 = (d - sqrt(2*R*h1))^2 / (2*R). For our 40000km diameter planet we'll use in this example the radius will be 20000km and the apparent radius due to atmospheric refraction will be 20000*7/6=23333.33km=23333330m for 50 km away we'll have h2 = (50000 - sqrt(2*23333330*(5.071)))^2 / (2*23333330) = 25.68m ((50000 - sqrt(2*23333330*(1.551)))^2 / (2*23333330)=37.9m if we were to use Vivi's eye height rather than the full height which still gives us a short minimal height), so in this planet with 40000km diameter you can see objects as short as 37.9m from 50km away and as such the mountains will be easily visible from that distance since 37.9m is a negligible value compared to their heights, so we really can't deduce the planet's diameter with the method used in the blog which gets a 1,611,864 km diameter planet (a very large difference from the 40000km used here) for viewing these mountains from 50km away. (For a planet with a diameter of 90000km (50000 - sqrt(2*52500000*(1.551)))^2 / (2*52500000)=13.2m which is pretty much nothing when we're talking about mountains)
 
So what would be an alternative method to accurately calculate the planet size?

There its another method propose by YmTheSuper, in One Piece General Discussion, about using Luffy travel between Sabaody and Amazon Lily.

The speed of travel:
We can use this part of the anime to find Kuma's speed which should be similar to Luffy's since they are using Kuma's devil fruit.

Frame 1, Frame 2, Kuma's size

in 1 frame Kuma moves from the point of coordinates 1222, 717 to 1217, 715 (in pixels)
d = sqrt((1217 - 1222)^2 + (715 - 717)^2) = 5.39px

Kuma height: 6.89m=13px
d=5.39px=2.86m

The video is 24 frames per second as shown here (The title of the video is misleading).

Speed: 2.86/(1/24)= 68.64m/s
The time frame:
Gloriosa stated that it took Luffy 2 days to arrive to Amazon Lily to Sabaody so that's out timeframe

Sizes:
Scan 1, Scan 2
Distance from Amazon Lily to Sabaody: 172800*68.64=11860992m=11860.992km=449px
Half of Grand Line width: 166px=4385.13km

Half of Grand Line width: 30px=4385.13km
Blue planet Diameter: 505px=73816.36km
Corrected planet diameter = sqrt(1-(tan(35)(505/773))^2/((tan(35)(505/773))^2+1))*73816.36 = 67126.43km
 
One of the main supporting arguments for Blue being much, much bigger than Earth is distance to horizon. Results based on it are actually very close to current used size. In absense of other reliable methods for calculating size, this calc could probably cement status of Blue as being Sun-sized.


Could, if not for atmospheric refraction. Calculator that was used in calc calculates true horizon, not apparent horizon(which is influenced by this refraction).
So, what problems does it pose to this method?
1. Density at surface is greater than density at higher altitudes, which results in greater apparent horizon (usually by 8% for Earth). Correcting for this is pretty easy, it would just lower calced radius of Blue to around 690,000 km. Doesn't sounds too bad, isn't?
2. Noticed now I accentuated on "usually". Temperature and density gradients can vary considerably by time and location, which can result in apparent horizon being much further away(potentially up to 750 km under best conditions).
3. Noticed how I accentuated on "Earth". Exact value of atmospheric refraction depends on density profile of atmosphere (and associated with it temperature and pressure profile). We can't possibly know exact data for Blue, but we can speculate. We can be fairly sure that atmosphere of Blue is much bigger and thicker than Earth. And apparently, if we use current maps that are used for calculating size of the planet, atmosphere of the Blue can support airdrops at 114,000 km height. Indicating that Armstrong limit(which is defined by pressure) is massively higher than Earth one(19 km). What it does means?:
Thicker atmosphere means higher atmospheric refraction, and bigger apparent horizon. For example, Venus has true horizon of 3.5 km and would have been in pocession of apparent horizon much greater than 16 km(this link leads to pdf file), if not for funny atmospheric and temperature phenomena. But if we could see such a long horizon, and used it as method for calculating radius for Venus, we would get 128,000 km (compared to actual 6051 km for Venus), nuff said.

In short, this method would face two most important problems:
1. Size of apparent horizon(only thing we can see and directly measure) is greatly dependent on specific atmospheric phenomena, local temperature and density gradients, which can vary dramatically by time and location.
2. Using this method would greatly inflate size of planets with thicker atmosphere.

In conclusion, we shouldn't try to calculate Blue size via horizon measurements
Your argument based on Atmospheric refraction, from the example you're giving, is wrong.

Atmospheric refraction comes in 2 types.
  1. Celestial Refraction, where astronomical objects appear higher than they truly are.
  2. Terrestrial Refraction, where terrestrial objects appear higher than they truly are.
What you're accounting for doesn't solidly fit any of them, because we're not looking at how far a random object is, but the entire coast. But closest it'd be would be the terrestrial refraction.

You didn't account for this though
"Although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they actually are"
Which is damning when you realize that Alabasta's desert is 50ºC.

This is because based on the explanation of air density, cold air is far more dense than warm air. So your argument would be fine if we were regarding a colder environment, but unfortunately we are not, there is no refraction due to a dense atmosphere when the air is half as hot as the boiling point of water.

In fact, your second link is extremely damning.
It says this
"Due to atmospheric refraction the distance to the visible horizon is further than the distance based on a simple geometric calculation. If the ground (or water) surface is colder than the air above it, a cold, dense layer of air forms close to the surface, causing light to be refracted downward as it travels, and therefore, to some extent, to go around the curvature of the Earth."
So this is talking about landmarks regarding regular temperatures and such.

But then you see this
"The reverse happens if the ground is hotter than the air above it, as often happens in deserts, producing mirages."
And guess where the horizon shot is from?
The ground.
Which is damning when you realize that Alabasta's ground is so hot that you can grill food on the rocks.

So no. In fact, this would increase the true horizon distance.
 
So what would be an alternative method to accurately calculate the planet size?
You can do it like this using the timeframe of Luffy flying from Sabaody to Amazon Lily or you can use Alabasta's size directly to get the minimum width needed for the Grand Line so that Alabasta can be located within it or you can also find the height of the area we're seeing here and get another minimum size of the planet since the maximum part of the planet we can see at one time is 50% of its circumference.
 
Your argument based on Atmospheric refraction, from the example you're giving, is wrong.

Atmospheric refraction comes in 2 types.
  1. Celestial Refraction, where astronomical objects appear higher than they truly are.
  2. Terrestrial Refraction, where terrestrial objects appear higher than they truly are.
What you're accounting for doesn't solidly fit any of them, because we're not looking at how far a random object is, but the entire coast. But closest it'd be would be the terrestrial refraction.

You didn't account for this though
"Although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they actually are"
Which is damning when you realize that Alabasta's desert is 50ºC.

This is because based on the explanation of air density, cold air is far more dense than warm air. So your argument would be fine if we were regarding a colder environment, but unfortunately we are not, there is no refraction due to a dense atmosphere when the air is half as hot as the boiling point of water.

In fact, your second link is extremely damning.
It says this
"Due to atmospheric refraction the distance to the visible horizon is further than the distance based on a simple geometric calculation. If the ground (or water) surface is colder than the air above it, a cold, dense layer of air forms close to the surface, causing light to be refracted downward as it travels, and therefore, to some extent, to go around the curvature of the Earth."
So this is talking about landmarks regarding regular temperatures and such.

But then you see this
"The reverse happens if the ground is hotter than the air above it, as often happens in deserts, producing mirages."
And guess where the horizon shot is from?
The ground.
Which is damning when you realize that Alabasta's ground is so hot that you can grill food on the rocks.

So no. In fact, this would increase the true horizon distance.
Actually this actually helps to support his points
One of the main supporting arguments for Blue being much, much bigger than Earth is distance to horizon. Results based on it are actually very close to current used size. In absense of other reliable methods for calculating size, this calc could probably cement status of Blue as being Sun-sized.


Could, if not for atmospheric refraction. Calculator that was used in calc calculates true horizon, not apparent horizon(which is influenced by this refraction).
So, what problems does it pose to this method?
1. Density at surface is greater than density at higher altitudes, which results in greater apparent horizon (usually by 8% for Earth). Correcting for this is pretty easy, it would just lower calced radius of Blue to around 690,000 km. Doesn't sounds too bad, isn't?
2. Noticed now I accentuated on "usually". Temperature and density gradients can vary considerably by time and location, which can result in apparent horizon being much further away(potentially up to 750 km under best conditions).
3. Noticed how I accentuated on "Earth". Exact value of atmospheric refraction depends on density profile of atmosphere (and associated with it temperature and pressure profile). We can't possibly know exact data for Blue, but we can speculate. We can be fairly sure that atmosphere of Blue is much bigger and thicker than Earth. And apparently, if we use current maps that are used for calculating size of the planet, atmosphere of the Blue can support airdrops at 114,000 km height. Indicating that Armstrong limit(which is defined by pressure) is massively higher than Earth one(19 km). What it does means?:
Thicker atmosphere means higher atmospheric refraction, and bigger apparent horizon. For example, Venus has true horizon of 3.5 km and would have been in pocession of apparent horizon much greater than 16 km(this link leads to pdf file), if not for funny atmospheric and temperature phenomena. But if we could see such a long horizon, and used it as method for calculating radius for Venus, we would get 128,000 km (compared to actual 6051 km for Venus), nuff said.

In short, this method would face two most important problems:
1. Size of apparent horizon(only thing we can see and directly measure) is greatly dependent on specific atmospheric phenomena, local temperature and density gradients, which can vary dramatically by time and location.
2. Using this method would greatly inflate size of planets with thicker atmosphere.

In conclusion, we shouldn't try to calculate Blue size via horizon measurements

In fact, I actually agree with his assessment when it comes to doing a parameter on a specific part of the planet/land size and all.


Again, your points doesn’t debunk his points, it only helps reinforces his points if anything.
 
Also, I will also single out what he has said here too.

”2. Noticed now I accentuated on "usually". Temperature and density gradients can vary considerably by time and location, which can result in apparent horizon being much further away(potentially up to 750 km under best conditions).

He directly acknowledge the atmospheric conditions can varied considerably especially for a exoplanet like the fictional One Piece’s planet
 
Yeah I completely agree with this I already pointed out some other issues with the horizon calcs here, mainly this one:
We are not looking at mountains.

The coast is visible. The mountains are equally visible, but the coast, the bottom levels of it elevating above sea level, are visible.
Actually this actually helps to support his points


In fact, I actually agree with his assessment when it comes to doing a parameter on a specific part of the planet/land size and all.


Again, your points doesn’t debunk his points, it only helps reinforces his points if anything.
His entire point is based on the fact that atmospheric refraction regarding the air being hotter than the surface means that light refracts downwards allowing you to see things that are further back and lower past the horizon.

My entire point is that it's the opposite due to the temperature of the environment.

None of it helps support his point at all
 
We are not looking at mountains.

The coast is visible. The mountains are equally visible, but the coast, the bottom levels of it elevating above sea level, are visible.

His entire point is based on the fact that atmospheric refraction regarding the air being hotter than the surface means that light refracts downwards allowing you to see things that are further back and lower past the horizon.

My entire point is that it's the opposite due to the temperature of the environment.

None of it helps support his point at all
Your scan that say the temperature for the desert can range up to 50 Celsius during the day.









"Although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they actually are"

Which means the opposite can been true as well as mentioned above.

Not to mention he listed a source for Venus which ranges from 86 to 158 Fahrenheit (30 to 70 Celsius) on the surface and Venus is a completely hostile hot planet to human life and all.



Which is a example of someone inflating their calculations for the horizon of Venus and this will also applies here.


Like there is nothing stopping the opposite being true that the horizon is apparently further than what
It actually is here.

Edit: Another source here.



Speaking of which, I will list the another source for @Qurbonboev anyway.
 
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Your scan that say the temperature for the desert can range up to 50 Celsius during the day.









"Although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they actually are"

Which means the opposite can been true as well as mentioned above.

Dude.
If he is saying
"Light refracts downward, causing lower objects to appear higher, which makes the horizon distance seem closer out, so it needs to be lowered to be more accurate"
And I'm saying
"The opposite effect is the case"

Then it means that I'm saying
"Light refracts upwards, causing higher objects to appear lower, which makes the horizon distance seem farther out, so it needs to be increased to be more accurate"

The entire point is that the opposite of what he's saying is the case.
The coast is being made to look like it is farther out than it really is, aka the coast is being made to appear like it's further away, and in fact it's not the case, it is closer, making the true horizon distance larger, making the planet larger.
Not to mention he listed a source for Venus which ranges from 86 to 158 Fahrenheit (30 to 70 Celsius) on the surface and is also a hot spot for the planet.



Which is a example of someone inflating their calculations for the horizon of Venus and this will also applies here.


Like there is nothing stopping the opposite being true that the horizon is apparently further than what
It actually is here.
Venus has an thick C02 atmosphere 90x the pressure of earth based on the runaway greenhouse gas effect from volcanic gassing and a lack of tectonic plates which hold carbon into the crust of the planet.
For this to be valid, it would need to have the same mechanics as earth, not something 90x the pressure based on a completely screwed planet.
 
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