Magnitude of Visible Earth’s Curvature in a Photograph

The magnitude of the curvature that appears in a photograph of Earth’s curvature depends on several factors:

  1. The observer’s altitude.
  2. The camera’s field of view or focal length.
  3. The distortion characteristics of the camera lens.

Flat-Earthers like to dismiss a photo of Earth’s curvature by comparing it to another photo showing a different amount of curvature. In reality, to compare the visible curvature, we need to ensure all the images were taken from the same altitude, same field of view, and account for the lens’ distortion.

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Modus Operandi of Flat-Earthers to Obtain “Images of Flat Earth” to Deceive Us

If Earth is a sphere, how is it possible for flat-Earthers to show us “images of flat Earth” taken from high-altitude balloons? These are the modus operandi of unscrupulous flat-Earthers to obtain such images in an attempt to deceive us.

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Why Fisheye Lenses Are Used

Cameras with a fisheye lens are used in the ISS, high-altitude balloons, rocket bodies, and other purposes. The reason is that fisheye lenses have several advantages over rectilinear lenses.

Flat-Earthers claim there is an evil intention behind the usage of fisheye lenses. In reality, the use of fisheye lenses is not unreasonable. If it is desired to have a rectilinear image output, then it is not hard to defish fisheye images to rectilinear ones..

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Felix Baumgartner and Red Bull Stratos

Red Bull Stratos was a high-altitude diving project involving Felix Baumgartner. In 2012, Felix Baumgartner flew 39 km (24 mi) into the stratosphere in a helium balloon before free falling in a pressure suit and then parachuting to Earth. Flat-Earthers invented various excuses to dismiss the resulting footage from the project.

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Fisheye Videos

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In images taken using a fisheye lens, a straight line will remain straight if it crosses the center of the image. We can use this attribute to determine if a line is straight in reality.

In any fisheye videos taken from a high altitude, there should be plenty of moments where the horizon crosses the center of the image, and we can use those to determine that the horizon line is curved in the real world.

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Pictures of Earth’s Surface from the UAE Astronaut Hazza Al-Mansouri

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The United Arab Emirates astronaut, Hazza Al Mansouri, took pictures of Earth’s features like the Nile and the Persian Gulf during his visit to the ISS. Flat-Earthers claim the pictures are fake because the various objects appear very large compared to the size of the Earth in the picture. The reason is that they do not understand that the ISS is only about 400 km above Earth’s surface, and only a very small amount of the Earth’s surface is visible from the ISS

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Excessively Defishing Fisheye Images to Flatten the Curved Horizon

Defishing is a process for removing barrel distortions in fisheye images. It takes fisheye images, and convert them to normal, rectilinear images that preserve straight lines. Different fisheye lenses can have a different amount of distortions, and thus, require a different defishing strength.

Some flat-Earthers would deliberately use stronger defishing parameters than necessary for the lens being used. Their intention is not to remove the barrel distortion in the resulting images, but also to introduce pincushion distortions to the images. Pincushion distortion is the reverse of barrel distortion. It would curve a straight line to the other direction from what would be produced by the barrel distortion in fisheye lenses. At a specific position in the scene, it would make the curved horizon to appear flat.

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The Space Protest by ASAN That Was Hijacked by Flat-Earthers for Provocation

In 2017, the group who name themselves ‘ASAN’ staged a protest to Donald Trump by sending a high-altitude balloon carrying a camera and a crude message, which was quoted from a statement by Edgar Mitchell, an astronaut from the Apollo 14 mission.

Some unscrupulous flat-Earthers hijacked the protest and turned it as if ASAN did it to prove Earth’s curvature and to insult them. These flat-Earthers pointed out that ASAN somehow “forgot” to conceal the fact that a fisheye lens was used. In reality, it is never the intention of ASAN to prove Earth’s curvature, nor to throw insults to flat-Earthers.

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The Curvature Fitting Game

The amount of curvature that appears in a photograph of a sphere depends on 1. The radius of the sphere, 2. Camera distance from the sphere, 3. Field of view of the camera, and 4. The distortion characteristic of the camera being used.

The ‘curvature fitting game’ has been flat-Earthers’ favorite pastime. They would try to fit a photograph of Earth’s curvature with another. If they find the result is not proportionally correct, they will make fun of it. They are wrong. Two different photos of a sphere can be taken differently and would show a different curve, even if the object being photographed is the same object.

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Fisheye Lenses Can Make Curved Lines Appear Flat

A fisheye lens distorts images. It results in images having barrel distortions. In a fisheye lens, a straight line can appear curved. But some flat-Earthers don’t realize that the opposite is also true, a fisheye lens can easily make a curved line look straight.

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Curvature of the Horizon in High-Altitude Balloon Footage

High-altitude balloon footage is often abused by flat-Earthers to show us that the Earth is flat when seen from a high altitude.

We analyzed more than two dozens of footage taken from high-altitude balloons on YouTube, and we can easily conclude the curvature is there and usually easy to spot, including in the cases where flat-Earthers use the video as ‘proof’ of a flat Earth.

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The Little Piggy Balloon Footage Proves Earth is a Sphere, not Flat

Little Piggy is the nickname of a helium balloon launched by IndianaCaver. It reached the altitude of almost 37 km before it finally ruptured and fell to the Earth. Before that, it took several hours of video, and IndianaCaver made these video available on YouTube.

Then, some flat-Earthers cherry-picked bits of the video where the horizon looked flat and presented it as ‘proof’ of flat-Earth. These are widely circulated in various memes and forms, even years after the originals were published.

But, can we use these videos as ‘proof’ of flat-Earth?

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Fisheye Lenses and Earth Curvature

A good majority of pictures of Earth taken from space are being dismissed by flat-earthers merely because they are made using fish-eye lenses. They believe any curvature of Earth shown in those pictures is the result of the fisheye effect, and thus, cannot be used as evidence of Earth’s curvature. They even take a step further and assume a fish-eye lens is deliberately used to take every picture of the Earth taken from a high altitude so that they would have a curvature in it.

These claims are, of course, ungrounded. In some cases, we can conclude the curvature is there, even when a fish-eye lens is being used. We can use this useful property of any photographic lens:

A straight line will appear straight as long as it crosses the center point of the image.

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