Geometry of Perspective

Perspective is a relationship between the size of an object, its distance, and its apparent/angular size. The angular size is larger if the object is closer or larger.

Often, flat-Earthers would claim that we cannot see a distant object is not the result of Earth’s curvature, but because of perspective. In a way, it is correct to say that perspective might result in an object having angular size too small to be seen by our eyes. However, perspective alone cannot ‘hide’ a portion of an object, while revealing the rest of it.

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Curvature Analysis: (Allegedly) Myllom West Platform from Cleveleys, Fylde Coast

General Information

  • Claimed by: P1000 Coolpix (YouTube)
  • Object (claimed):
    • Name: Millom West Platform
    • Distance: 34.5 miles (55.5 km)
    • Height: unknown
  • Observer:
    • Location: Cleveleys, Fylde Coast, Lancashire.
    • Elevation: 24 ft (7.3 m)

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The Lack of Motion Blur in Earth Photos

The surface of the Earth close to the equator is moving at the speed of about 1670 km/h due to Earth’s rotation. To take a sharp picture of the Earth with the resolution of 10000×10000 from a stationary position in space, it would require the shutter speed faster than 2.7 seconds. It is not difficult at all to take a sharp picture of the entire Earth without perceivable motion blur.

Flat-Earthers claim that it should be impossible to take a sharp picture of the Earth from space due to the speed of Earth’s rotation. To them, the fact that a photographer cannot take a sharp photo of a speeding race car from the sidelines (they actually can) tells us it should be impossible to take a sharp picture of the Earth moving at 10× the speed.

They are wrong. Motion blur is caused by the angular speed of the object relative to the camera, not from its absolute speed. The vast distance required to take a photo of the Earth results in a very low angular speed, making it not difficult at all to take sharp images of the Earth.

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How to “Prove” a Basketball (or any Spherical Object) is Flat

If we were to magnify the surface of any spherical object with large enough magnification, then at some point, it would appear flat. This can be easily demonstrated using a macro lens as the Redditor ‘Useless-Pickles’ did. He magnified the surface of a basketball using an extreme macro lens as a philosophical demonstration.

This shows that the surface of a spherical object can easily look flat if the object is large enough, or the observer is small enough.  And the basis of all flat-Earthers’ belief that the horizon appears flat is insufficient to determine the shape of the Earth. By applying the same “logic” as these flat-Earthers, we can actually “prove” a basketball is flat, which, as we all know, is clearly wrong.

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Lens Flare, Not a Mysterious Celestial Body

A photograph of an object does not necessarily look the same as the real object. There are various optical imperfections, which are impossible to avoid by both the designer of the optical system and the photographer taking the picture. One of those imperfections causes lens flare.

Some flat-Earthers noticed the existence of a ‘mysterious celestial body’ next to a photograph of the Sun or the Moon. They would use such sightings to ‘explain’ various celestial phenomena which cannot be readily explained in the flat Earth model, like eclipses. They are wrong. The ‘mysterious celestial body’ was merely a lens flare.

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Suez Canal

The Suez Canal is a waterway connecting the Mediterranean Sea to the Red Sea. The level of water on both seas is practically the same, and the Suez Canal contains no locks system.

Flat-Earthers are claiming that the Suez Canal was constructed without accounting for curvature. They said if the Earth were spherical, then the middle of the canal should have been 1666 ft deep. This is merely a misconception. The surface of the water is equipotential. It has roughly the same distance to the Earth’s center of gravity. It is not necessary to dig 1666 ft in the middle of the Suez Canal. The engineers only need to ensure the base of the canal is below sea level for sea water to flow.

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Circular Reasoning

Circular reasoning is a logical fallacy in which the proposition is supported by the premises, which is supported by the proposition, creating a circle in reasoning where no useful information is being shared.

Flat-Earthers often commit the fallacy of circular reasoning to defend the notion that the Earth is flat. Such reasoning is never useful, and cannot be regarded as evidence of anything, despite what they are claiming.

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Curvature Analysis: Oahu from Kauai, Hawaii

General Information

  • Claimed by: Terry Robinson (YouTube)
  • Object:
    • Name: Oahu
    • Distance: 108 miles (174 km)
    • Highest elevation: 4003 ft (1220 m)
  • Observer:
    • Location: Wailua River Overlook, Kauai, Hawaii
    • Elevation: 200 ft (61 m)

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Curvature Analysis: Toronto from Niagara-on-the-Lake

General Information

  • Claimed by: GARY IS RIGHT! (YouTube)
  • Object 1:
    • Name: CN Tower
    • Height: 1815 ft (553 m)
    • Distance: 30 miles (48.3 km)
  • Object 2:
    • Name: First Canadian Place
    • Height: 951 ft (290 m) (top floor)
    • Distance: 30 miles (48.3 km)
  • Observer:
    • Location: Niagara-on-the-Lake pier
    • Elevation: unspecified, assumed to be 2 m

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Curvature Analysis: Anacapa Islands from Miramar Beach

General Information

  • Claimed by: bmlsb69
  • Object 1:
    • Name: West Anacapa Island
    • Height: 930 ft (283 m)
    • Distance: 31.63 miles (51 km)
  • Object 2:
    • Name: Middle Anacapa Island
    • Height: 325 ft (99 m)
    • Distance: 31.63 miles (51 km)
  • Object 3:
    • Name: East Anacapa Island
    • Height: 250 ft (76 m)
    • Distance: 31.63 miles (51 km)
  • Observer
    • Location: Miramar Beach, CA, USA
    • Height: 3 ft (1 m)

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Curvature Analysis: Platform Hillhouse & Platform Habitat from Miramar Beach

General information

  • Claimed by: Taboo Conspiracy & bmlsb69
  • Object 1:
    • Name: Platform Hillhouse
    • Distance: 6.2 miles / 9.98 km
    • Height: 98 ft / 29.87 m
  • Object 2:
    • Name: Platform Habitat
    • Distance: 9.41 miles / 15.14 km
    • Height: 90 ft / 27.4 m
  • Observer:
    • Location: Miramar Beach, CA, USA
    • Elevation: 1 ft & 35 ft

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Lunar Craters

At any time, the Sun illuminates one half of the Moon and the other half dark. The phase of the Moon is the shape of the sunlit portion of the Moon as viewed by observers on Earth.

The phase of the Moon can never be adequately explained using the flat Earth model. To deal with this inconsistency in their theory, some perpetrators of flat Earth invented an ‘explanation’ that the phase of the Moon is not caused by sunlight. They are wrong. We can observe the Moon very carefully using telescopes of high-zoom cameras, and it will be evident how the lunar craters are lit. And this can only happen if the Moon is sunlit.

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Circumpolar and Non-Circumpolar Stars

A circumpolar star is a star, as viewed from a given latitude on Earth, that never sets below the horizon due to its apparent proximity to one of the celestial poles. Circumpolar stars stay up there in the sky, even during the day.

Flat-Earthers claim the Earth is stationary because the same stars are always visible in the sky. They are wrong. Only circumpolar stars are always in the sky. There are others that are not circumpolar. Some are only visible during certain times in a year.

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Sun Path

In the Northern hemisphere, the Sun appears to move to the right. In the Southern hemisphere, it appears to move to the left. During sunrise and sunset, the path of the Sun forms an angle that roughly corresponds to the latitude of the observer. This phenomenon occurs because observers on the different locations on Earth’s surface is not standing on the same plane.

The path of the Sun observed from many different locations on Earth’s surface is evidence of spherical Earth. This observation cannot possibly occur on a flat Earth.

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Football Field and ‘Flat-Earth Convergence Experiments’

A properly designed football field does not lie perfectly flat. Its middle portion is slightly raised to promote runoff of excess water. Without it, the field can become muddy & uncomfortable.

Some flat-Earthers conducted the perspective convergence ‘experiment’. They put a camera on the surface of a football field, and record a person walking away across the field. The person started to disappear from his feet first. Because they felt the football field is flat, they took the wrong conclusion that the person disappeared due to ‘perspective’. They were wrong. The field is, in fact, not perfectly flat. If it is perfectly flat, the person would appear fully at the end of the field.

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Earth’s Curvature Calculation

The amount of obstruction of a distant object that is caused by Earth’s curvature depends on:

  1. The distance of the object.
  2. The height of the observer.
  3. The height of the object.
  4. The magnitude of atmospheric refraction.

Flat-Earthers like to use the visibility of a distant object to prove Earth’s curvature does not exist. Very often, they failed to account for observer’s height and atmospheric refraction, or make other mistakes, like unit conversions errors, distance calculation errors, etc. Once all are considered for, and mistakes are fixed, everything will be consistent with spherical Earth.

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Real Photos of the Earth

The first photo showing the entire Earth was taken in 1966 from the spacecraft Lunar Orbiter 1. Since then, there are too many photos showing the whole earth taken from various missions to space.

The advent of computers in the 80s introduced a new technique of generating such pictures. A satellite can be used to take many photos of the Earth from a low orbit, and computers can be used to assemble those pictures into a single photo of the Earth.

Flat-Earthers ‘discovered’ such technique, then they concluded that all pictures of the Earth taken from space are all composites, the results of manipulation or assembled by computers. They are wrong. Just because there were pictures created using such technique, it doesn’t mean there is no genuine picture showing the entire Earth, not composites, not stitched, and were taken from a single shot.

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Orbital Station-Keeping

A satellite in a high enough orbit can remain operational for a very long time because in space there is practically no air resistance. This is a situation that never occurs in our everyday life. A car requires a constant consumption of fuel to keep running, but a satellite can remain in motion without consuming any fuel because there’s practically no force stopping it.

Flat-Earthers claim that satellites cannot stay up there for such a very long time because ‘we never refuel any satellites.’ They are wrong. In space, there is practically no drag, and satellites only need to consume fuel to adjust their speed periodically.

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Infrared Vision

When we are unable to see a distant object, then it is due to one of these reasons:

  • Our eyes lack the sufficient angular resolution to recognize the object.
  • Atmospheric condition limits visibility.
  • The object is far enough and obscured by Earth’s curvature.

Some flat-Earthers like to show that a previously unseen distant object can be brought into view using infrared vision. They would take that as ‘evidence’ of the non-existence of Earth’s curvature. They are wrong. Infrared vision can reveal hidden objects caused by visibility limitations, but not ones obscured by Earth’s curvature.

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Newton’s Law of Universal Gravitation

Gravity is a natural phenomenon by which all things with mass or energy are brought toward each other. In 1687, Isaac Newton explained the phenomenon as a force, which was formulated in Newton’s law of universal gravitation.

Flat-Earthers insist that gravity does not exist. But this is only a result of a mere ignorance on how gravity works. Everything in our lives is consistent with what is explained in Newton’s law of universal gravitation.

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