Different reasons can cause a distant object to be not visible:
- The angular resolution limit of the observer.
- The visibility limit imposed by the atmosphere.
- Obstruction by another object, including by Earth’s curvature.
Flat-Earthers incorrectly presumed “a distant ship is not visible only because of Earth’s curvature.” Incorrectly concluded if we can bring the ship back into view, the curve must not exist. In reality, Earth’s curvature is not the only thing that can cause a distant ship to be not visible; other reasons can also cause it.
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A point source is a source or reflection of light with a smaller angular size than the angular resolution of the observer. It is visible as a bright dot if bright enough against a dark background but not resolvable, or no detail is discernible.
Flat-Earthers claim the ISS should not be visible like a distant plane is not visible. In reality, aircraft lights can be seen from 60 km in a dark sky but are not resolvable. We can see them because they are point sources on a dark background.
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There is no such thing as the “maximum range” in the specification of any camera. Just because a camera cannot see something at a certain distance, it does not mean it must not be able to see another thing farther away.
Flat-Earthers claim that the Moon cannot be 384400 km away because a camera cannot see another thing much closer than that. In reality, an object’s distance is not the only thing that determines if a camera can see it, but the object’s size also matters.
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At the longest zoom, the Nikon P1000 has a field of view of 0.2°, which is equivalent to 1342 km at the Moon’s distance.
Flat-Earthers zoomed their Nikon P1000 at the Moon and claimed that they could not find flags and landers from the Apollo missions. In reality, the smallest objects on the lunar surface they can observe using their cameras are large city-sized objects.
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Angular resolution is the minimum separation between distinguishable features in an image. Objects smaller than the angular resolution are indiscernible in the picture. The theoretical maximum angular resolution is determined by the diameter of the aperture of the optical instrument.
Flat-Earthers like to demand images of the lunar landers taken with a telescope as proof that the Apollo Moon landings did occur. In reality, no optical telescope on Earth is large enough to resolve the landers.
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Visibility range is a measure of the distance at which an object can be clearly discerned. Angular resolution is the ability of an optical system to resolve detail in the object.
Unlike the claim from flat-Earthers, there is no such thing as the “maximum range” of a camera. A germ on our hand is well within the visibility range, yet a regular camera lacks sufficient angular resolution to see it. On the other hand, an airplane is much farther away, but it has a larger angular size and can be seen by the camera.
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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.
Continue reading “Geometry of Perspective”