Tag: angular-size

Moonlight and Inverse Square Law

Light intensity is inversely proportional to the square of its distance. The light we receive from the Moon increases 50000× if we land there. But so does the Moon’s apparent size, spreading the increase in intensity over a larger area.

Flat-Earthers incorrectly claim the inverse square law means the Moon would be too bright if we land there, and they use the argument to “prove” it is impossible to go to the Moon. In reality, the inverse square law applies to a point source. For a large light source, its change in apparent size must also be considered.

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Different Reasons Why a Distant Object is Not Visible

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Different reasons can cause a distant object to be not visible:

  1. The angular resolution limit of the observer.
  2. The visibility limit imposed by the atmosphere.
  3. 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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Point Source

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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Forced Perspective

The Sun & the Moon are about the same apparent size, but they are not the same size. They only appear the same size because the Sun is 400× larger and also 400× farther away. To illustrate this, we can use forced perspective in photos.

Flat-Earthers insist that the Sun & Moon are the exact sizes just because they appear the same size. By the same ‘logic,’ we can say the girl above is the same size as the Eiffel Tower.

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ISS Size Compared to an Airplane in a Photograph

Flat-Earthers compared the apparent size of the ISS and an airplane that appeared in photographs and then incorrectly concluded that the ISS could not be 410 km above us. Their mistake was equating altitude with distance and failing to account for both the ISS’ and the airplane’s downrange distance.

If an airplane is at an altitude of 12 km, it does not mean its distance from an observer is also 12 km. Its altitude and distance are equal only if the airplane is directly above the observer. If the plane is not directly above, then its distance is greater than its altitude.

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Camera “Maximum Range”

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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Apparent Size of the Sun & the Moon

The Sun and the Moon appear about the same size in the sky, but they are not perfectly the same size, and their sizes are not constant because their orbits are not perfectly circular.

Flat-Earthers claim it is too much of a coincidence that the Sun is perfectly 400× larger than the Moon and perfectly 400× farther, making them appear perfectly the same size. In reality, the Sun and the Moon are not perfectly the same size in the sky.

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Zooming at the Moon

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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Earth Seen From the Moon vs the Moon Seen From Earth

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Earth seen from the Moon will appear 3.7× larger than the Moon seen from Earth. However, if a photograph of Earth is compared to that of the Moon, the sizes of both objects also depend on the field of view of the cameras that were used to capture them.

Flat-Earthers discovered the size of the Earth in a photograph is not 3.7× the Moon in another picture. They used the fact as “evidence” of wrongdoing. In reality, the two photos were not taken with the same field of view, and cannot be compared directly.

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Angular Resolution

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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The Apparent Size of the Moon

The apparent size of the Moon remains constant in a single day. This can only happen if the Moon is practically at the same distance all day.

In the flat-Earth model, the Moon is thought to be moving in a circle above the flat Earth. Such a notion should cause the Moon apparent size to vary in a day. However, in reality, the Moon appears in the same size all day, and it proves that the flat-Earth model does not represent reality and that the Moon is much farther.

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The Apparent Size of the Sun

The apparent size of the Sun is practically constant throughout the day. This can only happen if the Sun is practically at the same distance all day.

In the flat-Earth model, the Sun is close to the surface at the distance of about 5000 km (3500 miles). The Sun is supposed to be moving in a circle, and it completes the circling motion once in a day. This fact should cause the Sun’s apparent size to change during the day. But it does not happen. The Sun’s constant apparent size is evidence that the flat-Earth model is wrong, and that the Sun is very far away.

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