Flight Dynamics: the Assumption of Flat & Non-Rotating Earth for Simplification

In making mathematical models, physicists often remove real-world details that have little influence over the final results for simplifications. In flight-dynamics, it is often perfectly adequate to assume Earth is flat & non-rotating, even if the final aircraft will be flying over spherical & rotating Earth.

Flat-Earthers claimed to have exposed ‘a secret document’ from NASA, saying that Earth is flat & non-rotating. In reality, the document is simply a derivation of a flight dynamics problem, assuming flat and non-rotating Earth, which is a common assumption made to simplify flight models. It does not imply the Earth is flat and non-rotating.

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Selenelion: The Phenomenon Where Both the Sun and Moon Are Visible During a Total Lunar Eclipse

A selenelion occurs during a lunar eclipse when the sun and moon are observed above the horizon. Atmospheric refraction bends light rays and lifts the image of the sun, and the moon typically up to 0.6°, so both can appear above the horizon.

Flat-Earthers assert that a selenelion should not be possible if Earth is a sphere due to the fact during a lunar eclipse, the sun and moon are 180° apart. In reality, a selenelion is possible because Earth’s atmosphere refracts light.

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Oblate Spheroid Shape of the Earth

The Earth is an oblate spheroid. Its diameter is longer across the equator than between the poles. The difference is tiny, only about 0.3%. It is not possible to notice the oblateness from photographs taken from space without careful measurement.

Flat-Earthers claim that in photos taken from space, Earth appears as a perfect sphere, unlike what science tells us, and they use it to discredit science. In reality, it is possible to notice the oblate shape with careful measurement of the images.

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Simulation and Observation

To determine if an observation is consistent with the spherical Earth model, we can create simulations to understand the expected result, and then see if they match the actual observation.

Flat-Earthers like to reject the results of simulation as being unreal, not real-world observation. In reality, the simulations are presented not to dispute their observation, but to demonstrate that their observation is consistent with expectation if Earth is a sphere.

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Curvature Dilemma

A ship disappearing from the bottom first is an effect of Earth’s curvature. It is not a direct observation of the curve itself. We can only directly see the curve from a high altitude, not from near the surface.

Flat-Earthers present this reality as if it is a dilemma: 1. Earth is too big for us to see the curvature, but 2. We can see ships go over the curvature. It is a false dilemma. Ships disappearing from the bottom first is an effect of Earth’s curvature. Such an observation is different from directly witnessing the curve itself.

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Subjectivist or Relativist Fallacy

The subjectivist fallacy occurs when someone claims that something is true for some people but not for someone else, when, in fact, it is true for everyone, as demonstrated by empirical evidence.

The shape of Earth is not a matter of belief or preference, but an objective truth from observations that applies to everyone. It is impossible Earth is both spherical and flat at the same time, depending on what we prefer or believe.

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Video Glitches

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In digital video, a missing or corrupted signal may result in glitches in the video. It can be caused by things like signal interference, scratches on Bluray discs, bad weather with satellite TV, damaged cables, Internet link congestion, etc.

Flat-Earthers like to scrutinize videos taken from space. If they find the glitches, they will swiftly use them as “evidence” of manipulation. In reality, such glitches in the videos are not unusual. We can easily encounter them on other occasions.

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Observation of Chicago From Michigan

Chicago’s skyline is visible on clear weather across Lake Michigan from Michigan as long as the observer is on high ground, or if atmospheric refraction is strong enough. This observation is consistent with the expectations if Earth is a sphere.

Flat-Earthers claim that the visibility of Chicago from Michigan is not possible if Earth is a sphere. In reality, they failed to account for the height of the observer or atmospheric refraction and ignored the fact that only the upper parts of the buildings are visible.

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Helical Motion of Planets

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The Solar System is in motion around the Milky Way galaxy, while the planets in the Solar System are in orbiting motion around the sun. As a result, from an observer outside the Solar System, planets will appear to move in a helical motion. Someone created an animation of this helical motion; it went viral and had a lot of media attention.

Flat-Earthers noticed the animation and use it to reinforce their arguments. They claim if the animation is correct, then stars should appear moving & star trails should be impossible. In reality, the animation does not show us the vast distances to the stars.

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Camera Entrance Pupil Size and the Zoom Factor

The entrance pupil is the opening in front of a camera that allows light to enter. If it is partially obscured, light can still come through the unobscured part, and the camera can still see the object.

In one of those “experiments,” flat-Earthers placed an obstacle in front of a camera, very close to the lens, so that an object is partially visible. At the widest angle setting, the person appears partially visible. But it turned out that zooming in will fully reveal the person. Flat-Earthers claim it is how objects can vanish behind the horizon if Earth is flat and how they can reappear by zooming in. In reality, zooming enlarges the camera’s entrance pupil, letting the camera to see over the obstacle.

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Human Senses

Human senses have limitations and cannot detect beyond a certain threshold of external stimuli. However, we humans possess intelligence that enables us to create instruments and allow us to perceive beyond the limitations of our senses.

Flat-Earthers argue if our senses cannot perceive a thing, then it does not exist. In reality, the instruments we made enable us to detect many things that our senses cannot.

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Eötvös Effect: Direct Evidence Earth is a Rotating Sphere

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Eötvös effect is the change in perceived gravitational acceleration when moving eastward vs. westward. An object will weigh slightly more when moving westward than when it is stationary or moving eastward.

The slight difference in weight due to the Eötvös effect can be measured in an experiment on a flight. The Eötvös effect is direct evidence that the Earth is a rotating sphere.

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Visibility Range vs Angular Resolution

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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Conditions in School vs Science & Professional World

In an exam in school, students are expected to solve problems with limited references and tools to assess their knowledge. On the other hand, in the science & professional world, there are no such limitations. We are free to use any resources available to us to solve the problems at hand.

Some flat-Earthers become annoyed every time we use some things like computer simulations and other tools to solve problems, especially when they help us prove spherical Earth. They would proclaim because they feel they can solve their own specific problem with pen and paper, they think they are more right than these “cheaters” with computers and other technology. In reality, the tools being used do not decide which one is more right. These flat-Earthers are merely unfamiliar with real-world cases beyond school.

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Apparent Motion

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Apparent motion is the appearance that celestial objects move due to the motion of Earth. If all the objects that appear in the sky are moving similarly, then it is far more likely that the movement is only apparent and caused by the motion of the observer.

Flat-Earthers claim that the motion of celestial objects “proves” that Earth is stationary, and the celestial objects are moving. By the same “reasoning,” we can conclude that the train we are in is stationary, it is just all the objects outside, as luck would have it, are moving in a very similar fashion.

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Apollo Astronauts and the Demand to Swear on the Bible

In the early 2000s, an unscrupulous Moon landing denialist lured Apollo astronauts into an audience with him under false pretenses. Then he insulted them as liars and pressed them to swear on the Bible that they went to the Moon.

Flat-Earthers use this incident as “evidence” that we never went to the Moon. In reality, the offender did not meet the astronauts with the best of intentions. This incident tells us more about the offender than it does about the astronauts.

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Coriolis Effect Misconception & Strawman Argument

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The Coriolis effect acts on an object that is launched to another location closer to or farther from Earth’s axis of rotation. The object retains the inertia from the surface it was launched from, but it no longer matches what is required to keep it moving in a straight line, according to an observer on the surface.

On the equator, Earth’s surface is moving at a speed of 465 m/s. Flat-Earthers assert that if that is the case, then an object launched upward should move away from the observer at the same speed. It does not happen, and they use it to disprove the Coriolis effect and Earth’s rotation in general. In reality, the Coriolis effect is not what they describe.

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Stellar Aberration

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Stellar aberration is the apparent shift of stars about their actual positions, depending on the direction Earth is moving in its orbit around the sun. It occurs because the speed of light is finite; it takes time for light to reach the observer.

Stellar aberration was discovered in 1727 by James Bradley. It was the first direct proof of heliocentrism, that Earth is in orbit around the sun.

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Mars One

Mars One was a questionable organization that received investments by claiming it would use it to land humans on Mars. It was not a credible company, and many consider it was a scam to take money from investors and participants.

Mars One had a lot of media attention, but it was dissolved without any achievement. Flat-Earthers use it to discredit space travel. In reality, the company was not credible in the first place, and practically nobody in the aerospace industry thought Mars One was serious in their objective.

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