Density vs Free Falling Acceleration

At a lower altitude, the air density is lower, and falling objects are accelerated faster. Conversely, the air density is higher at a higher altitude, and falling objects are accelerated slower.

Flat-Earthers deny gravity and invented the “explanation” that an object falls only because it is denser than the air surrounding it. But if it were true, an object should fall faster at a higher altitude where the air density is lower, but it falls slower instead. This fact disproves flat-Earthers’ density theory.

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Gravitational Acceleration in Archimedes’ Formula

Archimedes’ principle states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces. Today we usually use B =  -ρgV to calculate the buoyant force, where ρ is the fluid’s density, g is the gravitational acceleration, and V is the volume of the displaced fluid.

Archimedes discovered buoyancy earlier than Newton discovered gravity, and flat-Earthers dispute the presence of g in the buoyancy formula. In reality, buoyancy depends on the weight of the fluid, and the distinction between weight and mass only occurred after Newton. Archimedes’ principle still applies, only that we now have a better understanding of what weight is.

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Isaac Newton and the Falling Apple

The fall of an apple inspired Isaac Newton to understand that the same force that brought the apple falling toward the ground also keeps the Moon in motion around Earth. However, his work involved much more than just observing the falling apple.

Flat-Earthers downplay Newton’s contribution as if it was only about the falling Apple and use the episode as a means of ridicule. In reality, Newton’s works were much more than that.

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Variation of Earth’s Gravitational Acceleration

The acceleration of free-falling objects on Earth varies. It depends on various factors. The figure of 9.8 m/s² is just a nominal value to use if the actual local value is unknown or unimportant. These variations can only be explained using the law of gravity and that the Earth is a rotating sphere.

Flat-Earthers claim that science tells us that Earth’s gravitational acceleration is always 9.8 m/s² everywhere on Earth, and they use it as “evidence” Earth is flat and stationary. But, in reality, Earth’s gravitational acceleration does indeed vary in different locations.

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What We Feel as “Weight” is the Force of Gravity

The weight of an object is the force exerted on the object by gravity. The gravitational force exerted by the Earth on an object is what we feel as the ‘weight’ of the object.

Many flat-Earthers fail to understand that the gravitational force is just another name for ‘weight’. Much misinformation in flat Earth communities arises from this misunderstanding.

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Force Vectors

Many misinformation within flat-Earth communities is present only because of their lack of understanding on how forces work on an object.

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Newton’s Cannonball

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Newton’s cannonball was a thought experiment Isaac Newton used to explain the principle of orbital motion. It was the first explanation of an orbit and still the easiest to understand.

Newton visualizes a cannon on top of a very tall mountain where the air resistance is no longer a factor. As more charge is used with each cannon shot, the speed of the cannonball will be greater, and the cannonball will hit the ground farther and farther. Finally, at a certain speed, it will not hit the ground at all. It will fall toward the spherical Earth just as fast as the Earth curves away from it. In the absence of drag from the atmosphere, it will continue forever in orbit around the Earth.

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Uniform Circular Motion

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The motion of a specific location on Earth due to Earth’s rotation is a uniform circular motion. We can separate it into a uniform linear motion and a centripetal acceleration toward Earth’s center. From the reference frame of an observer on Earth, the latter results in a constant centrifugal acceleration, which is felt simultaneously with Earth’s gravitational acceleration.

We often use the uniform linear motion of everyday objects to explain the effect (or the lack of thereof) of uniform motion of Earth’s rotation. Flat-Earthers incorrectly reject it just because “it is not a circular motion unlike Earth’s rotation” In reality, a uniform linear motion is one component of a uniform circular motion. And these explanations are correct and still apply.

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Hill Sphere

The Moon orbits the Earth —not the Sun— because the Moon lies well within Earth’s Hill sphere. Hill sphere is the region around Earth where Earth —instead of the Sun— dominates the attraction of satellites.

Flat-Earthers noticed the Sun exerts a stronger pull to the Moon than Earth does to the Moon. They incorrectly concluded that according to science, the Moon should orbit the Sun, then proceeded to use it to discredit science. In reality, they did not account for the centrifugal acceleration resulting from the motion around the Sun, which is one of the factors that determines Earth’s Hill sphere.

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Elegance

Our understanding of gravity explains a phenomenon clearly and directly. It is one idea, easy to understand, explains so many phenomena, can account for a large amount of data, and answers many questions. In other words, we can say that gravity is elegant.

In contrast, each of the different concepts in the flat Earth model requires a separate explanation and often in conflict with each other. We can say it is ugly. It is why flat-Earthers cannot accept that a single idea of gravity can explain so many phenomena.

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“What is Gravity”

In a StarTalk episode, Neil deGrasse Tyson was given the question “what is gravity?” He quipped “we have no idea” before elaborating more. Flat-Earthers quoted it out of context to discredit Neil and gravity, completely disregarding what Neil explained afterward.

In reality, Neil did provide a very comprehensive answer to the question “what is gravity” but flat-Earthers only gave an emphasis to the “we have no idea” part of his answer, and skipped the rest of his answer.

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Repulsive Force

Gravity does not possess repulsive force like magnetism. These are two different phenomena with different characteristics.

Flat-Earthers use the lack of a repulsive force in gravity to deny its existence. In reality, there is no requirement for an attractive force to have a repulsive force. Gravity does not act like magnetism, and the fact does not disprove gravity.

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Weightlessness, Free Fall, and Microgravity

In orbit, objects are weightless because both the objects and the spacecraft have the same speed and direction, and both are affected by the same gravitational influence. We use the spacecraft as the frame of reference. Because the objects are not in motion relative to the spacecraft, they appear to float.

In Earth orbit, the objects are still affected by Earth’s gravity, but yet they float. Flat-Earthers use it to disprove spaceflight. In reality, the objects float because we are using the spacecraft as the frame of reference, which is also moving by the same amount and is affected by the same gravity as the objects themselves.

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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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Flat-Earthers’ Alternative Facts for Gravity

Flat-Earthers reject gravity because it does not support the flat Earth model. To explain the various phenomena explained by gravity, they invented many different ‘alternative facts’ in place of gravity.

Flat-Earthers agree only on a single thing that the Earth is flat. However, as flat Earth is not fact-based, flat-Earthers cannot agree on practically everything else. Different flat-Earth denominations have their alternative explanations for gravity, all of which lacks predictive power and cannot adequately explain real-world facts.

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Airplanes Will Never Fly Into Space

An airplane relies on the lift from its wings, which depends on the airplane’s speed and the air density. As a result, a cruising airplane will fly at a constant altitude, following the curvature of the Earth.

Flat-Earthers claim if Earth is a sphere, an airplane has to dip its nose down periodically, or it would fly into space. In reality, an aircraft will follow Earth’s curvature and is unable to fly to space even if the pilot deliberately attempts to do that

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Curved Appearance of a Rocket Trajectory

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Rocket launches have a curved trajectory because their objective is not only to reach space but also to enter Earth orbit. To achieve it, a spacecraft needs to gain a sufficient horizontal speed, parallel to Earth’s surface.

Flat-Earthers claim the curved appearance of a rocket launch trajectory “proves” rockets never reach space. In reality, it is caused by the motion of the rocket parallel to Earth’s surface, perspective effect, and the curvature of the Earth.

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Fictitious Force

A fictitious force is a force that appears to act on every object when the frame of reference is accelerating. The term “fictitious” does not mean the force does not exist, but it is not an actual force that arises from an interaction between objects.

Flat-Earthers noticed gravity is considered a fictitious force and use the fact to “prove” gravity does not exist. In reality, we can feel a fictitious force. It is merely a term we use for forces that arise due to an accelerating frame of reference.

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Cavendish Experiment

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The Cavendish experiment was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational constant.

Flat-Earthers are in a constant effort to discredit the Cavendish experiment. They would invent various “explanations” to “explain” the result of the experiments. However, the experiment was not only done once by Henry Cavendish in 1797-1798, and has been replicated numerous times by multiple independent parties for centuries, all yielding consistent results.

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Spirit Level on an Airplane

During cruising, an airplane is practically level. It is flying perpendicular to the direction of gravity. The aircraft is still flying following Earth’s curvature and continuously changes its orientation. However, not only its orientation changing but also the direction of gravity, having the same amount of change. As a result, a spirit level on a flight will not show us the difference in orientation of the airplane due to its motion following the curvature of the Earth.

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