The Curvature Fitting Game

The amount of curvature that appears in a photograph of a sphere depends on 1. The radius of the sphere, 2. Camera distance from the sphere, 3. Field of view of the camera, and 4. The distortion characteristic of the camera being used.

The ‘curvature fitting game’ has been flat-Earthers’ favorite pastime. They would try to fit a photograph of Earth’s curvature with another. If they find the result is not proportionally correct, they will make fun of it. They are wrong. Two different photos of a sphere can be taken differently and would show a different curve, even if the object being photographed is the same object.

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Airborne Early Warning & Control (AEW&C): Mitigating Limited Radar Range Due to Earth’s Curvature

An AEW&C (airborne early warning and control) system is a radar system attached to an aircraft. It can detect objects at a very long range compared to any surface mounted radar system.

The reason is that Earth’s curvature limits the range of a surface-based radar. An airborne radar system mitigates this problem.

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The Earth is Spherical and The Nile Never Flows Uphill Anywhere

The Nile never flows uphill, or in other words, ascend to a location farther from sea level anywhere in the Nile basin.

Flat-Earthers often claim that if the Earth is spherical, then the Nile will have to flow uphill to overcome the curvature of the Earth. They are wrong.

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The Dip of the Horizon

There are two kinds of the horizon:

  • Astronomical horizon: the horizon at the eye level.
  • True horizon: the line that visually divides the Earth and the sky.

Because the Earth is a sphere, the true horizon always lies below the astronomical horizon, or the eye-level. The angle between them is the dip of the horizon. The higher the observer, the larger the dip of the horizon.

Flat-Earthers claim there’s no dip of the horizon. They are wrong. It is not hard to observe the drop of the horizon and prove the curvature of the Earth.

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Crow’s Nest on Ships

A crow’s nest is a structure in the upper part of the ship, especially old-fashioned ones. It is used as a lookout point and positioned high above to increase visibility over the curvature of the Earth.

On the deck of a ship 4 m (13 ft) above the surface of the ocean, an observer can spot a 20 m (66 ft) high ship from at most ±25 km (16 mi). On the other hand, from a 35 m (115 ft) high crow’s nest, an observer will be able to spot the same ship from ±40 km (25 mi) away.

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Shadow on Clouds

Before sunrise or after sunset, the Sun is below the horizon and not directly visible. But the sky and clouds above are illuminated because they are high above, and sunlight can reach them.

If there’s a mountain between the Sun and the clouds, it can cast a shadow on the clouds. The flat-Earth model assumes the Sun is always high above, and thus, this phenomenon cannot possibly occur in a flat-Earth.

The fact that a mountain can cast its shadow on clouds far above it is evidence that the Earth is spherical.

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The Reason We Cannot See Earth’s Curvature When Standing on a Beach

We can’t directly observe and subjectively perceive the curvature of the Earth from a position close to the surface. And this matches the expectations in the spherical Earth model.

Flat-Earthers often take the fact we can see the curvature by standing on a beach as ‘evidence’ the curve doesn’t exist. They are, once again, wrong.

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Fisheye Lenses Can Make Curved Lines Appear Flat

A fisheye lens distorts images. It results in images having barrel distortions. In a fisheye lens, a straight line can appear curved. But some flat-Earthers don’t realize that the opposite is also true, a fisheye lens can easily make a curved line look straight.

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Curvature Calculators and Atmospheric Refraction

Atmospheric refraction causes a distant object to appear higher than its actual position. As a result, the object can be physically behind Earth’s curvature but is still visible because the light coming from it is refracted by the atmosphere.

There are many curvature calculators and simulation tools that don’t account for refraction. They would give us the correct results indicating the object’s physical positions but fail to show us the correct apparent position of the object when visually observed.

Flat-Earthers are often too happy with the calculator showing them the results they want to see and fail to see the reason for the discrepancy.

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The Earth is Spherical and The Mississippi River Never Flows Uphill Anywhere

The Mississippi River never flows uphill, or in other words, ascend to a location farther from sea level anywhere in the Mississippi River basin.

Flat-Earthers often claim that if the Earth is spherical, then the Mississippi River will have to flow uphill to overcome the curvature of the Earth. They are wrong.

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Atmospheric Refraction and the Position of the Sun in the Flat-Earth Model

If the Earth is flat, then the Sun would have been visible from the entire Earth, but that’s not the reality. So, to rescue the concept of the flat-Earth from being falsified, they invented an ad-hoc hypothesis that the Sun appears to set because of perspective and refraction.

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Water Level Demonstrates The Dip of the Horizon and Proves Earth’s Curvature

As the Earth is spherical, the horizon is below the eye-level (or the astronomical horizon). The angle between the eye-level and the horizon is the dip of the horizon. The angle becomes larger as we go higher.

Flat-Earthers often claim that “the horizon always rises to eye-level”, and thus ‘proving’ the flat Earth claim. Despite their insistence to use a water level to ‘prove’ water is flat, the same device can be used to demonstrate the dip of the horizon, proving the water surface has curvature, and consistent with the spherical Earth model.

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Curvature of the Horizon in High-Altitude Balloon Footage

High-altitude balloon footage is often abused by flat-Earthers to show us that the Earth is flat when seen from a high altitude.

We analyzed more than two dozens of footage taken from high-altitude balloons on YouTube, and we can easily conclude the curvature is there and usually easy to spot, including in the cases where flat-Earthers use the video as ‘proof’ of a flat Earth.

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The Eratosthenes Experiment: Proving the Earth is Spherical

In 205 BC, Eratosthenes successfully determined the circumference of the Earth by measuring the length of the shadow cast by a rod. He did the measurement in Alexandria and timed it to coincidence when the Sun is directly overhead Syene.

2222 years after that, some flat-Earthers tried to refute the Eratosthenes experiment. They say the experiment can be applied to the flat-Earth model.

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The Earth is Spherical and The Amazon Never Flows Uphill Anywhere

The Amazon never flows uphill, or in other words, ascend to a location farther from sea level anywhere in the Amazon basin.

Flat-Earthers often claim that if the Earth is spherical, then the Amazon will have to flow uphill to overcome the curvature of the Earth. They are wrong.

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Equipotential: a Property of the Surface of Water

Gravity causes water to seek the lowest potential, which can be simplified as the position as close as possible to the Earth’s center of gravity. As a result, the surface of the water will have equipotential surface and form an approximately spherical surface which has the same center as the Earth. Every location along the surface has the same potential.

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Atmospheric Refraction

Light waves are not always moving in a straight line. When it passes through a medium of a different refractive index, the waves will deviate. The phenomenon is called refraction and described according to Snell’s Law.

Earth’s atmosphere has variation in air density that depends on the altitude. As the refractive index changes with the density of the medium, light waves passing through Earth’s atmosphere also experience refraction.

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Long-Range Wi-Fi and the Curvature of the Earth

Wi-Fi is one of the most common ways of getting connected to the Internet. Practically all short-range wireless network use WiFi. Using specialized equipment, Wi-Fi is usable over a very long distance, even over hundreds of miles.

When designing a long-range Wi-Fi link, we must account for the curvature of the Earth.

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Lake Pontchartrain Power Transmission Lines: Evidence of Earth’s Curvature

Lake Pontchartrain is a lake in Louisiana, United States. There are power transmission lines about 24.27 km (15 mi) across this lake. They are practically straight, and each tower is uniform and has the same height, making these towers ideal for observing the curvature of the Earth.

They were first popularized by Soundly who presented evidence of Earth’s curvature using a series of photos and videos of the power lines in June 2017. As of now, the towers and other objects on the lake are probably the most popular Earth curvature tourism spot in the world.

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Surface of Water and Communicating Vessels

Gravity is not the result of a particular shape of an object. It is caused by mass. All objects with mass exert gravity to each other. The larger the mass of an object, the greater the force of gravity.

On Earth, water forms a spherical surface which has the same center as the Earth. It applies to every surface of fluid which is under influence by Earth’s gravity, unaffected by another force. In a 10 cm wide container, the amount of curvature is only 0.0000002 mm. It is the reason the surface appears flat in small containers.

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