## Sunrays are Practically Parallel, but not Perfectly Parallel

The sun emits sunrays in every direction. But as the sun is very far, the sun rays that reach us are practically parallel. From Earth, any two sun rays form a maximum angle of ~0.53°. Sun rays are practically parallel, but not perfectly  parallel.

For most practical purposes, we can assume sun rays are parallel for  simplification. But in other cases, the small angle is critical to the problem & we need to take it into account.

## Polaris Distance and How It Does Not Appear to Move

In a very casual observation, Polaris appears stationary in the sky because it is very far & we do not live nearly long enough.

Flat-Earthers use that Polaris always appears in the exact location as “evidence” of a stationary Earth. In reality, it does not appear in motion the same way mountains do not appear to move if we move less than an inch.

## 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.

## Direct and Indirect Measurements

Measurement can be direct, like measuring length directly with tape or a ruler. But it can also be indirect, like measuring distance by emitting a sound, listening for it, and measuring the delay the sound is received after being bounced back by an object.

Flat-Earthers like to discredit measurement results —like the distance to the Sun— by mentioning these are just results of calculation, not measured directly. In reality, many everyday instruments do measure indirectly. They measure a different value, then use calculations to get the desired calculation.

## Weight and Air Density Experiment

Using a precise digital kitchen scale and a smartphone with a pressure sensor, we can easily measure the change in weight and atmospheric pressure in different locations.

Flat-Earthers claim that an object falls down because it is denser than the air surrounding it. However, simple measurements show that things weigh less at a higher altitude where the air is less dense, contrary to the expectation if their claim is true.

## Frame of Reference

A frame of reference consists of an abstract coordinate system and physical reference points that uniquely fix the coordinate system and standardize measurements. Speed or velocity is relative to a specific frame of reference. It is possible that two speeds/velocities are measured relative to a different frame of reference and thus cannot be directly compared.

Flat-Earthers like to compare two different speed measurements like an airplane moving at 900 km/h (560 mph) and Earth’s surface near the equator at 1674 km/h (1040 mph). They would conclude the airplane should not be able to catch up with Earth’s surface and would not land if the Earth is rotating. In reality, both the speeds are measured relative to a different frame of reference, and therefore, cannot be compared directly.

## Scale in a Diagram of the Solar System

Diagrams of the Sun, Earth, and the Moon or any other celestial bodies are rarely made to scale because of their extreme smallness relative to the vast distances between them.

Flat-Earthers assume that the diagrams are not made to scale as a form of deception. In reality, it is just impossible to draw a diagram of celestial bodies with the real scale on physical media and still convey what we want to describe.

## Negative Parallax

Stellar parallax is the apparent shift of closer stars against more distant stars due to the orbiting motion of Earth. Negative parallax, or stars going the wrong way— occurs due to measurement errors placing the nearer star as the farther one and vice versa.

Stellar parallax directly proves Earths’ motion around the sun, and flat-Earthers use negative parallaxes to dismiss it. In reality, negative parallaxes are just statistical uncertainties.

## Moonlight and the Cooling Effect Myth

Flat-Earthers claim that moonlight is cold and cools down objects exposed to it. It is merely a myth from the 19th-century flat-Earthers, reinforced by confirmation bias in various so-called “experiments” performed by today’s flat-Earthers.

Flat-Earthers experimented and insisted that moonlight has a cooling effect because they failed to control other factors affecting the experiment and maybe even deliberately introduced them to influence the results. They also did not account for measurement errors —the variation between several measurements— and cherry-picked the results that fit their desired outcome while ignoring the rest.

## Earth’s Axial Precession

Axial precession is the change in Earth’s rotational axis. It is a slow change with a cycle of 25772 years. As a result, the role of pole star will pass from one star to another.

Contrary to flat-Earthers’ assertions, due to Earth’s axial precession, Polaris has not always been the North Star and will not remain as the North Star. The star Gamma Cephei will replace Polaris’ place in 2000 years as the North Star.

## Stellar Aberration

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.

## Stellar Parallax

Stellar parallax is the apparent shift of the position of a nearby star against the background of distant stars. It is the result of Earth’s orbital motion around the Sun. It is tiny and difficult to observe. Successful measurement of stellar parallax was done only after the 19th century.

Some flat-Earthers claim that stellar parallax has never been successfully observed, and they use it as ‘evidence’ Earth is stationary. In reality, stellar parallax has been successfully measured in 1838 and is now used as the basis for measuring stellar distances.

## Proper Motion

Proper motion is the apparent motion of stars, caused by the movement of the stars themselves, relative to the solar system. Stars will appear to shift over time, relative to other, more distant stars.

Flat-Earthers assume stars are only in motion around Polaris, or the north celestial pole. They are wrong. Stars have other apparent movements, one of which is proper motion.

## The Legendary AutoCAD Diagram Involving the Pythagorean Theorem from Flat-Earthers

There is a legendary diagram of spherical Earth from flat-Earthers that was made using AutoCAD involving the Pythagorean theorem, flaunting the fact that it is was created “using AutoCAD 2016 with 15-digit precision”™. The diagram is not wrong, but it does not account for the height of the observer and atmospheric refraction. And therefore, it is unsuitable for determining the obstruction of a distant object due to Earth’s curvature.

The numbers in the diagram will give us a much higher number than it should be. If a distant object is visible, but according to the diagram it should not, then flat-Earthers will incorrectly conclude that the Earth is flat.

## Leveling

Leveling is the process of determining the elevation of a point relative to another point. The curvature of the Earth and atmospheric refraction affect the result of leveling. There are techniques and formulas to correct the effect of Earth’s curvature and atmospheric refraction.

Flat-Earthers assume that construction works like roads, bridges, railways, etc. are built without accounting for Earth’s curvature. They are wrong. The leveling in such works are done in such a way it minimizes the errors due to Earth’s curvature and atmospheric refraction.

## Seismometer

A seismometer is an instrument that responds to ground motions, such as caused by earthquakes, volcanic eruptions, and explosions.

Seismometers are sensitive but they cannot detect Earth’s motion. Flat-Earthers use this to ‘prove’ the Earth is stationary. They are wrong. A seismometer is mounted on Earth’s surface and is already moving at the same speed as the surface itself. It can only detect motion if there is a change in speed —or an acceleration— exerting a force to the seismometer.

## Measurement Error

Measurement error (also called observational error) is the difference between a measured quantity and its true value. A measurement error is not a mistake. Variability is an inherent part of the results of measurements and the measurement process.

Flat-Earthers often point out at ranges of quantities, errors in measurement results, varying results in different attempts of measurement, as well as highlighting the adjectives ‘about’ and ‘approximately’; then present them as ‘proof’ that science does not know it for certain. They are wrong. Any measurement has an error, and it can never be eliminated.

## 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.

## Earth’s Curvature Calculation

The amount of obstruction of a distant object that is caused by Earth’s curvature depends on:

1. The distance of the object.
2. The height of the observer.
3. The height of the object.
4. The magnitude of atmospheric refraction.

Flat-Earthers like to use the visibility of a distant object to prove Earth’s curvature does not exist. Very often, they failed to account for observer’s height and atmospheric refraction, or make other mistakes, like unit conversions errors, distance calculation errors, etc. Once all are considered for, and mistakes are fixed, everything will be consistent with spherical Earth.

## The Angle of a Shadow During Equinox

During an equinox (March 20 and September 22-23), the Sun is directly above the equator. If we are on the equator, an upright stick will not have a shadow in the middle of the day.

On any other location, the angle between the stick and the direction of sunlight will be the same as the observer’s latitude.

This fact can only occur if the Earth is a sphere, and only if the Sun is very far relative to the size of the Earth.