First, the dude in that video questions why Polaris remains fixed above the North Pole. It certainly appears to remain in the same position over the short course of human a few millennia, but it won't always be in that position. All of the stars we can see with the naked eye are in our galaxy, and it takes the Sun more than 200 million years to make one galactic revolution. So, the local stars, all moving in the same direction and at roughly the same angular speed, appear fixed to us in our cosmic blink of an existence. He demonstrates a curious lack of understanding of the science he calls into question.
He then asks why the stars appear the same in June and December. He needs to take a course in high school trigonometry to understand parallax. Flat-Earthers will often protest that it's impossible for Polaris to appear always above the North Pole considering that the earth is traveling around the sun along an orbital path 940 million kilometers in circumference. This argument is actually irrelevant with respect to the shape of the Earth and is merely a (bad) argument for a stationary Earth.
Nonetheless, flat-Earthers simply lack understanding of the geometry of the heliocentric model. The distance the earth travels during its annual orbit is minuscule compared to the distance of Polaris.
Consider this:
- The diameter of earth's orbit is about 300 million km (186 million miles).
- The distance to Polaris is around 3.6 quadrillion km (2.4 quadrillion miles).
- That's a distance ratio of 1:12,000,000
To put that into perspective, imagine you are staring straight ahead at a distant mountain located 100 kilometers away. Now take a step eight millimeters to the left. Obviously you are still staring straight at the mountain. If you are the Earth and the mountain is Polaris, that 8 mm distance is the equivalent of the change in earth's relative position after six months of orbit.
The exact distance of Polaris is not what's important for this discussion. What matters is that it's far enough away that its rays are parallel, that all its light comes in at the same angle. The result of this position of Polaris in relation to the earth -- its location and its parallel rays -- is that the apparent altitude of Polaris above the horizon is determined solely by the curvature of the earth.
The congruous relationship between the altitude of Polaris and latitude of the Earth is impossible on a flat Earth. The geometry of a close star suspended above a flat plane is very different. To a traveler on a flat Earth who is moving away from Polaris directly south, the apparent altitude of the star will appear to decline, but not at a constant rate as would be seen on a globe. In fact, the farther away the observer gets, the slower Polaris will appear to descend. It's a matter of simple geometry. As the degree of altitude decreases, concurrent distances increase exponentially. This means that the altitude of Polaris will almost never agree with an observer's latitude. To see Polaris at an altitude of 0° on the horizon (as is observed at the equator) would actually be impossible because an observer would have to be an infinite distance away. Basic trigonometry reveals why. If you can solve a right triangle (or use an on-line right triangle calculator), you can verify this for yourself.
He then goes on to say that Polaris has been seen as far south as about 23.5° degrees latitude below the equator. Yes, some flat-Earthers will claim that Polaris can be seen from latitudes well south of the equator, as far as the Tropic of Capricorn at 23.4° S latitude. This is absolutely false, of course, which is why they can't substantiate such claims with verifiable evidence, or any credible sources, i.e., sources other than archaic, pseudo-scientific, flat Earth texts.
In truth, Polaris is typically not visible from locations near the equator. It's not bright enough. Like most stars near the horizon, its light dissipates due to increased atmospheric interference (a.k.a. atmospheric extinction) and because of light pollution, that artificial skyglow that hangs over populated areas. However, under the right circumstances, from remote locations, Polaris can be observed south of the equator. This is due to atmospheric refraction which will cause objects in the sky to appear slightly higher than their actual positions.
There is no way to reconcile this inconsistency of the flat earth model with observable reality. The apparent position of Polaris in the sky, as observed from any location in the northern hemisphere, indicates beyond question the curved shape of the earth. This is empirical evidence that anyone can validate for themselves by simply measuring the altitude of Polaris with a homemade clinometer and comparing the result to their latitude. If they match, you're on a curve.
There is no theoretical distance above a flat earth where Polaris could be positioned that can mimic this relationship. It's impossible. A flat plane can't mimic a curve.
It's not just Polaris that doesn't jibe with the flat Earth "model". None of the celestial objects above a flat earth would appear where they do in reality, including the sun. Like Polaris, the sun is far enough away that its rays are virtually parallel when they reach the earth. During equinox, the sun is positioned directly over the equator, therefore the sun's angle of altitude will be 90° at the equator and 0° at the poles. With regard to latitudinal position, this means that an observer's latitude will always be equal to the sun's angle as measured from 90 degrees overhead (the angle that is complimentary to the sun's altitude). This is called the
Zenith angle.
Finding the Sun's zenith angle is how celestial navigators use the sun to determine their position of latitude. During equinox, at solar noon, the Sun's zenith angle will always be equal to the latitude from which it is being measured. To find the Sun's zenith angle simply subtract its altitude from 90°. For example, if you are in New Orleans which is at a latitude of N 30°, at solar noon, on March 20, you will see the Sun at (90° - 30° =) 60° above the horizon. If you are in Edinburgh, Scotland located at N 56° you will see the Sun at (90° - 56° =) 34° at solar noon. From Minneapolis, MN you will see the sun at 45° because it lies at N 45° latitude. On a flat Earth this would be impossible. As with Polaris, on a flat plane, the sun's altitude is not directly related to latitude, so that simple formula--which mariners have used for centuries to determine latitude while navigating the oceans--cannot work on a flat Earth.
