Frontal perspective over the flat Earth

There are a few issues connected with perspective over the flat Earth that will not be not so easy to understand. Hence, it will be useful to analyze them immediately. One is about the problem connected with ships disappearing within the horizon: they start disappearing from the bottom. As a consequence,  somebody could consider this fact as an evidence proving the curvature of the globe.

On the contrary, we know that this is a result due to perspective, in fact, you just need to take a binocular. Immediately, you will be able to behold the whole ship again, from bottom to the top. This phenomenon is not due to the Earth curvature but to perspective. How can this situation be explained? Why does perspective hide the ship starting from the bottom?

An apparent south pole in the celestial sphere

A second point, linked to perspective as well, is the presence of an apparent south pole in the celestial sphere. As you can see in the following image seem to be both the north and the south celestial poles.

An observer, watching the stars trails in the southern hemisphere, would see an apparent South Pole axis around which the stars seem to spin. You know, of course, that the flat Earth has

no south pole. Consequently, you will easily understand the fact that this phenomenon is due to perspective.

Ships disappearing within the horizon

Let’s consider the first point: why a ship disappears over the horizon starting from the bottom.

Due to perspective, an object departing from the observer finishes becoming a single point over the horizon. This point is the convergence point of perspective.

The same happens in the case of a ship.  Anyway,  this is not enough to explain the reasons why the ship begins to disappear from the bottom.

Walking along a shiny, long corridor

To prove that this fact is due to the curvature, someone could use a video leaning the camera at the floor level while a man is walking along an unending hospital corridor, smooth and shiny. Shoes become smaller and smaller due to perspective but they do not disappear from the bottom. This could appear to be a clear evidence that over the sea water surface a ship disappears due to the fact the Earth is a globe. So they say.

In reality, we have to consider the difference between the real horizon and the perspective one. This is due to the waves, ripples or reliefs that hide the perspective horizon. Even the neatest sea has small waves that form a far real horizon, a little higher than the perspective one. Only a perfectly smooth plan, like the one of the hospital corridor, admits the sight of the perspective horizon. The difference between the two horizons can be very small, but it always exists. The departing ship is initially big, but slowly it becomes smaller and smaller and its overall changing dimensions become comparable (not too different) with the distance between the two horizons. The ship converges toward the vanishing point on the perspective horizon, but the real horizon starts to hide it more and more. If we try looking at the ship with a binocular, the distance between the two horizons becomes smaller and we can see the ship again.

In the image, the red line is the perspective horizon (lower than the real horizon). As the ship departs, its dimensions become comparable with the distance between the two horizons. So, the real horizon slowly covers the ship that converges toward the perspective horizon. Since the perspective horizon is hidden, the ship arrives to be hidden too.

And now… the second point.

Let’s imagine the following situation: an observer is looking at the North Pole and making a time-lapse of the stars trails. Quite immediately, he can clearly perceive that the stars are spinning around the North Pole axis, i.e. around the polar star. However, it would seem that a similar thing is happening over the South Pole.

Anyway, things are different. We know that over the flat Earth there is a Dome in which all the stars are nestled. Stars are hence all rotating with the same angular speed and always at the same height. An observer on the northern hemisphere will see the stars rotating around the North Pole. This observer will not be able to see the lower stars of the dome, but only the higher ones, due to perspective.

The lower stars are hidden by the real horizon of the observer. The real horizon is higher than the perspective one. Since stars are very far from the observer, a lot of them will not be visible.

On the other hand, let’s consider an observer on the southern hemisphere, maybe on the Land of Fire in South America. He will see part of the stars, the highest of them, rotating around the North Pole, which appears very low on the horizon (Polaris can be seen just till the equator or only a little more southern, due to the effect of perspective). If our astronomer watches toward the south, he will have the possibility to see a lot of stars rotating around an apparent south pole. These stars are near to him. We are imagining he is placed in a far southern part of the world. In reality, this observer will not see the entire obit of the stars. He will behold them, as far as they are placed near him. Anyway, by continuing their orbit, they will finish being very far from the observer.

In the picture aside, the visual field of the guy is highlighted in the dome. The paths of the lower stars he sees are the red ones in the picture.  Due to his limited visual field, he can’t see the whole orbit, but only the nearest part.

The lower stars run an orbit in the observer’s sky similar to that of the sun: the stars rise, make their travel in a short portion of the sky and they set. The rise and the set phases are completely due to perspective. When the stars are further from the observer, they are on the vanishing point of the perspective horizon. Then they go higher and again vanish due to perspective. Each of these lower stars is tracing in the sky a curve around a central point situated on the horizon. This ideal point could be seen by an observer appearing like something similar to the North Pole. The difference is that the north pole of the sky is real and can be looked at any height, depending on the position of the observer. The south apparent pole is an apparent point that can be only perceived at the horizon level.

The south pole does not exist, but it is a perspective phenomenon.

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