The Earth is Round, of Course, but Not on That Basis!
The Photograph on the Lake Portchartrain
We know that our planet is round like a ball. This is scientific and technological fact. There are endless proofs of its roundness. Nevertheless, a kind of dogma about the scientific denial of this fact still persists in current times as a generic foundation for use in government policy situations and even in the conduct of communities in general.
In this present text we will analyze an image that is very popular in social media, where it appears as a paradigm of incontestable proof of the curvature of our planet. The picture corresponds to a photograph of the electrical power transmission line over Lake Portchartrain in the North American region. Let’s make it clear that the nature of the Earth’s shape is not at issue here, which, of course, is round.
To achieve our objective, we used as a methodology the articulation of elements through mathematical calculations on reliable data:
- The topographical features surrounding the geographic location corresponding to the landscape in the photograph.
- Trigonometric calculations.
- The geometric properties of the circle.
- Basic knowledge of the geometry of light.
🔷Geographic Location
As an initial preparation we searched the location on Google Earth:
Three strategic points were drawn on the map in an enlarged scale, to support the analysis: A, B and C:
Each point of this represents on the ground the position of the ends of the maritime sections of the power transmission line:
🔷 Geometric Data
In the second step, we need to collect the data indicated in the following table:
👉The Arc Length
Using the Google Earth Pro tool, we will determine the distances of each section, these distances, obtained in this way, already consider the curvature of the Earth, that is, the result will be the measurement of the circumference arc length.
The same procedure was performed for the other AC segment. So now we have the partial data:
👉The Length of Chord Segment
To determine this data we will use the trigonometric ratio:
or
where
corresponds to the radius of the Earth’s sphere.
In this way, after carrying out the calculations, we complete our table
According to the results, the differences between the bow and string measurements correspond to 231 and 228 meters, this gives an idea of the influence of the Earth’s roundness, in this case in the horizontal direction. We now need to evaluate this vertically.
For this we will again use the trigonometric relations in the right triangle using the expression:
this result, h, gives us the smallest height of an obstacle positioned in the center of the arc segments that can be observed from the end. Once calculated, we have:
and
🔷A comment Based on What Physics Says
As the energy transmission towers have an average free height of 20 meters, therefore, from 12 kilometers away, in the AB section, the visual effect of the Earth’s roundness would actually start to appear in the “line of sight” on the transmission line. Prior to that this effect would be very gradual.
However, it must be considered that at that distance of 12 kilometers, visual perception is very impaired, it would be comparatively the same as observing something as soon as you were on top of Mount Everest. Superimposed on this difficulty are the inherent distortions, the so-called mirages by refraction of sunlight in layers of heat in the air, explained by Physics. See that there are two types of mirages: the inferior mirage and the superior mirage. The latter has the effect of suspending the observed object as if floating in the air.
This mirage effect would probably occur much earlier than 12 kilometers.
In short, then, we are faced with factors that interfere with the claim that such a photograph could be direct evidence of the curvature of the Earth.
