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How to arrive at the coordinates for the sun from any position on earth?
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The video in the OP shows many vectors representing the two descriptive angles that position the sun in the sky.
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A vector includes a magnitude but we're not concerned with that for this exercise, so it can be ignored.
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All we're looking at is the DIRECTION of each vector, given by the compass bearing and vertical angle above the horizon of the sun.
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In astronomical observations ascension and declination are used for this purpose, by which any star in the night sky is located.

That’s nice and appears a slam dunk ... until you realise that the ability or inability to reconcile the vectors to all meet at a point would depend upon what projection of the globe model onto a flat surface one is using.

One could just reverse the process by assuming all the headings have to agree in that sense and then create a projection that places all of the origins of the vectors in relative positions that make them meet at a point.

That would be mathematically possible. Whether such a projection is feasible based on other data like known distances among locations and how light travels is another question (I believe it’s a priori impossible for ANY flat model to preserve all distances in all directions if a spherical model accounts for them)

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The accuмulation of all the data could turn into a considerable task, especially when one considers the fact that the geoid produces level lines that are not neat and clean aspects of a perfectly spherical earth.
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If I could find the video where this is explained very well, I'll post it.
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In other words, a so-called vertical line at point A might point to the star Vega, but then another so-called vertical line from point B only a mile away might point about 2 or 3 degrees away from Vega. 
This cannot be explained by the curvature of the earth (where a nautical mile translates to just one minute of arc, and 4 seconds of sun movement in its course), but it CAN be explained by the variation in level due to perturbations in the geoid.
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What is "level" at point A might not be "level" when sighted from point B, by some small amount.
And then you could have a point C even further away where a level line of sight confirms that of point A again.
The geoid has highs and lows something like the surface of calm water, which average out to the curvature of the earth.
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With the aid of satellites more and more refinement in the contours of the geoid are being developed over the years.
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Therefore, it is no longer a question of whether the earth is spherical or not, but just how irregular its shape is in approximation to spherical.
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That's why we say it is a SPHEROID and not a sphere.
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There is a place in eastern Canada where a major river would appear to flow uphill if you only consider its astronomical direction of flow.
That's because the attraction due to gravity changes direction along the river as though the center of the earth would appear to be moving as one follows along the path of the river.
But if you check with surveying instruments you find the water is flowing where "downhill" would appear to be based on how gravitational force is directed at each point.
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