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I created a geometrical simulation of how the Sun is reflected on a wall along the day and along the year, using Geogebra:

sun simulator

https://www.geogebra.org/classic/dckhbc8h

Playing with parameters, I found an oddity: in some specific cases, changing the "season angle", i.e. inclination of su circle w.r.t. horizon, I can see the "sun reflection line" always passing in same point on the wall along whole year:

case 1 case 2 case 3

Overlapped:

overlapped

Is this a real behaviour or just an error in my simulation?

Does it happens always at same time of the ay? My simulation currently does not show the times along the "sunLine" segment.

How could I build a Geogebra formula to directly draw the "convergence point" of all the sunLine lines along the year?

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  • $\begingroup$ Somewhat close to my recent question Math behind a heliostat, I think. Maybe you could help me with mine, please? I never heard of GeoGebra before, so it looks it could be easy for you? $\endgroup$
    – B--rian
    Apr 6, 2021 at 16:27
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    $\begingroup$ Yes, I already have a ready-made source code for an heliostat, I wrote it some years ago: jumpjack.wixsite.com/progetti/sorgenti-ipsun $\endgroup$
    – jumpjack
    Apr 6, 2021 at 18:38

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When the "sun angle" is zero, the position of the "sun" doesn't depend on the season angle, so the lines will cross at the point that is the image of the sun at "sun-angle 0"

One important aspect in your model is that the season doens't change the "angle" but the position of the sun. In summer, the sun rises and sets in the north East and north west and describes a small cirle around the north celestial pole. In winter it rises and sets in the southeast/west. And only at the equinox does it describe a great circle.

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  • $\begingroup$ no, it looks like it happens for sunAngle = 0.5 . Apart from this, do you think the model is correct? Probably I should limit "seasonAngle" depending on mirror latitude: I think currently the model covers the whole globe. $\endgroup$
    – jumpjack
    Apr 1, 2021 at 10:52
  • $\begingroup$ Found a major error in my model: there was a "stranded" "e" before "elevation" parameter in "mirror", which resulted in "e * elevation" being the argument, rather than "elevation"... $\endgroup$
    – jumpjack
    Apr 1, 2021 at 11:30

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