An interesting analysis, covers a lot of ground, but no mention of the "analemma" (https://en.wikipedia.org/wiki/Analemma), an annual figure-eight curve that results from earth's elliptical orbit around the sun, and that must be included for reliable calculation of solar position and rise-set times.
Calculating the analemma requires multi-term Fourier analysis to reliably pin down the sun's position, without which nautical sextant calculations would fail. Even in the GPS era, professional sailors are required to (demonstrate their ability to) turn sextant sightings into geographical positions, against the possibility of a high-tech failure.
Apropos, during my around-the-world solo sail (https://arachnoid.com/sailbook), because of just such an equipment failure, I was obliged to navigate from French Polynesia to Fiji using a sextant -- and reliable solar positions.
Calculating the analemma requires multi-term Fourier analysis to reliably pin down the sun's position, without which nautical sextant calculations would fail. Even in the GPS era, professional sailors are required to (demonstrate their ability to) turn sextant sightings into geographical positions, against the possibility of a high-tech failure.
Apropos, during my around-the-world solo sail (https://arachnoid.com/sailbook), because of just such an equipment failure, I was obliged to navigate from French Polynesia to Fiji using a sextant -- and reliable solar positions.