You've got the ideas right, but a few technical corrections :) (unless I get them wrong as well!)
> At around noon, when the Sun reaches the zenith
The sun approaches zenith, but unless you're at specific places and times of year (under the tropics, at specific time of year for each latitude), it doesn't really reach zenith. At its peak, I believe the Sun is towards Earths orbital pole[1], which is offset from the geographic north/south pole, although those directions coincide at solstice.
> Doing this other than noon is going to get more distortions,
Indeed, the sun approximately describes a circle around the north/south celestial pole at 360 degrees per day, or 15 degrees per hour. Near the equator the circle tends to be larger and follow direct east-west discussed earlier (in particular at those times when it reaches zenith, that near equinox in tropical regions, i.e. less than Earth's inclination latitude). This can be accounted for if you know your latitude and day of year. (I'd love to dive into the math of this)
> Thinking about this, this is probably how the clock and the sextant lets people navigate on the open ocean during the age of sail.
Indeed, very fascinating to me :) If you take measurements very precisely, you can approximate both your bearing and latitude position very well. If you have an accurate clock you can also infer your longitude, i.e. a celestial based GPS!
I don’t think it is exactly zenith at exactly 12 noon, though now that you mentioned it, I remember that the apps I use shows it might shift as much as +/- 30 mins where I am at. Playing with the app (Sun Seeker), I can see what you mean by different places and times of the year as it relates to clock time and zenith.
On the note about the age of sail, I remember that accurate maritime clocks revolutionized and enabled sailing, and colonization. Though at the time, I was mystified by how the sextant and clock would get location.
Two of my hobbies are permaculture and astrology, so I spent a lot of time observing the path of the sun as it relates to my location on earth.
> At around noon, when the Sun reaches the zenith
The sun approaches zenith, but unless you're at specific places and times of year (under the tropics, at specific time of year for each latitude), it doesn't really reach zenith. At its peak, I believe the Sun is towards Earths orbital pole[1], which is offset from the geographic north/south pole, although those directions coincide at solstice.
> Doing this other than noon is going to get more distortions,
Indeed, the sun approximately describes a circle around the north/south celestial pole at 360 degrees per day, or 15 degrees per hour. Near the equator the circle tends to be larger and follow direct east-west discussed earlier (in particular at those times when it reaches zenith, that near equinox in tropical regions, i.e. less than Earth's inclination latitude). This can be accounted for if you know your latitude and day of year. (I'd love to dive into the math of this)
> Thinking about this, this is probably how the clock and the sextant lets people navigate on the open ocean during the age of sail.
Indeed, very fascinating to me :) If you take measurements very precisely, you can approximate both your bearing and latitude position very well. If you have an accurate clock you can also infer your longitude, i.e. a celestial based GPS!