Celestial nav on a flat earth?
In [Andy Schell’s] 2019 article ‘Back to basics: Offshore sailing by celestial navigation alone’ [he] wrote, “In simplified terms, when we take a sextant altitude of the sun we’re creating a right angle triangle between it, the earth’s surface at the GP, and ourselves. Grade school geometry tells us that the two angles in a right-angled triangle must equal 90°.”
Technically this is incorrect. The light from the sun is arriving nearly parallel to both your observer position and the
GP, and the path between you and GP is a curve over the surface of the earth, not the flat base of a triangle. When we subtract from 90°, we are not getting the complement angle in a triangle, we are getting the sun’s decline from our own zenith, which we then treat as angle drawn from the centre of the earth (not from the sun) to sweep out the partial circumference between us and the GP.
I mention this only because your mention of a right triangle is being used by flat earthers to misrepresent how the sextant and celestial navigation works, claiming it can only work on flat earth (because the base of a triangle must be flat). I loved the article otherwise.
Thad Phetteplace
Andy’s reply:
Of course Thad is correct, and indeed the earth is round! But when I teach celestial for practical navigating, I use a variety of mental models to simplify what’s going on in the real world in order to more easily visualise the process.
Understanding the steps of a sight reduction intuitively makes for far better navigators than memorising those steps. My right-angled triangle example is one of these mental models that I have found helps to explain the zenith distance concept early on in the navigators learning of the subject.
Another mental model we use is visualising the celestial sphere as a single plane in which all stars, planets, the sun and the moon are embedded. Of course this is also an inaccurate reflection of reality, but it helps in practically navigating. I’ve found that when the folks I teach get really interested in celestial beyond a basic understanding, these mental models gradually evolve into the real concepts – eventually a light-bulb moment will occur when a new navigator, on their own, realises that the right angle triangle model must be wrong because indeed the earth is round. And then bingo! The deeper concept emerges quite naturally in the learning process.
Andy Schell, 59° North