The June 18, 2019 edition of Yachting World carried the article ‘Back to basics: Offshore sailing by celestial navigation alone’ by Andy Schell. Flerfs have seized on the following paragraph from that article.

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°.

They claim that this proves celestial navigation uses a right angled triangle with flat sides in order to measure the elevation angle of a celestial object. One of the sides of this triangle is the earth’s surface, therefore the earth must be flat.

Schell is clearly wrong, so why would he write this?

A letter published in Yachting World March 10, 2022, questioned Schell’s words:

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.

To which Andy Schell responded:

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.

This has been repeatedly pointed out to flerfs, yet still they misrepresent Schell and use their cherry picked quote.

#GotToLieToFlerf.