# Debunked: "Celestial navigation is based on elevation angles from a Flat Earth"

You seem to have come up with a number for "very very far", as that's one of the inputs necessary for getting a number out.
No. On the globe, the main change is tilt, which depends on the observer's position, and time, not the distance to the stars.
As your parenthetical "infinitely" indicates, you're justified in just taking the limit as the number you chose tends to infinity, and that leads to a tilt of 0⁰ in the limit (which is well behaved). You were right at the outset, the adding of numbers has fuzzied things.
In empirical practice, the width of Earth's orbit needed to be utilized to discover stellar parallax with astronomical instruments. That means, apart from tilt, the sky is pretty much the same (for household purposes) everywhere on Earth.
"All finite things are but nothing to the infinite" - Epifatphilus, famous non-existent non-greek non-philosopher.
"The finite is annihilated in the presence of the infinite, and becomes a pure nothing. " — Blaise Pascal, On the Wager for God’s Existence

No. On the globe, the main change is tilt, which depends on the observer's position, and time, not the distance to the stars.
There was no globe!? There was no tilt!? Did I misread something?

In empirical practice, the width of Earth's orbit ...
OK. I misread something. There were no orbits in what I read.

"The finite is annihilated in the presence of the infinite, and becomes a pure nothing. " — Blaise Pascal, On the Wager for God’s Existence
Damn! I'm gonna have to re-evaluate how smart that Fatphilistarchus was.

My brain got a bit tired of infinity.

And I realise that none of what I was discussing does much to the "navigation angles based on a flat earth" point.

Then I got onto thinking about a flat earth with a horizon that rises to eye level and what that means about elevation angles measured from the horizon.

But my brain coped with that worse than it did infinity and I had to give that up too.

Maybe someone else can theorise on it better.

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There are various ways to check the validity of this claim.

Noooo. I'm not going to waste even one attosecond of my life checking the validity of any flat Earth claim. In many ways...I think people keeping on 'explaining' things to flat earthers is precisely what gives them a sense that they have something worth explaining. They don't. People believe in flat Earth because they are stupid. I mean...let's finally say that and move on.

I missed this the first time around.
The first premise is commonly accepted by flat earthers, and the group I linked to will happily use it in their imagery, while celebrating their knowledge of this formula. This is one of the images they use:

to anyone who's mastered trigonometry, it's clear that the "flat" version of this must involve the sinus of 54⁰. The fact that it doesn't proves that the 3240 nautical miles is in fact an arc length. Arc lengths are directly proportional to angles, straight ("flat") distances are not.

I learned a lot of interesting stuff while explaining to Flat Earthers—though rarely from them.

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