Does government document Pub. 200 prove the Earth is Flat?

Flat Earth Claim

Government Document claims you can see mountains despite "56,527 feet" of Earth Curvature.

Reality

I have to admit, this one surprised me a little bit and I had to do a little research.

First of all, Pub 200 Sailing Directions (Planning Guide and Enroute) Antarctica does, in fact, actually say this -- right in the middle of a whole bunch of other stuff about Refraction and extreme conditions and how difficult this makes it to judge distances...

Of course, it ALSO shows Antarctica is a small continent that is only about 10,000 miles around which makes it utterly impossible to be the far outside edge of a circle some 12,000 miles in radius!

According to the Flat Earth model that should be about 75,000 miles around and concave instead of 10,000 miles around and convex.  So good job Flat Earthers!  Give them a round of applause.

Next, look at the text more carefully:

There is almost no dust or solid particles in the Antarctic air and the prevailing winds blowing off the continent have small moisture content. Consequently, the visibility is usually very good and often exceptional, a fact which, if not appreciated, may lead the observer into serious error when judging distances.
...
Mirages—Abnormal Refraction.—An unusual lapse rate of temperature (and therefore density as well) with height immediately above the sea (or land) surface produces a distortion in the appearance of objects near the horizon; such a phenomenon is known as mirage.

They are saying that the viewing distance is very great due to extremely clear air conditions and that there are often usual amount of refraction and under some extreme and specific set of viewing conditions you can see SOME mountain at 300 miles.  They do not say you can see ALL mountains from 300 miles away.

Now the question is -- is it possible under REASONABLE conditions to see a mountain from 300 miles -- assuming the air is sufficiently clear to allow viewing of that distance?

The first thing of note here is there are vast swaths of Antarctica that are 3000 meters and points that are closer to 4000 meters, and peaks up to 4892 meters (16,050').  We're not at sea level with our eyes half-way under water looking at something 300 miles away!  Why must Flat Earthers continue to make this same mistake time and time again?

As we have shown MANY times previously, you MUST take into account the observer height to find the amount of a distance object that would be hidden by Earth's curvature.

If we're way up high, and there is a lower elevation area between and some other point is way up high YOU CAN SEE THAT DISTANT PEAK MUCH FURTHER AWAY THAN YOUR HORIZON.

This should be OBVIOUS with even a trivial sketch of the geometry in question.

There are also a lot of fairly high mountains that rise up over the land.

And if you add in even a MODICUM of refraction (which is called out in the article in question in the VERY next paragraph seeing a mountain peak from 300 miles away shouldn't be impossible:

That said I would like someone to PROVE to me they are seeing a seeing a mountain from 300 miles away -- from what exact latitude and longitude and which mountain are they seeing and what does it look like (a photograph perhaps)?

Give me those details and then we can see how things work out.

Until then we can only guess -- maybe it was really 280 miles away and not 300?  What actual observation backs up this claim?  We don't know, this is just some random statement, it's not a factual claim nor backed by any data at all.

But what I have shown here is that there ARE mountains over 14,400' high on Antarctica and it's POSSIBLE to see something 14,400' high from 300 miles away, given PLAUSIBLE conditions. Standard refraction is 14% -- I lowered it to 5% here for this example.  Even a small amount of refraction makes a big deal over 300 miles of atmosphere - 14% would lower obscured to under 10,000' making the tops of whole mountain ranges visible.