Here are my questions about it, and I hope they will get some attention from the RE-ers:
1. What if the stars (and the GPS satellites) are actually wrongly mapped? That won't be something, well, weird.
If the stars were mapped wrong, then using the data from the maps to point telescopes wouldn't work. The locations from celestial maps
do work to routinely and accurately point telescopes at objects in the sky, and, conversely, to identify objects based on their position in the sky. Ergo, the maps must be correct.
If the GPS satellites weren't where they were predicted to be, then your location calculated by the GPS would be wrong. That should be easy enough to verify; when your GPS says you're at or near some location, are you at or near that location?
Let me explain: Ptolemy's map of stars was wrong, and he used that map and the observations by other astronomers from the cities to determine the coordinates of cities. Needless to say, he got the wrong results, but it took thousands of years time to discover that error. How do you know that's not exactly what's going on here (and you see different stars in Australia than on the north hemisphere!)?
I'd like a citation for the comments about Ptolemy and his maps, please. I'm not familiar with this and it sounds interesting.
As to the last question, again, we know that current maps of the stars are correct because they
work. You can use the data from them (or, often, catalogs of the data they're made from), to find things in the sky, and they're right where they are predicted to be by the maps or catalogs.
2. The shortest path from the South America to Australia, according to the globe, is obviously across Antarctica. So, even if the Earth is round, we are still not using the shortest path. Have you, RE-ers who use the distance calculations in arguments, verified that your calculations do not actually give the hypothesed paths across Antarctica?
It's easy enough to do using a string and a globe. A great circle from Sydney to pretty much anywhere in South America doesn't get closer than a few hundred miles of the coast of Antarctica. From Perth, in far western Australia, to the eastern cities in South America, the great circle route does cross the Antarctic continent, but are there any flights between those locations?
3.What is more likely: that the Earth is round, or that people who have done the measurements believed that the Earth is round and made mistakes in the measurements simply because they were biased?
That one's easy. The Earth is
spherical. If there were consistent and significant mistakes in the measurements, shipping and air schedules would be consistently and significantly wrong, and fuel requirements would be consistently and significantly miscalculated, with potentially disastrous results. Do you have any information that such problems routinely occur?