@ItIsFlat said in #1:
> Why is everybody denying it, it is obvious.
The only thing that is obvious is that the surface of the Earth APPEARS nearly flat locally. By locally I mean from altitudes much smaller than the radius of the Earth R (≈6371 km). We usually experience Earth's surface from altitudes of well below a single kilometre (0.016% of R).
From such low altitudes the Earth's (small, local) curvature is nearly unnoticeable to the naked eye, but you can still measure it in carefully performed experiments (go out on a clear day and observe landmarks on the other shore of a 10 km long lake from different elevations above the water).
This is to be expected. Any continuous curved surface in three dimensions appears nearly flat locally (when zooming in a lot). It's the same with continuous functions (or curves in two dimensions), the more you zoom in the straighter they appear until you're so close that you can barely distinguish the curve from a straight line.
The global curvature of Earth can also be demonstrated with relative ease:
At solar noon (around "midday") on the vernal equinox (20th of March) simply measure the angle (of elevation) of the sun at a minimum of three different locations (along a single line of longitude of your choosing). This is an experiment heavily inspired by Eratosthenes of Cyrene (c. 276 BC – c. 195/194 BC).
Assuming the Earth to be perfectly flat you can use basic trigonometry (a bright kid in middle school could do this) to derive the height of the sun (in terms of a pair of measured elevation angles) above the assumed flat Earth.
If the flat Earth hypothesis were correct, the height derived should yield the same result regardless of the pair of locations (or rather pair of angles) used to derive it. The sun can only have one unambiguous height.
However, when you actually do this experiment you find that each pair of measured angles predicts a different height of the sun, the observations are incompatible with the flat Earth hypothesis. The nearer one of your locations is to the north or south pole, the more ludicrous the predicted height of the sun becomes (because the elevation angle becomes very shallow). Fixing the first location near the north pole you obtain predicted heights as low as 5 -10 km (where airplanes would crash into the sun) and all of the secondary locations disagree not only about the exact height of the sun, but also on where (above which country) it's currently located.
By contrast, assuming a spherical Earth of radius R ≈ 6371 km with a distant sun one expects (from basic geometry and the fact that light rays from the sun are very nearly parallel to each other) that the observed elevation angles of the sun should be 90º minus the observer latitude. And that's almost exactly what is indeed observed:
Greenwich (UK, Greater London: 51.48ºN 0.00ºE):
Greenwich (on the vernal equinox: 20th of March) at solar noon (12:07 UTC):
2023: angle of elevation 38.4º
2024: angle of elevation 38.7º
2025: angle of elevation 38.6º
2026: angle of elevation 38.5º
2027: angle of elevation 38.4º
Average elevation angle of the sun: 38.52º
Expected value from 90º minus latitude: (90 - 51.48)º = 38.52º
Relative error: 0%
Gavarnie (France, Hautes-Pyrénées: 42.74ºN, 0.01ºW):
Gavarnie (on the vernal equinox: 20th of March) at solar noon (12:07 UTC):
2023: angle of elevation 47.1º
2024: angle of elevation 47.4º
2025: angle of elevation 47.3º
2026: angle of elevation 47.2º
2027: angle of elevation 47.1º
Average elevation angle of the sun: 47.22º
Expected value from 90º minus latitude: (90 - 42.74)º = 47.26º
Relative error: 0.085%
Calpe (Spain, Alicante: 38.65ºN, 0.04ºE):
Calpe (on the vernal equinox: 20th of March) at solar noon (12:07 UTC):
2023: angle of elevation 51.2º
2024: angle of elevation 51.5º
2025: angle of elevation 51.4º
2026: angle of elevation 51.3º
2027: angle of elevation 51.2º
Average elevation angle of the sun: 51.32º
Expected value from 90º minus latitude: (90 - 38.65)º = 51.35º
Relative error: 0.058%
The spherical Earth hypothesis agrees very well with past and future observational data.
Data from
www.timeanddate.com/sun/ – a trusted website – but feel free to check that it's correct yourself.
If you're interested in the calculation showing that these angles are inconsistent with each other assuming a flat Earth, let me know.
Have a nice day on this beautiful planet of ours :-)