There's an easy experiment anyone can do at or near their home to demonstrate to themselves that the earth is not flat.
You will need:
* A camera capable of long-exposure photography
* A tripod (or something to prop the camera on)
* A spirit-level
* A protractor, or some other way of measuring an angle
* A dark, clear night
* Something circular and of a good size, like a large plate or a record.
Point your camera directly at Polaris (or towards the south if you are in southern latitudes). Use the spirit level and the protractor to measure the angle above 'level' the camera is pointing. Note this value down. (NB: If you check on a map, you should see that the angle you measured corresponds fairly well to your latitude).
Now take a long-exposure photograph (or a sequence of long-exposure photographs and composite them) in order to capture star trails.
You will observe that the star trails are circular and concentric.
Now take your circular object (an LP record is ideal), place it on the floor, and take a photo of it from directly above (I'll call this 'on-axis'). You will observe that it appears visually circular.
Now move your camera off-axis, to the side, keeping the record centered in the viewfinder. You will observe the record no longer appears visually circular, but elliptical, and that this effect becomes more pronounced the further off-axis you move.
(Obviously it won't change colour. If it does, you have problems that extend beyond the scope of this experiment).
Bonus points: observe that not only does the record become visually elliptical, but its form is no longer visually concentric. This is difficult to see with the naked eye because our brains are accustomed to compensating for perspective. As you can see from the image below, however, a line drawn through the centre does not span the visually widest part of the record, and there are clearly more red pixels below the line than above it.
If you experiment with photographing the record from different heights and different distances off-axis, you'll notice that there is less distortion from moving (say) one foot off-axis when you are shooting from high up than if you move one foot off-axis shooting from lower down.
Recall the angle you measured when photographing Polaris. This time, aim the camera DOWN by that angle (since we're working on the floor. If you want to stick the record to the ceiling instead, knock yourself out. Not literally).
Without adjusting the angle of the camera, move the tripod or support so that the record is centred in the viewfinder. You have now created a simulation of what star trails close to Polaris would look like if you viewed them from a flat earth: elliptical and not visually concentric.
How the Round Earth model accounts for these observations while FE cannot.Recall that deviations off-axis that are small relative to the height above the record do not induce significant distortion of the circular appearance of the record. The key word here is 'relative'. In order for star trails to appear circular where you live, it must therefore be the case that your distance from the pole is relatively tiny compared to the distance to the stars.
But if that is the case, then on a flat earth it would be impossible to go anywhere and see Polaris anything other than directly or almost directly overhead. You can check this yourself with your record: you'll find that you can't get anywhere near your measured angle of Polaris without seeing significant elliptical distortion.
So how does the Round Earth model accommodate this?
Quite straightforwardly: in the REM, the deviation of Polaris from directly overhead is not induced by lateral distance from the pole (movement away from the axis), but by the fact that what constitutes 'overhead' is different at different latitudes. All locations on earth are negligibly distant from the polar axis when compared to the distance of the stars.
What if the sky were a dome?If the sky were a dome, we would still see elliptical distortion of star trails when shot from locations distant from the pole on a flat earth. The only difference is that they would deviate from being concentric in a different way.
Doesn't scale make a difference?No. A 20cm circle viewed from a height of 1m and 1m off-axis (ie, from an angle of 45 degrees) is visually identical (in that it would exactly obscure) a 200m circle viewed from a height of 1000m and 1000m off-axis. The experiment with the record is a valid representation of what star trails would look like on a flat earth with Polaris at the angle you measured from the horizon.
If the earth orbits the sun, why doesn't THAT cause Polaris to deviate from over the pole?It does - just not very much. Polaris is around 27 million times further away from earth than the earth is from the sun. Seeing the deviation of Polaris caused by the Earth's orbit is like trying to see something a kilometre away wobble by less than 1/13th of a millimetre - impossible with the naked eye, but detectable with the proper equipment. The deviation caused by the earth's rotation over the course of a day, however, is millions of times smaller than that and completely undetectable.
In any case, this doesn't matter as far as disproving the FE model is concerned. Circularity of star-trails at all latitudes implies that stars must be very, very distant compared to the viewer's distance from the pole. On a flat earth, this would mean Polaris would be directly or nearly directly overhead, everywhere on earth, which it manifestly is not.