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A common argument from flat earthers is that we ought to see totally different stars now vs in half a year from now.
I must also add that it might also be a serious question about why that is not the case from people who are just curious.
The idea is that we look in two different directions at those two times and places, something like this
The figure describes two points in time, half a year apart. The dotted blue line is the orbit of the Earth around the Sun.
I will here explain the problem with that figure and argument, first using figures, then by a little experiment you can do in your living room
The figures
The biggest problem is that we assume that the comparison is just at midnight at the two positions, but we can see stars as soon as it is dark enough. For many places, that is from just a while after the sun has set, to a while before the sun goes up. At those times, we definitely don’t look in the same directions as in the above figure, and we also have to remember that we can look in different directions than straight up. If you are in a very open area, say in a boat out far away from land, you can see about half the sky. Say you are close to the equator, then we could have a situation somewhat like this in the figure below.
So, say A is at a point just after sunset in the spring, and B is just before sunrise in the autumn. The field of view from those points would overlap quite substantially. If we instead look at the other ends of the two nights, we have almost the same situation.
All in all, quite much of the field of view between the two times will overlap. Actually, most of it.
The stars we cannot see in one of those points but in the other, and the other way around, are the stars too close to the sun in the sky. That would, for example, be the stars in the Zodiac.
If you live further away from the equator, like I do. Then, much of the sky above the opposite hemisphere will never be seen, and a large portion of the sky will be seen throughout the nights over the whole year. It is like the above situation, but seen from the side.
We then have a combined situation, where some stars are seen every night, some never, and some in parts of the year.
The living room experiment
Let us say the walls of your living room are the sky, and you are the earth. Now look, say to the north – and pretend the sun is behind you. You are now at midnight, and you can probably see about half the room if you move your eyes without moving your head. This will be like looking to the sky at midnight on Earth.
Now turn your head, say 80 degrees to the left or the right. Those positions will be like in the early night, or just before sunrise, but still in darkness. The light from the sun (say a lamp) will not reach your eyes. All in all, in between those two angles, you will have seen quite a large part of the room/sky. Now move in a little circle so that you are facing south, so that the “sun” is behind you to the north. Then you do the same experiment, turning your head 80 degrees to the left or the right. Yet again, you will see a large portion of the room, and very much of it would be overlapping what you saw “half a year ago” when you were looking north.
The idea behind all of this was to try to explain why you can see quite many of the same stars throughout the year, and that is even at points half a year apart.
There are a lot of apps for phones and computers that can show what you can see in the sky at different times, and all of them are built on the spherical earth model, and all of them fit the observable reality.
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