How as an individual can I know if the Earth is a sphere or a flat disc? What experiment can I do that doesn't involve trusting information from a 3rd party that would prove what the geometry really is?
You can prove yourself that the earth is a sphere with some facts:
-You can't see the star Polaris from the Southern hemisphere because is at a declination of a bit over 89 degrees, if the earth was flat we should be able to see it anywhere.
-You can see the International Space Station and even predict where and when will passover of your city doing by yourself the calculations using the spherical earth model or use a website like (
https://www.heavens-above.com/PassSummary) I know this is 3rd party information but you will be able to see the ISS with your own eyes (I have done it many times).
-Buy a decent telescope, watch others planets and you will see how they are round, that is not a direct evidence but if you think like Flath Earth Society (
https://twitter.com/FlatEarthOrg/status/935644892721762305), you can also with the telescope watch the ISS and see that is not a airplane, a ball, a missile, Chuck Norris or whatever as some people says.
-Which ever hemisphere you live, watch the sky in the night and watch the direction of the rotation of the stars and call a friend of the opposite hemisphere and ask for the the direction there, you will see that they are opposite. I know is not just like that but that is the essence of the experiment
If anybody want to believe that the earth is flat its ok to have different opinions, personally I think that is a sphere or whatever is the name that scientist use