It was suspected thousands of years ago that the earth is spherical, or geodesic to be precise. A papyrus from 230 B.C. Tells us what gave them the idea, and how we can improve on their work to form a conclusive proof:
Eratosthenes Finds Reasonably Accurate Diameter of Earth.Alexandria Eratosthenes peered into a well here, at noon, and came up with the diameter and
circumference of our planet! The summer solstice, the Sun and a trip to Syene was all it took...........
Here is the experiment: http://outreach.as.utexas.edu/marykay/assignments/eratos1.html
Two wells or (alternatively two sticks) actually does not prove the earth is round because it does allow for a tiny sun very much closer than the moon to the earth, to be possible. We now know that isn't the case so we can use two wells or sticks, but it's cheating because the ancients never knew this.
To prove it conclusively you actually need the geometry of three wells or sticks. By doing three in a line and three in a triangle. Too much trouble?
BUT NOTE: still DISPROVE the small sun theory using two sticks or wells, because using geometry and shadows you could eliminate the "close to earth" small sun theory, and taking the distance of the required near sun, calculate the shadow angles and zoom the sun further away until it's far enough to match the known modern distances between your chosen cities work backwards. So it's still possible to ultimately prove it using two, and more mathematics but technically speaking the ancients never had that information. Nowadays we can easily just reset the odometer of a car or use GPS or maps.
You can cheat using a cell phone by phoning a friend a few hundred kilometers to your West and timing the gap between the sun disappearing over your horizon (on the shore of a lake, or ocean to guarantee eliminating hills and valleys unless the friend is very far away)
And here is a slightly more complex one by an Islamic scholar in the 11th century.
How Al-Biruni Calculated the Circumference of the Earth Using a Mountain in the 11th century:
Another aspect Flat-Earthers struggle to explain is timezones, how it can be midnight somewhere and midday somewhere else, and orbiting satellites and the space station you can view with your telescope.
We saw from our first example that the angles don't correspond to the mathematics, let alone the problems the below invokes refuting gravity etc. It also can't account for complete darkness and relies on a domino effect of requiring everything from the moon landings to orbiting GPS satellites. broadcast satellites, the space station etc being fakes. Its a very needy and unrealistic chain of hundreds of refution points requiring every science discipline, every nations Space Agency, Broadcaster etc to be in on it.
They also don't explain how no moon or meteor, or planet can be anything but round over a certain mass, that way they fail to correctly understand gravity. It's a state of mind relying debate on every point of science having to have proof experiments done right in front of them otherwise they reject them. I have no issue with rejecting anything. Who am I to judge? But rejection of everything Scientific in an age of computers, cell phones and aereoplanes is apparently cognitive dissonance. There is a word for that. It's not skepticism, it's paranoia.