How to prove the earth and moon isn't flat?

If you were suddenly in a time portal and sucked back to long ago when it was very uncommon (?) to assume that the earth and moon were spherical, how could you PROVE (using the technology in those times) that the earth and moon weren’t flat?

They would have a good argument too: You don’t fling off the earth as an object which has momentum flings off what is on it. You can never personally visibly see curvature from the ground, or if you can it is not enough to extrapolate a completely curved earth. Also, the moon couldn’t be observed in a set rotation because one side of the moon is always facing us.

I will say that the use of telescopes is okay for this exercise.

Would you permit the use of a gnomon?
Eratosthenes even figured out a pretty good circumference…not just that it wasn’t flat.

I think the idea that (educated) people in the olden days thought the earth was flat is a bit over-taught…

I got interested in the method that observes sailboats sink below the horizon as they get further away. We spend a week every summer at an ocean beach, and I’ve been looking for a nice example of this happening, and in over 25 years I’ve never been able to observe it. The horizon is always too indistinct and hazy for this to work. It sounds like it should work, but I don’t think it does.

Hmm, never heard of a gnomon, but I allow it. The basic idea is to not use tools which are more advanced (such as viewing earth from a spaceshuttle).

Napier, that sounds like a good idea. Perhaps if you looked through binoculars or a telescope at the ship as it was sailing away it would work? Also, while I believe this would provide evidence, it wouldn’t provide proof.

Traveling over great distances north and south, the stars have measurably different locations. What you see over the southern horizon in the north, will be overhead at the equator, and in the north when you reach the south. At the poles, there’s nothing in common. You can even measure the changes to calculate the earth’s radius.

I imagine that the sailboat-horizon approach worked better with two tall ships.

You climb up in the rigging to the main mast head and look out with a glass and you might be able to see the topgallants of the enemy. Meanwhile when you went down to the deck you wouldn’t be able to see the other ship. At least that’s how C. S. Forester described it :-).

The OP didn’t give a firm date; he just said your time machine takes you back to when most people assumed the world was flat. Surely there must have been some time at which this was the case, even if it was many thousands of years ago.

It wouldn’t need much technology at all. Just enough time money and patience to make the trip, and a careful enough eye and memory (or pen and paper) to note the changes.

I have personally witnessed this. Possibly I was just lucky to have good weather where I was.

An illustration from the early 1200’s shows that people were aware of this way back then. In that example though, it’s an observer in the crow’s nest of the sailboat who is observing the appearance of the port on the shore; he sees the port long before someone on the deck of the ship does. He would have had a much higher observation point than you or I might have had, which might have made the phenomenon even more distinct.

It works better with tall buildings, as they’re easier to distinguish from a distance. If there is a skyscraper close to the sea, that effect is easy to spot.

True, but if you go back too far, the question becomes meaningless, because they were unaware of how large the world is. Their awareness extended only as far as the local neighborhood, and the question of flat or round never even occurred to them. I would say that a belief in the world being flat presupposes an understanding of how big it is.

Assuming we’re not locked into some bizarre delusion that the sky is a hoax (I mean, who would do that?), here’s how I’d do it:

A time lapse picture of the sky (or just a carefully-measured and hand-plotted chart) over the course of several hours reveals the apparent paths of celestial objects to be (near enough) circular - demonstrating that something is rotating (doesn’t matter whether it’s the Earth or sky, for the purposes of this experiment).

A journey parallel to the arcs of those celestial objects, with an accurate clock, uncovers the notion of time zones - so the earth is rounded in an east-west direction, at least (but the Earth could still be a cylinder or cone or ovoid or something at this point)

A journey perpendicular to the arcs of celestial objects changes the angles through which they are viewed, establishing that the Earth is rounded in a north-south direction also.

From then on, it’s fairly simple trig to calculate the diameter.

Wasn’t the shape of the Earth’s shadow on the Moon during a lunar eclipse what some Greek used? A sphere would cast a particular shadow, a flat disc something else.

So, wait for a lunar eclipse.

I have yet to figure out copy and paste on this android, but look on wiki for round earth.

Trying to think this through: wouldn’t it work to get a decent watch, note sunrise and sunset times, then drive north a few hours and do the same thing?

Hmm, how about a variation on this xkcd strip? Instead of a cherry picker, just observe the sunset laying down on the ground, then get up really fast and observe it from standing height.

I think it proves the Earth is not flat, although the actual shape might be a sphere or a cylinder or an ellipsoid, etc.

Going back in time so far that people think the earth is flat is going to be going back before the invention of decent watches. Though I think that even in ancient times travellers had observed that at higher latitudes there was a much greater variance in the length of the day throughout the year.

Time traveling particulars: lets say you have travelled back in time with only a few simple items at your disposal. You come across a tribal group which sees you pop out of the wormhole. You talk with them, at which point you two disagree about the shape of the earth (or moon). They end up telling you that unless you can prove to them that these objects are spherical, they are going to cannibalize you. How do you prove it to them?

If you don’t know any methods that would work back then, while it doesn’t fulfill the time travel idea I am still interested in hearing how you can prove a spherical earth and moon even if the method is modern.

Attach a light to the top of the mast and one at the water line. Send it out at night.