A ship disappearing below the horizon is not at all important to the theory, anyway. That the earth is a sphere explains why the ship disappears. But to my knowledge this was never cited by Aristotle or any philosopher before him as evidence for the spherical shape of the earth. Nor has it ever been an important part of the theory since then. There is much stronger evidence.
There's a lot of misinformation out there about what led the Greek astronomers and philosophers to the sphere earth theory.
Here's a good example, with my comments in brackets:
https://www.aps.org/publications/apsnews/200606/history.cfm
External Quote:
It was around 500 B.C. that Pythagoras first proposed a spherical Earth, mainly on aesthetic grounds rather than on any physical evidence. Like many Greeks, he believed the sphere was the most perfect shape. [Mostly true.] Possibly the first to propose a spherical Earth based on actual physical evidence was Aristotle (384-322 B.C.), who listed several arguments for a spherical Earth [False. He's the first whose writings have survived. This was a team effort, and Aristotle himself was not an observational astronomer.]: ships disappear hull first when they sail over the horizon [False. In no place in Aristotle's surviving writings does he mention this. Nor did any of his contemporaries, that I know of.], Earth casts a round shadow on the moon during a lunar eclipse [He cites this idea, but it was probably originated by someone earlier.], and different constellations are visible at different latitudes. [Almost true. Aristotle cites the position of stars rather than constellations.]
This is what Aristotle actually wrote:
http://classics.mit.edu/Aristotle/heavens.2.ii.html
External Quote:
Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent.
Some people, it seems, are having a hard time visualizing why stars appear and disappear on a sphere Earth as you move north and south (not east and west). I haven't seen a good visual demonstration of this anywhere. The best thing I can recommend is getting a really big ball, the kind they have in a gym. Put your eye up to it really close at the top and then and move your head - without moving the ball - down across the surface. Notice what parts of the room are visible and not visible.
Here's a crummy little GIF I made:
The red line is your line of sight at your local southern horizon: things "below" the red line are hidden by the rim of the earth. Below the southern horizon, in other words. This is why
new southern stars become visible as you move farther south on the sphere earth. Just reverse this and you'll see why Polaris disappears. The rim of the Earth is hiding it.
The fact that the Greek astronomers of Aristotle's time had observed this phenomenon was the cruncher for them. From this time on the Greeks took it as fact that the earth is spherical.
This explains why Europeans, when they sailed for the first time into the deep southern hemisphere saw things in the southern sky at night that no European (that we know of) had ever seen before. Things such as the Magellanic Clouds.
https://en.wikipedia.org/wiki/Magellanic_Clouds
Ships are relatively small objects seen at relatively short distances. And the atmosphere can play tricks. At times you can see the ship quite clearly, at other times it is highly distorted. This muddies the waters.
You can sort of put a spin on the ship disappearing below the horizon phenomenon by citing largely fictitious quirks of refraction or fuzzy ideas about perspective, just because of the small scale involved. But how can you explain away the macro-phenomenon of new stars continually coming over the southern horizon as you travel hundreds or thousands of miles south?
The real proof to the Greeks was the behavior of the stars and it should be immediately apparent in our time. This phenomenon is tremendously well established through the experience of millions of people over history. It is also easily noted if you personally travel a significant distance to the north or south, (and you are capable of keeping track of individual stars.)
As has been pointed out, if you don't want to put in the effort of traveling hundreds of miles and observing stars. Rather than looking at ships, it's much better to look at relatively large things - e.g. islands - and change your altitude by hundreds of feet not just a few. You'll see big differences. Ships small, islands big.
But it remains that the stars are best.
I have to add one more thing. Another bit of misinformation: Aristotle himself made these observations of the stars and he originated the idea that this was proof of the sphere earth. False.
There were many astronomers in his time but almost all records have been lost. Aristotle's writings do exist and preserve the earliest extant argument. But this was a team effort and Aristotle was citing a general consensus of the time.
