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I am considering setting my next D&D campaign on an earthlike but small planet. By "small," I am imagining a world that still feels vast, yet is circumnavigable over land and/or water with low or no magic, though probably with significant difficulty. I was thinking perhaps 1/6 earth radius, though I'm making that number up. Physical properties would be assumed to be earthlike (probably), due to greater planet density, and there would likely be a diversity of weather phenomena around the planet. As for geography, I am imagining a single large continent, as well as an archipelago of islands covering a large portion of the planet.

For further size context, I imagine that military conquest on the scale of Alexander the Great's campaigns, or maybe the Mongol conquest of Russia, should be able to seize the entire world. The setting is a traditional middle-ages style D&D world, with magic existent but not abundantly used.

Without significant magic, how likely is it that a landlocked city would realize that the planet is spherical and small?

EDIT: Naval technology is high middle ages, around 9th century. The continent is essentially a very large island, so sailing is necessary in order to circumnavigate.

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    $\begingroup$ Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! $\endgroup$ – Secespitus Dec 13 '17 at 21:43
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    $\begingroup$ Reminder to Close-Voters: The OP can't fix a problem if he is not aware of it. We are talking about a completely new user here, please give him some feedback! @Gday: This question currently has 3 votes to put it on hold temporarily because people think that your question does not align with the guidelines of the site. The problem is that we are not a discussion forum, but a Q&A aimed at providing clear answers to clear questions where answers can be somewhat objectively rated against each other. $\endgroup$ – Secespitus Dec 13 '17 at 22:12
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    $\begingroup$ Asking for general ideas is therefore off-topic. "Interesting" is also pretty subjective. What is interesting for you might not be interesting for me - how do you define this? And what is "string magic"? I have never heard that term. Speculating about cultures tends towards what we call "opinion-based" or "too broad", too. $\endgroup$ – Secespitus Dec 13 '17 at 22:12
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    $\begingroup$ Cultures are a huge topic and one where guessing is a valid option most of the time. For a start: are there some physical effects you would expect? Or some that you would like to see? This might help to focus the question on something answerable. You can later ask additional questions when you got the hang of the site. If you want general open-ended discussions I recommend our chat, once you have 20 reputation. If your question gets put on hold any edit from you will automatically send it to the reopen review queue. $\endgroup$ – Secespitus Dec 13 '17 at 22:12
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    $\begingroup$ Ok it's down to one question. If this isn't specific enough I'll give up on this post. $\endgroup$ – Gday Dec 13 '17 at 23:03
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On a planet this size, the roundness of the world will be far, far more obvious than it is on Earth, and it was known on Earth in classical times. It would be pretty obvious to any trading or sailing culture on this world.

The horizon will be only a bit more than a mile away. It's about 3 miles away for a 6-foot-tall observer on Earth; on a planet with 1/6 radius, it will be (square root of 6) or about 2.45 times closer:

https://en.wikipedia.org/wiki/Horizon#Distance_to_the_horizon

Therefore, the effect of ships disappearing over the horizon, hull first and mast/sails last (visible even on Earth) will be incredibly obvious here.

Also, the variation in day length and sun angle as one goes from place to place will be tremendously more obvious. One degree of latitude on this planet would be only about 11 1/2 miles, vs. 69 miles on Earth. (Eratosthenes used the variation in sun angle at different latitudes to calculate the size of the Earth in the 3rd century BC.)

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  • $\begingroup$ This is really helpful as far as naval societies are concerned, but what about for a landlocked people in the middle of the major continent? Would they still figure it out pretty quickly? $\endgroup$ – Gday Dec 14 '17 at 4:35
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As has been stated by @cometaryorbit and several commenters, the roundness can be discovered fairly easily even on land by observing the angle towards the sun.
Since you stated that this planet should be circumnavigable with reasonable effort, i think it is safe to assume that it has been done, adding further backup to the idea of he spherical planet.

But they would never discover that it was small.
Not because they couldn't calculate it's size, which they could feirly easily, but because they would come to a different conclusion: that their planet is perfectly normal in size. Just like we on earth typically think of our planet as normal.
To be more precise, because it feels normal to us, we generally don't think about our planets size at all. After all, none of us have ever been to a bigger planet. And while today we can easily look up the size of earth as compared to the other objects in our solar system, which should lead us to the conclusion that earth is fairly small, it normally doesn't, because neither does comparing a planet to a sun make very much sense, nor does comparing a rocky planet to a gas giant.

I think it is safe to assume that pretty much the same will happen on your world: The people in general don't think about their planets size. They will soon learn that there are other planets, and moons, and that other planets can be bigger, but snce their world is special (it's the one they live on, so it has to be, right?), comparing it to other planets simply doesn't happen.

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    $\begingroup$ +1 the concept of large and small in relation to planets is really only relevant to spacefaring civilizations who inhabit multiple planets. $\endgroup$ – adaliabooks Dec 14 '17 at 11:14

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