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If this earth were cubed shape would it be possible for Magellan to prove that the earth is cube-shaped without going to space and looking at earth?

It might seem strange to think that earth might be shaped like a cube. Remember I am not saying perfect cube but rounded cube at the edge. Do you remember Comet 67P/Churyumov-Gerasimenko where spacecraft Rosetta landed? It was odd shaped. So couldn't earth be odd shaped other than a sphere? If Magellan had to prove what the shape of the earth is like that then would it be possible for him to prove that earth is cube-shaped using his floating ship? I just want to know if it were possible.

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    $\begingroup$ No it's not possible. Why? Watch what happens to a lump of dough when a pizza maker spins it: the dough spreads out. Likewise, the Earth is large enough and spinning fast enough that it formed into a slightly squished sphereoid. $\endgroup$ – RonJohn Aug 30 '18 at 3:17
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    $\begingroup$ I feel like the physics aren't important here. I mean obviously there's no way this could exist, but I feel like this question would be better served if we ignored that aspect and focused entirely on the actual question. $\endgroup$ – Sydney Sleeper Aug 30 '18 at 4:46
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    $\begingroup$ You don’t need a ship and you don’t need to go anywhere. Just stay at home and look at the shape of the shadow that the Earth casts on the Moon during lunar eclipses. $\endgroup$ – Mike Scott Aug 30 '18 at 5:13
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    $\begingroup$ One important distinction is that even if the planet was somehow cube shaped, gravity would still pull towards the center. So from the perspective of the people on the planet, most of the world would be on an incline/slowly rising mountain until you reached the edge. The direction of gravity would be a little confusing in different areas, as relative to where you are standing it would make for an ever sharper incline until you reached one of the tips. $\endgroup$ – Tyler S. Loeper Aug 30 '18 at 12:43
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    $\begingroup$ People are having no fun at all (@RonJohn). We have tags that should be applied here: alternate-reality and alternate-earth. Telling the OP that their scheme won't work because their changed laws of physics don't match our laws of physics is mean-spirited on a site that celebrates flights of fancy and permits changed laws of physics. $\endgroup$ – JBH Aug 30 '18 at 17:38

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A planet-sized cube will collapse under its own weight into a sphere. The comet you mentioned has too little mass for that (and it would become a sphere if it was liquid). Our Earth is essentially a bubble of lava, with a thin solid crust. And it is the weight of the rock that turns lower levels into liquid lava.

So I will assume your cube planet is made of unrealistically strong materials that prevent a collapse (or it is a hollow artificial construct), the vertices of the cube will work like mountains and edges -- like mountain ridges. So you cannot sail from one face to another. Instead of planet-wide ocean, you will have lakes in the middle of each face. See Figure 1 here: https://arxiv.org/pdf/1206.3857.pdf

In fact, you might not be able to walk or fly across the edge, as earth-sized atmosphere will be nonexistent near the edges. Gas (just like a liquid) will try to form a sphere around the cube, and if there is not enough of it, the edges and vertices will stick out. In fact, you will have a ring of habitable land on each face, between the central lake, and the end of the atmosphere. In fact, you can have completely different atmospheres on each face.

If you have enough gas to encase the entire cube (see Figure 3), the atmospheric pressure will be a lot higher, giving you (I think) a Venus-like hot world

People will notice the change in gravity angle as they travel towards edges (Figure 2), but they will just think that they are climbing a mountain ridge. Fog and dust in the atmosphere will prevent people from seeing all the way across the face of the cube, so they will assume they live in a square-shaped valley surrounded by impassable mountains.

The first proof of Earth shape was The Eratosthenes Experiment (250BC): https://www.astro.princeton.edu/~dns/teachersguide/MeasECAct2.html It was based on the angle of the sun. On your cube, the sun will have the same angle with the surface. But just as Eratosthenes, your people will measure angle vs. up-down gravitational field line (see Figure 2). So exact replication of his experiment (with 2 points, North/South of each other) will lead to the same conclusion: the planet is round.

Repeating experiment with points East/West of each other might show that shape is not round, or doing the experiment with more than 2 points. I am too tired to figure out the angles :)

user535733's idea of measuring time between sunrize and sunset is valid, but requires a clock (renaissance technology) or lots of patience with hour-glass and more complex theoretical argument.

The "magellan" approach of travelling across faces requires oxygen tanks and breathing masks, or space rockets, or tunneling under the ridge/edge.

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    $\begingroup$ "And it is the weight of the rock that turns lower levels into liquid lava" The compression forces (and resulting frictional flows) certainly help, but the vast majority of the heat within the Earth comes from the decay of radioisotopes like potassium-40 and uranium-235. Given time, the radioisotopes would eventually run out, the Earth would cool, and the planet would end up looking similar to the moon or Mars. (Un)fortunately, the sun will expand, becoming a red giant and torching the Earth, well before this will have a chance to occur. $\endgroup$ – realityChemist Aug 30 '18 at 13:45
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    $\begingroup$ Traveling toward the edges will seem like climbing a mountain, but walking toward and across the center of a face will be weird. You'll travel "downhill" to the center and "uphill" once you cross it, but the ground will remain totally flat. You'll be climbing an ever-steepening mountain without ever seeing it rise in the distance. $\endgroup$ – Nuclear Wang Aug 30 '18 at 15:30
  • $\begingroup$ As you say, no matter the shape of the planet, around the centre of gravity, the atmosphere forms a sphere (the clue is in the name!) $\endgroup$ – Oscar Bravo Aug 30 '18 at 16:26
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    $\begingroup$ @NuclearWang - Not so. The ground will appear to rise as you approach the edges, and fall as you move away. "Horizontal" is perpendicular to gravity, not the local surface. $\endgroup$ – Paul Sinclair Aug 30 '18 at 16:56
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    $\begingroup$ I don't see how you can have totally separate atmospheres. While there isn't substantial mixing there will be some and over the gigayears that should keep them from being radicallly different. $\endgroup$ – Loren Pechtel Aug 31 '18 at 1:22
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You can figure out whether or not your planetary body is cube-shaped by simply recording the rise/set times of celestial bodies, including ordinary sunrise/sunset, along a line of latitude.

At Earth's equator, for example, the sun and moon and stars rise about one hour later as you move 1000 nautical miles westward. The change is gradual and consistent.

On a cube-shaped planet, one entire face will have (essentially) the same rise/set times. As you move 1000 nautical miles increments westward, the sun keeps rising/setting at the same time on your clock...and then suddenly comes up six hours later after you round to the next face of the cube.

That day (or night) you transit between two faces, the change in the sky should be quite apparent to a keen observer. The sun and moon move noticeably faster or slower than usual (or perhaps backward). If you transit onto one of the polar faces, the changes will be even more apparent.

This should be (and was) readily detected, recorded, and calculated by Bronze-age societies (at the latest). For Magellanic-era sailors and technologies, the shape of the planet should be (and was) old news.

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Is it a gravitational anomaly which caused the planet to form into a cube, or was it a cubical structure that is held by artificial means (such as alien design)?

1- Gravitational anomaly: The inhabitants of one "side" of the cube will think the Earth is flat, and all indications will seem to confirm that. they will be unaware of the cubical shape. When they venture to the edge and look over the horizon they will see a vertical world just below them. Water will behave the same, so oceans will form part of the cube surface.

2- Cube held by an artificial structure: The gravity will pull the mantle to form a sphere but something prevents it from doing so. On the other hand, nothing will hold the oceans that way. The ocean will flow and gather at the center of each "side" forming a dome. The observers on land will see it and will think this is a water mountain amid a flat Earth. The inhabitants will still think the Earth is flat, unless they look over the edges. On the other hand, as they walk towards the edge, they will feel the ground gets steeper as if they climb a mountain. This is the same force which would otherwise make the cube collapse into a sphere and the water converge to form a dome. That's also the reason why rivers will tend to flow towards the center -- following gravity.

One thing will not change in either case # 1 or #2: Lunar eclipses. They will all indicate the Earth is cubical: The shadow of the Earth on the moon will always be the projection of a cube's shadow. The outlines of the shadow will always be straight lines with straight or obtuse angles, and never the side of a disk or a circle...

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    $\begingroup$ Optically it will look flat... But gravitaionally, they'll probably think they're inside a bowl. This is because as you move away from the centre of a face, the vertical plumb-line starts to tilt - it's as if you're going uphill. The further from the centre, the more the deviation. Getting to the edge would be like reaching the top of a steep mountain ridge. Construction would be challenging on this world... $\endgroup$ – Oscar Bravo Aug 30 '18 at 16:31
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In the following I am not challenging the premise that the planet is shaped as a cube, just taking it for granted

The Earth is a cube, and there is somebody navigating on the seas direction East, until they reach the edge and move to the next face of the cube. What will they see?

enter image description here

Let's say they start from position A in the below picture: they see the sky limited by their local horizon, with the 3 red stars low on the horizon to the East.

This stays the same also when they are in B and check the position of the stars at the same time of the night.

When they reach C, however, they will notice that the 3 red stars are now high in their local sky, and when they travel further East the 3 red stars will be low on the horizon at West.

In this way, having knowledge of some projective geometry, they can figure out that the Earth is a cube.

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Oke, imagine the earth is cube shaped and has normal gravity. There would be no water at the 12 edges, since it would be pulled inward, assuming a bulbed form. Maybe the moon/sun gravity could mess things up a bit. But I think the boats would be stranded before going over the edge.

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    $\begingroup$ Hi there Gerhard, welcome to Worldbuilding.SE! If you haven't had a chance to check it out yet, don't miss the tour! This answer makes a good point, alluding to the general principles of hydrostatic equilibrium (which is the reason the Earth isn't a cube in the first place) and the geoid. Maybe you could expand this answer out, perhaps adding an illustration or a link (with context) to help show us your point. $\endgroup$ – realityChemist Aug 30 '18 at 13:36
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I'm going to take a different angle on this. First off: no physics. You're building a fantasy world - if you want an earth-like world that happens to be a cube, you've got it. To heck with traditional gravitation. Second: no obvious lunar eclipses. As people have pointed out, lunar eclipses could give the game away pretty easily. So we'll say that the planet is much larger than the moon (so it's merely a flat edge occluding the moon) or even that the moon doesn't lie on a similar orbital plane.

So, what now?

First up, the idea that our earth is a shaped body wasn't intuitive. It's simply too large for a person to get a sense of its scale through everyday life - for all intents and purposes, it functions as a flat plane. Erotosthenes proved it was round simply because observations didn't match the expected flat-plane earth. (Or in other words, Flat-Earth was the default theory until it was proven wrong.)

And here's the kicker: all the early observations that anyone would make would on your cubical planet line up to the world being simply a flat plane. Because, well, they're living on the flat planar side of a cube. The default theory would stay true for a lot longer, simply because observations would match up with the default flat-earth theory. Eratosthenes wouldn't observe two wells miles apart having different angled shadows; he wouldn't calculate the 'radius' of the earth because, well, it was 'obviously' flat.

It wouldn't be until travel over the edges that observations would start deviating from the "flat earth" theory. And, well, once someone makes it to an edge, it'd be blatantly obvious something weird was going on - regardless of how much 'cube rounding' you did. Keep in mind, on that flat world, there's no such thing as a horizon limitation. Someone in New York would be able to see the Rocky Mountains, or even the city lights from hundreds of miles away. (https://www.livescience.com/33895-human-eye.html) Once you take someone from that sort of world, and then plunk them down in a situation where there is a horizon effect? They're going to notice awfully quickly, even if the curve is over hundreds of miles.

The funny thing is, Magellanic explorers in our world were easily able to get their latitude from the position of the stars, but had problems getting their longitude due to not having accurate ship-board clocks. Magellanic explorers in the cubic world wouldn't use the stars for either latitude or longitude because the positions would be constant across the cube face, BUT it actually makes it more obvious what's going on to them. Since the stars would only change position as the earth rotated, once they saw any sort of non-standard rotation as they traversed the edge of the cube, they'd know something was up.

So basically, the short story: while the civilization hasn't reached the edge: they have no clue they're on a cube (because all their observations match a flat-world.) And once they reach the cube's edge, the jig is up: it's obvious what's going on.

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I don't think you'd be able to sail around this cube planet because gravity would pull all water to the center of the six surfaces. There would have to be a very deep ravine along an edge for water to accumulate there and be contiguous with the centers.

However, I think you would be able to deduce it's cube shape without having to squarumnavigate it. Consider the following graphic that shows the pull of gravity to center while showing the grade against the surface of the planet.

Cube Earth

You can quickly visualize that as you approach an edge gravity would have you feel an apparent parabolic slope, however, you would visually gain no vantage. Deduction would lead you to at least call this planet flat with a mysterious pull to a deep center about one half the earth's breadth long 1. If you could travel to any edge, assuming no issues with atmosphere, you'd quickly realize that you've rounded a corner and are perpendicular to where you once were, with the mysterious pull at the center being the only constant. The fact that you would have rounded only one quarter of a circle, instead of one half, would tell you that you are not on a flat earth, but a cube one.

Traveling to the edge would feel like the following, but remember that you would still see a relatively flat earth.

Cube earth feels like this

For this earth to exist, it would have to be very small or made out of stupendously sturdy material. Alternatively, gravity would have to operate differently, because without flight, it's easy to see that circumnavigation would be nearly impossible 2.


1. This "great pull to the deep center" would be truly mysterious to ancient peoples and I would certainly enjoy a fanciful story about how they discovered their planet was a cube.

2. This structure would seem that livable earth was deep within a chasm, surrounded by great mountains with no visible slope, yet you would feel that slope ever more greatly as you approached the peaks. Carving out planes perpendicular to gravity would have you feel as if you were walking on a wall, with the ground to one side of you and the sky to the other. Only significant excavation or flight would make surmounting the edge possible. Such an endeavor would possibly change words even, as you would "dig up and over the mountain".

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Assumptions assumptions. Liquid core. Blended materials in molten phase with graduate density due to gravity. Shape since birth of solar system. Note many Mons Olympus is impossible too if you assume a large earth liquid core. But smaller orb hit by high speed asteroid late in solidification of core...voila Mons Olympus. Support of such large structure is supported by super thick crust and core nearing solid.

So look at the question more as 8 equidistant steel supported super mountains with connecting ridge lines and the question is definitely more possible in a post-liquid core planetary phase. A more cubic planet is possible if little of the core is liquid and the materials distribution is neither graduated nor homogeneous by depth. That is weird collisions could beat a solid iron core squarish and later overlaid with lots of low density "crust". Layer on the light crust materials later after the molten mixing bowl phase. I'd think more engineered myself.

Yes there are limits to squareness or peaks supported by large solid natural steel. I say it would still be mostly round and gravitational subsidence making it more round every day.

Yes even distribution of gravity would weird. But again stop assuming homogeneous planetary density. Why not lesser density material at center of cube faces (crustal rock versus shallow beuried steel at edges and corners? Plus lack of liquid core might well mean no life since our magnetic field might not exist or be weird due solid steel/iron core.

But a more interesting question than simply saying Earth is the standard for all planets and the existence of all life. Nobody said this new Magellan was a human did they?

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Eclipses

A lunar eclipse is caused by the moon passing into the Earth's shadow. In our world, this is a disc that slowly covers and obscures the moon. If the Earth is instead a cube, then the way this works will be completely different. Folks will be able to work out the shape of the earth from the way the shadow progresses.

This doesn't actually require a ship, but it is quite reasonable that someone in the Magellanic era could figure it out in this way.

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On a curved earth, distant ships are first visible as their masts appear over the horizon. Since the curvature is constant, the distance at which you can first see a ship of a given height is the same no matter where on earth you are.

On cube earth, though, the curvature is not constant. The distance at which an approaching ship first appears depends on how close you are to the edge, and the speed at which the entire ship becomes visible after the mast first appears depends on the curvature of the edge. (The sharper the edge, the quicker the full ship comes into view.)

See the first graphic in @fredsbend's answer; I thought that was demonstrating a visual horizon effect at first.

This is also similar to @L.Dutch's answer.

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