If this earth were cube shaped would it be possible during Magellanic era using a float ship to figure out that the earth is cube shaped?
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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The shape of the Earth is mostly a result of its gravity pulling its mass into the most efficient shape available. The oceans are also pulled towards the centre of mass, and collect on the lowest parts of the surface - covering a huge area to a depth of only a few miles because the planet is so smooth.
If Earth managed to be sufficiently rigid and hold a cube shape, its gravity would still pull on average towards its centre of mass, which would be the centre of the cube. Any water would pool in the middle of the flat faces of the cube to form roundish oceans. You could think of it as a spherical planet with several ridges reaching hundreds of miles high.
The ocean(s) would bulge outwards as if trying to form parts of a sphere. The gravity of the extremities of the planet would flatten the bulge a bit, but they'd be a lot deeper (and therefore narrower) than the current oceans. Unless there was far more water available, they would never reach the edges of the cube so a boat couldn't sail from one face to another.
As well as water, the atmosphere would pool in the lower regions, so five of the cube's faces are probably inaccessible to humans until they learn to make pressurised vehicles.
Your explorer might be able to determine the shape of the world by other means. Ancient Greek-style geometry could prove that the sea curves and the land doesn't, and as Peter Taylor pointed out, you could see the shadow of at least part of the Earth on the moon during a lunar eclipse.
So couldn't earth be odd shaped other than a sphere?
No. Something the size of the earth has significant gravity. There isn't material strong enough over large distances to result in anything more than a slightly wrinkled surface for an earth-sized object. Put another way, the vertexes of the cube would be very high mountains that wouldn't stay that way very long, let alone a mechanism to create such mountains in the first place.
If the earth were scaled to the size of a ping-pong ball, it would be much smoother than a ping-pong ball.
Note that even the significantly smaller moon is still much more rounded than a cube. The comet you are referring to has an odd shape that hasn't collapsed to a ball because it is so small. The adhesion of its material is much stronger relative to the comet's tiny gravity, than piles of rocks are relative to earth's 1 g gravity.
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While the other posts did already explain the issues with the cube-formed Earth, I just want to give a feeling of the dimensions we are speaking of.
Imagine that the centre of the cube's faces are at Earth's radius, about 6300 kilometres above the cube's centre (that is, the cube is sized so that actual Earth would be the inner sphere). Then the corners of the cube would be about 4600 kilometres high “mountains”. And even the cube's edges would be about 2900 kilometres high. For comparison, the space shuttle orbits Earth at merely 300 kilometres above ground. In other words, on this cube-Earth you could hike right into space.
Indeed, such a cube planet, if it could exist, would likely have six independent habitats, one on each face of the cube, and it would be impossible to go from one of them to the other with equipment from Magellan's era. Basically, you'd need a space suit just to walk there.
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