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There must be some scientific reasons for why earth is a spheroid but what are they? If Earth would be a cuboid, Would it matter?

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Short version: The Earth is round because it was molten once. It would definitely matter if our planet were a cube, because gravity near the points would be off from "vertical."

Longer version:

Smaller objects in our solar system are indeed more oddly shaped - they often look like a bunch of small blobs stuck together. They slowly build up in size as bits of matter in our solar system collide and stick together (or, more rarely, slam into each other and knock parts off).

Earth formed from a large number of high-velocity collisions between small pieces of matter, creating a central body whose gravity drew in even more matter at higher speeds. These high-speed collisions released a lot of energy, specifically in the form of heat. The mixture of rock and metal that makes up our planet was thus so hot that it was molten.

Because gravity pulls equally in all directions at once, and gravity was the main force shaping our planet, Earth ended up as a sphere - every point on the surface is the same distance from the center and experiences the same gravity. Gravity acts equally at every different angle, so Earth is a shape that looks the same no matter how you rotate it.

As to your second question: If Earth were a cube, remember that gravity would still be pulling toward the center of the cube. If you're in the middle of one of the faces, things would be fairly normal, and gravity would straight down... but if you were near an edge, gravity would pull quite a bit off to the side! Taking a trip to the edge of a face would feel like climbing a mountain.

Notes:

I'm simplifying slightly in all of this:

  • We're not perfectly a sphere because Earth is also rotating, which gave us a little bulge around the equator.
  • Not every point on Earth has exactly the same gravity because of that and because of local variations in the composition of our planet.
  • Gravity at the edge of a cube face might not be directly toward the center of the cube; I'd have to do a bit of thinking and math to figure out the exact direction.

I hope that was helpful for you!

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    $\begingroup$ Being molten doesn't really matter. What matters is the strength of materials: that is, why the maximum height of a mountain on Earth is about 50,000 ft/16.000 m. A pile of rock higher than that will experience plastic flow from the force of its own weight. If an Earth-sized body started out as a cube, the corners would flow outwards, until the body became an approximate sphere. $\endgroup$
    – jamesqf
    Commented Apr 28, 2015 at 18:23
  • $\begingroup$ I'll agree with that. It helps to be liquid, certainly, but it's not required. $\endgroup$
    – Colin Fredericks
    Commented Apr 28, 2015 at 23:29