The moon is currently theorized to have been formed after a Mars sized planet collided with the young Earth.
The moon was mostly liquid when it formed, a result of the hot molten rock floating in orbit around Earth.
This rock started to clump together and its own gravity pulled it into a spherical shape. The Moon then took millions of years (possibly billions) to cool sufficiently for it’s core to become solid.
But even then it’s not perfectly round. Even the Earth isn’t a perfect sphere, it’s an oblate spheroid. The Earth bulges out a bit around the equator because the centrifugal forces of the Earth spinning countered Earth’s gravity a tad and made material collect there.
Spacetime doesn’t affect the shape of celestial objects but certainly gravity does. The more massive the object the more gravity it has. The force of gravity likes to pull it’s surroundings towards it’s densest point. If the object were a cube then the corners would be farther away from the centre of the cube than the sides of the cube are. So, over time, the cube flattens itself out to one bland surface, a sphere (or something much more round than a cube).
Imagine placing an ice cube (or really any other shape) on a stretched out piece of fabric. The fabric under the cube has now changed shape, but look now the fabric around the edges of the cube undergoes different stresses. If you want the forces to be equal on every spot along the edge you have to change shape to a circle, but first the ice has to melt.
That’s essentially what happens only on a way larger scale, the aforementioned fabric is being reshaped by gravity and it wants to be shaped like a circle (since gravity travels like a wave in all directions, thus making a circle). If the ice cube is solid it’s rigidity can allow it to widthstand some force, but if they get strong enough they’ll change it’s shape. Also if it melts (think lava) it will be easier to move.
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