If the observable universe is spherical and its radius is 45.7 billion light-years in all direction, that should make Earth the center of the observable Universe, so how did we find out that we are not?

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We *are* the center of the observable universe. However this is just the consequence of the limited speed of light, it doesn’t imply that we are the center of the universe as a whole.

We don’t know how big the universe is or our position in it for sure, but signs point to it being infinite and that would mean there is no such thing as a center. *If* the universe is finite then it might be possible we actually are at the center, but we couldn’t know it.

The observable universe == the universe. We’re the center of what we can physically see, but not of the whole thing

The Earth IS the center of the observable universe, but that’s more or less by definition: the part of the universe which can be observed is a sphere around the observer. Every object is the center of the observable universe at that point in spacetime; so any two objects will have slightly disagreeing definitions of “the observable universe.”

We are the center of the OBSERVABLE universe. But this is true for litterally any point in the universe. We have no clue about anything beyond that.

The universe expands faster than the speed of light. However, this does not mean that it expands outward from a single point. It actually refers to the fact that the space between things is increasing. Large celestial systems such as Galaxy clusters are bounded together but between such things the forces of attraction are too weak to over come expansion.

Because of this, everything is getting further away from everything else at the same point. At any point, everything is moving away from that point. But that point isn’t the center of the universe, just the center of what is *observed*.

One way to contextualize this is to imagine an infinite grid. In math, we use such a plane by labeling every point based on an x and y coordinate. The origin exists at point (0,0). That would appear to be the “center,” but it actually isn’t. This is just a reference point. In an infinite plane, there can’t be a center because you are never halfway to forever.

Now imagine that the distance for a coordinate to increase by one can be defined as one unit. If you move one unit in the ‘positive’ direction from the origin along the x axis, you are at point (1,0). The gridlines are along whole numbers, so the nodes (intersections) exist at regular intervals.

If a person stood at each point, they could look around and see other people. Everyone sees the same thing, regardless of where the stand, and are the center of what they observe.

Then, the grid expands. This happens so that the distance between each grid line is now two units, with people still at each node. From anyone persons perspective, everyone seems to be moving away from *them*. They all see themselves as their own origin point. The distance they can see is the same, but they can’t view as many people. If expansion continues they will eventually be too far from everyone else to see anything. Someday, we will be in that situation. But not yet.

TL;DR: the ‘center’ of the universe is relative, since every single point is the center of its *observable* universe.

Actually, the universe has no center. We know Earth is not at the *edge* of the universe but nothing in particular is at the *exact center.*