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You should not be confident of that because it is incorrect. The universe is not at all likely to be a 3D sphere since it does not have a center or an edge. It might be infinite or it could (but is not likely to be) some unknown topology.Therefore I am confident that my planet is a little sphere surrounded by a massive sphere of space containing stars.

Also, to add to what @Bandersnatch correctly said, it is not a hard fact that the universe is flat. It is known to be flat to within pretty much our ability to measure it, and it almost certainly IS flat, but it is possible that it is not flat.

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There are three types of universe described by the Einstein field equations, called open, flat and closed. Which type you have depends on the average density of matter in the universe. Note that all of these are four dimensional structures, and while you may see them illustrated as sheets of paper or the surface of a beach ball this is because drawing 4d structures always requires some simplification - in this case to just 2d. Don't mistake such sketches for the actual models.So what is all this nonsense about the universe being flat?

In open universes initially parallel lines diverge, in flat universes they remain parallel, and in closed universes they converge and eventually cross twice before returning to where they started (the similarity to lines of longitude on a globe is not coincidental). Closed universes are finite in size but boundaryless (did I get the terminology right that time @Bandersnatch?) and can eventually collapse into a Big Crunch (depending on the dark energy content), but the other two are infinite in size and expand forever. Our best measurements suggest we live in a flat universe, but we could live in one of the others if the scale of the curvature is so large that the observable universe is too small a patch for us to detect the deviation from flatness.

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Earth is not a sphere

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Thank you phinds for your very knowledgeable reply. Although I think my statement 'therefore I am confident that my planet is a little sphere surrounded by a massive sphere of space containing stars' is actually not incorrect. I did not say that the universe was a 3D sphere. In the context of the rest of my post, I said that an observer standing at multiple points on the earth's surface and looking upwards sees a massive sphere of space in which are many stars, I said nothing about what may be beyond his sphere of vision. I am just trying to conceptualize the shape of the universe in the same way as I can conceptualize the shape of our solar system, which is a 3D structure of orbiting planets in space, of which plastic models can be made. Is it actually impossible to do this for the universe, even at just one moment in time?You should not be confident of that because it is incorrect. The universe is not at all likely to be a 3D sphere since it does not have a center or an edge. It might be infinite or it could (but is not likely to be) some unknown topology.

Also, to add to what @Bandersnatch correctly said, it is not a hard fact that the universe is flat. It is known to be flat to within pretty much our ability to measure it, and it almost certainly IS flat, but it is possible that it is not flat.

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Yes.Is it actually impossible to do this for the universe, even at just one moment in time?

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What you are talking about here is called theI am just trying to conceptualize the shape of the universe

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That's pretty much the definition of "flat" isn't it? The spatial part of the metric in the flat case is actually just Euclidian.It might have been better to call it a "parallel beams" universe. Parallel beams of light in a vacuum and no gravity stay parallel.

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Sure. I'm trying to help out the OP.That's pretty much the definition of "flat" isn't it? The spatial part of the metric in the flat case is actually just Euclidian.

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Thank you for indulging my anal-retentiveness. It is appreciated.did I get the terminology right

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I can see how theoretical that probably is but what is the point to which they return?initially parallel lines ....in closed universes they converge and eventually cross twice before returning to where they started

Is it a point in space or a point in spacetime?

If the starting point is Las Vegas with Sinatra doing a residence do the parallel lines return to knock off his hat or has he long departed along with his gang of entertainers and only the space remains?

Can the parallel lines be two beams of light or is this just a geometric model/construct?

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They're lines along a plane of constant cosmological time, so they're just circles around the (model) universe. They're exactly like lines of constant longitude on a globe, except there are three orthogonal directions you can draw them in, not two.I can see how theoretical that probably is but what is the point to which they return?

This is just geometry and the lines are spacelike. If you want to send out light rays they follow null paths, not spacelike, but you can do it. They may not have time to circumnavigate the universe before the Big Crunch (depends on the dark energy content), and even if they do then issues about "where will you be in several trillion years" do arise in that case. You would need to be a co-moving observer in a true FLRW model universe for the light paths to project onto spacelike planes as neatly as circles on a globe, but you can (in principle) see the back of your head in the far distance in a closed universe that is sufficiently long-lived.Can the parallel lines be two beams of light or is this just a geometric model/construct?

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