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Does anyone know if physicists, mathematicians, or any other scientists have assigned an $X$, $Y$, $Z$ value for the known 3 dimensions we understand as 'space'?

If we were to attempt to build a 3D representation in a computer (of just our Galaxy for example), we would need to assign these axes for a coordinate system, so what I am asking is essentially if this $X$, $Y$, $Z$ has been used to map out space, and if so, is there an assigned 0 value for each axis?

I am not a physicist, nor a mathematician, so I know my understanding is limited, however I don't think it is too hard to imagine how we might simply map something out in a 3D application.

ProfRob
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Kalamalka Kid
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    The universe has no center (which is hard to understand for beginners). See Did the Big Bang Happen At A Point ?. – StephenG - Help Ukraine Nov 29 '22 at 22:34
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    See https://en.wikipedia.org/wiki/Astronomical_coordinate_systems & https://en.wikipedia.org/wiki/Galactic_coordinate_system & https://en.wikipedia.org/wiki/International_Celestial_Reference_System_and_its_realizations – PM 2Ring Nov 30 '22 at 02:35
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    Most star catalogs are based a spherical coordinate system. This is convenient because, while we know the position where any given object appears in the sky with great precision, we have much less certainty about the distance to most objects. If we mapped celestial objects using Cartesian (x, y, z) coordinates, then the uncertainty in the distance to an object would affect all three of its coordinates. But with a spherical system, we can write down precisely in which direction to point our telescopes to see it. – Solomon Slow Nov 30 '22 at 02:35

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For problems in our own Galaxy then we use a set of Cartesian 3D Galactic coordinates. This coordinate system is centred on the Sun and is measured such that positive $X$ is towards the Galactic centre, positive $Y$ is orthogonal to this, in the plane of the Galaxy and in the direction of Galactic rotation. The $Z$ coordinate is perpendicular to these and points out of the Galactic plane in the direction of the north Galactic pole.

This actually makes it a left-handed orthogonal coordinate system. Further details can be found here.

ProfRob
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For convenience, space scientists assign "north" to the direction pointing "up" out of the plane in which the planets orbit the sun.

But the way our universe is fundamentally constituted admits no special or privileged directions or locations anywhere in space i.e., there is no "north" or "south" to the universe as a whole, and no unique "center" at which to place the origin of an (x, y, z) coordinate system either- since the universe has no geometric center anywhere.

We can still assign directions in space which can be used by astronomers to identify the locations of points of interest, but those convention directions are entirely arbitrary.

niels nielsen
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  • Thanks for your answer. Is there a shared coordinate system used then by astronomers that would help them show other where objects are located in space? – Kalamalka Kid Nov 30 '22 at 01:57
  • Yes there is, but I do not remember what it is called. – niels nielsen Nov 30 '22 at 02:34
  • Of course, the plane of the orbit of the planets makes about a 60°-ish angle with the galactic plane. And each galaxy has an arbitrary orientation as far as we know. – John Alexiou Dec 01 '22 at 01:38
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No, even if the universe were only a three-dimensional spatial space, it would be represented by a Euclidean Space, which, mathematically, is an Affine Space. That is a set of points in $\mathbb{R}^3$ together with a 3D vector space of displacements between those points. There is no origin of space.

Of course, our universe is actually a 4-dimensional spacetime. This must be represented as a 4D manifold. A manifold is a generalization of the affine space: a set of points, which in any small neighborhood can look like $\mathbb{R}^4$, together with a vector space at any point (the tangent space). Again there is no origin, or indeed any preferred set of coordinates (axes).

Ben H
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