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Can an object not exactly sphere mapped by a spherical coordinate system?

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Can an object not exactly sphere mapped by a spherical coordinate system?

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It is well know that an earth is very close to a sphere, but not exactly. Can a spherical coordinate system describe it accurately using only two angle coordinates? People with some knowledge about curved surface may answer immediately: Yes, Of course, because the earth surface is still a simple curved surface with exactly the same topology as a sphere and with unique correspondence between a physical point and a pair of coordinates (Longitude, Latitude). Click to go to the beginning of the FAQ.

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