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I'm trying to figure out WCS & just generic astronomical coordinates system, in order to better understand/use TESS data. I've been reading the mit docs, but I can't understand the reasons for these 2 representations:

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I do not really understand how they arrived at this 2 different projections. Is the one on the left obtained "as if" moving with the earth? This would be my guess, since ra/dec does depend on the position of the earth relative to the sun?

And what about the one on the right? Would it be centered on earth's lat/long at a given time? Or some sort of lat/long projection based on the sun?

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Neither projection has anything to do with Earth's motion. They just show different ways of defining locations on the celestial sphere. The locations of stars are more or less fixed on that sphere. The equatorial projection is divided into two hemispheres by the intersection of the plane of the Earth's equator with the celestial sphere. The ecliptic projection is divided by the plane of the Earth's orbit. The two planes are about 23.5 degrees apart. RA and dec for stars, and, for that matter lat and long, change very little from day to day - tenths of an arcminute. On a much longer time scale - 26 thousand years - they change considerably more.

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