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When reading up on celestial globes it talks about handedness and that many celestial globes are reversed so that the constellations appear as they do from earth.

I'm trying to arrange some bright stars on an overlay of the earth, using Right Ascension and Declination as Long/Lat. Am I right in saying that RA and Dec are essentially viewing the stars from "within" an imaginary map, and if so would an overlay be more accurate if you mirrored the image, so that the overlaid map is effectively being viewed from "outside" of the mapped system?

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Yes, in a way.

If you are looking (up) at the celestial North Pole, and could see the meridians, you would note that the angle of right ascension increases clockwise.

enter image description here

On the other hand, if you were in space looking (down) at the North pole, you'd note that the lines of longitude increase anticlockwise.

enter image description here

This is a result of "looking up" or "looking down".

You could, I suppose, create a map of the Earth with the "sub-stellar point" (the point on Earth that is directly "below" the star") of each star (at a particular time/date) shown on the map. If you did this, the constellations would appear mirrored from how we are used to see them.

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    $\begingroup$ Thank you for this informative and clear answer. Are you aware of any lists of sub-stellar points for stars? I imagine these move and so might be based on J2000 or something if there are lists. If that's not an option, do you think another appropriate answer to getting a view from "Outside" could be to change any longitude from east to west and vice versa? That should create a mirrored arrangement that is otherwise identical I think? $\endgroup$
    – Harzard
    Commented May 15, 2022 at 16:12
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    $\begingroup$ They move very fast! They go all around the Earth every day. (because the Earth rotates) $\endgroup$
    – James K
    Commented May 15, 2022 at 16:17
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    $\begingroup$ By construction, on the spring equinox (21st March) the stars with a right ascension of 0h will be above the Prime Meridian at 00:00 UTC. As one hour is 1/24 of a circle or 15 degrees, stars with a right ascension of 1h will be above the 15 degree meridan and so on. The declension of the stars corresponds directly to latitude, a star with a zero declension will be above the equator etc. So simply reversing longitude may get the effect you want $\endgroup$
    – James K
    Commented May 15, 2022 at 16:42
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    $\begingroup$ That helps a lot, think I'm getting there now! Just a quick further question if you have a moment. The Wikipedia star entries come with maps that apear to be from an "Outside" perspective, based on your explanation above, am I reading it right? en.wikipedia.org/wiki/Delta_Crucis the map goes counter-clockwise in terms of RA. $\endgroup$
    – Harzard
    Commented May 15, 2022 at 16:56
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    $\begingroup$ Ah, but that is looking towards the southern pole, and around the south pole RA goes counter clockwise, and longitude goes clockwise. So that view of the southern cross is also "looking up" $\endgroup$
    – James K
    Commented May 15, 2022 at 17:00

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