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If we take the convex hull of the 3D coordinates of the stars in Ursa Major and Ursa Minor: which hull has larger volume?

This is meant semi-humorous but we might also learn some interesting points from good answers, e.g. which metric to use when mass distorts space or how to measure with respect to frames of reference.

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You'll have to decide which stars to consider. Each constellation covers a defined region of the sky and extends all the way to the edge of the observable universe. Assuming you define a reasonable set of stars for each constellation (the ones forming the outline of the bear, or the ones that have been assigned names of the form Greek letter Ursa (Majoris|Minoris)), I seriously doubt that relativistic distortion of space is going to be significant. –  Keith Thompson Jun 9 at 20:08

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To calculate that you will have to build a 3D model based upon the distance of each of their stars and then calculate the resulting 3D object's volume. I know this may not answer the question, but I give the way to answering it. It's not an easy job.

Making a quick guess based upon the distances of the stars of both constellations in my opinion I guess the Small Dipper has a bigger volume since it's starts have bigger distance differences ranging from < 100 ly up to > 500 ly. In the case of the Big Dipper all distance are very similar since all stars come from the same open cluster. Their distance range between 78 and 124 ly.


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thanks, this is a good start –  eznme Jun 9 at 7:43

It's hard to say without some research, but I don't think the answer really matters much. Both constellations are chance alignments that have little or nothing to do with how close the stars really are to each other. It's not hard to envision a constellation composed of a few nearby stars and a few galaxies millions of light years away.

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Does not answer the question, only repeats it. –  eznme Jun 9 at 5:58
@eznme "I don't think the answer matters much", followed by why the answer doesn't matter much. It's a silly question, with no real relationship to the constellation (which is an artificial construct anyway), and the answer has no general application to any other constellations, and no connection to anything beyond the angular separation of these unrelated objects. –  Marc Jun 9 at 15:04
Then by all means downvote the question, or post a comment, or flag it if you think it doesn't belong here, or just ignore it. Answers are supposed to be answers. –  Keith Thompson Jun 9 at 20:10
"This question has no meaningful answer" is an answer to a question that has no meaningful answer. –  Marc Jun 10 at 0:04
@Marc that is not an answer. If you think this is not a proper question then, flag it or simply comment it. –  Joan.bdm Jun 10 at 6:13

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