Which is really larger, Big Dipper or Small Dipper, in 3D 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.

Update: to those asking about which stars to consider, just choose e.g. the canonical 7 stars of each. But this question is less about one arbitrary number and more about which things to consider, e.g. to show beginners that a bright star is not always close (and the other way around), and that size can be different in 3d than our arbitrary 2d-perspective.
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 &lt; 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.

Source:


Small Dipper stars
Big Dipper stars


Useful resources:


Big Dipper 3D model