Questions about patterns formed by group of prominent stars in the night sky.

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Determining planetary positions on the celestial sphere by Right Ascension and Declination

How would one go about determining the position of the different planets in our solar system with respect to the celestial sphere based on the following data set? Is there a practical way to calculate ...
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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 ...
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Why do the Pleiades look clearer when viewed indirectly?

I've noticed that the Pleiades look bright in the sky, but when I look directly at the constellation, it suddenly goes dim and it's more difficult to make out the individual stars. Why does this ...