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How can we tell if a star belongs to a star cluster or is in the space between the cluster and the observer?

Lambros Pantsios, Thessaloniki, Greece
All-the-stars
All the stars in a tiny region around the Southern Hemisphere globular cluster NGC 6397 are shown at left. Astronomers then plotted just those stars with proper motions similar to the globular cluster stars, shown at right. Using such a method shows a clear difference between the stars associated with a cluster and those that happen to lie in the same region. Astronomy: Roen Kelly, after Harvey B. Richer, et al.
Star clusters are families of stars of the same age bound by gravity and traveling together through the galaxy. The more of these shared properties we can measure for a star, the more confidently we can state it is (or is not) a cluster member.

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