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The term instability region and similar terms are used for a region (range of radii) around an astronomical body where an orbit around it would be unstable due to one or more additional orbiting bodies. The term is particularly used for a region surrounding multiple bodies in orbit, such as a binary star in a fairly close orbit: within a region close to the pair, a planet orbiting the pair would pass close enough to an individual star to significantly affect its orbit. This could be an effect that would immediately result in a significant change to any such orbit, or could be a secular instability: a small change to each orbit that would eventually lead to a drastic change.
Instability is a common phenomenon in physics and undoubtedly the phrase instability region (and similar phrases) are used for instances not related to the above. There is a strip-shaped region of the H-R diagram termed the instability strip because stars plotted within that region are generally unstable.