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During the initial days of Covid pandemic I discovered my interest in astronomy . I found it by gazing at night sky near Sirius that Adhara was undergoing a significant wobbling motion . I thought that there must be a heavier body near it which will make it go around their common centre of mass.

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Yes it is a binary. According to its WDS entry, the companion is separated by 7.9 arcseconds, which translates to a projected separation of around 980 au. The orbital period would last millennia: according to Jim Kaler it would be at least 7500 years. Needless to say, this is far too long to see it wobbling. The wobbling you saw was likely due to atmospheric conditions or movement in your instrument. Given the relative scale of a binary star system and the distances to the stars, any binary star that orbits fast enough to be perceived as wobbling is going to be too compact for the size of the wobble to be visible to skygazers.

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