Astronomers detect if a star is a part of a binary star system?

They detect this when the unaided eye detects them as one light, then is revealed as two. Also, definition of Binary Star System: A binary star is a star system consisting of two stars orbiting around their common barycenter. Systems of two, three, four, or even more stars are called multiple star systems. These systems, especially when more distant, often appear to the unaided eye as a single point of light, and are then revealed as double (or more) by other means. Hope it helps!

this is true, assuming that the allele is completely recessive and incomplete dominance is not a factor.