How do we calculate the magnitude of a system with binary stars?

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To calculate the magnitude of a binary star system, the individual magnitudes of the stars must be known. If there are multiple binary systems, the total magnitude can be derived from the individual magnitudes of all stars involved. The formula for combining magnitudes is used, taking into account the number of stars and their respective brightness. The discussion emphasizes the importance of knowing whether the system consists of one or multiple binaries. Accurate calculations depend on the specific details of the binary systems in question.
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How do we calculate the magnitude of a system composed by some binary systems of stars?
 
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You need to give us more information. *Some* binary systems? How many? Just one binary, or multiple binaries?

Do you know the magnitudes of the individual stars in the binary or binaries?
 
Yeah, suppose we know the magnitude of all the stars and that the number of binary systems is k (can be one or more).
 
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