Help with the color of a star cluster

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SUMMARY

The discussion focuses on calculating the B-V magnitude of a star cluster using the B-V values of individual star types, specifically F and K types. The user derived a formula for magnitude but encountered discrepancies when applying it to B-V values. Attempts to average luminosities and subtract B-V values from different star types yielded results that were still inaccurate. The user seeks clarification on the correct procedure for determining the B-V of a cluster from its constituent stars.

PREREQUISITES
  • Understanding of B-V magnitude and its significance in astrophysics
  • Familiarity with stellar types, specifically F and K stars
  • Knowledge of luminosity calculations and averaging techniques
  • Basic grasp of astronomical formulas and their applications
NEXT STEPS
  • Research the formula for calculating the B-V magnitude of a star cluster from individual star B-V values
  • Study the properties and differences between F and K type stars
  • Explore methods for averaging luminosities in astrophysical contexts
  • Investigate common pitfalls in B-V magnitude calculations and how to avoid them
USEFUL FOR

Astronomy students, astrophysicists, and anyone involved in stellar classification and magnitude calculations will benefit from this discussion.

Astrofun42
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TL;DR
Trying to calculate color of cluster from given distribution of stars, can't seem to get it right.
I am working on a problem which asks for the B-V magnitude of a star cluster given N stars of type F and M stars of type K. I have values for B-V for both stellar types. I've derived a general formula for computing the magnitude of the cluster from the magnitudes of each star type, which worked just fine for the first part of the problem (not shown here).

When I try to use the same formula for B-V values, I get an answer that is way off the mark. I then tried averaging the luminosities to get the luminosity of a 'typical' star in the B-V band, and what it's magnitude would be, and got closer to the answer, but not quite there.

Since B-V stands for mB - mV, I thought maybe the question is asking for the difference of the two stellar types' B-V color (subtracting one B-V from the other), which gave me the closest answer, but still .07 magnitude away. Am I missing a basic concept here?

What is the procedure for calculating the B-V of a cluster from the B-V of its constituent stars? Nowhere in the given data are there values for MB, so I'm at a loss. Thanks for any help.
 
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You need to show your work, e.g. the formula derived.
 

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