Basically you need to convert between luminosities (which you can add) and magnitudes using
M−Modot=−2.5log10(L/Lodot)
Let's call the total luminosity L0 and magnitude M0 and the individual luminosities and magnitudes L1, L2 and L3 and M1, M2 and M3.
Then, you have the total luminosity of the system, directly
L0/Lodot=10−0.4(M0−Modot)
and as the sum of the components
L0/Lodot=(L1+L2+L3)/Lodot=10−0.4(M1−Modot)+10−0.4(M2−Modot)+10−0.4(M3−Modot)
Solving these equations for M3 gives
M3−Modot=−2.5log10left(10−0.4(M0−Modot)−10−0.4(M1−Modot)−10−0.4(M2−Modot)right)
I'm assuming you have absolute magnitudes, but you can rewrite the formulae in terms of apparent magnitudes using
M=m+5(1−log10d)
but I think the result then also depends on the distance.
Sunday, 19 July 2009
How to calculate magnitude of a star in a triple star system?
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