Question

A double star has two components of equal brightness, each with a magnitude of 8.34. if these stars are so close together that they appear to be one object, what is the apparent magnitude of the combined object

Answer 1

Assuming that the magnitude is additive, then you simply have to add the brightness four times. This is because each star has 2 magnitudes of 8.34. As a result, you have to add 4 magnitudes of 8.34. The solution is as follows:

Magnitude = 4(8.34) 
Magnitude = 33.36