Binary Stars and Apparent Magnitudes

[LavaLynne]

Homework Statement

A binary star system at a distance of 85pc consists of two stars of equal luminosity that are so close together that they are observed in a telescope as a single image. If the apparent magnitude of the two stars combined is 10.7 what would be the apparent magnitude of just one of the component stars?[/B]

Homework Equations

m= -2.5 log(L)

m-M=5log(d)-5

[/B]

The Attempt at a Solution

I think I need to figure out what the two luminosities are added together?

 

[gneill]

Hi LavaLynne, Welcome to Physics Forums.

You should be able to work directly with the magnitudes if the sources are very close together (inseparable when imaged). You may have to do some fancy footwork with logarithms though.

Magnitudes are based on a logarithmic scale, but the actual logarithmic base is the (approximate) value 2.512.

A "linear" way to add values x1 and x2 that are based on a logarithmic scale of some base b would be:
$$b^{-x_{sum}} = b^{-x1} + b^{-x2}$$

That should be enough information for you to find a way to determine the magnitudes of your two identical stars.