Calculate combined apparent magnitude of two stars

[Benzoate]

Homework Statement

What is the combined apparent magnitude o a binary system consisting of two stars of apparent magnitudes 3.0 and 4.0

Homework Equations

m-n=2.5 log(f(m)/f(n))

The Attempt at a Solution

I know m= 3 and n=4 ,or vice versa. I'm not sure what this problem means by combined magnitude. Do they mean I should add m and n together?

 

[dynamicsolo]

Homework Statement

What is the combined apparent magnitude o a binary system consisting of two stars of apparent magnitudes 3.0 and 4.0

Homework Equations

m-n=2.5 log(f(m)/f(n))

The Attempt at a Solution

I know m= 3 and n=4 ,or vice versa. I'm not sure what this problem means by combined magnitude. Do they mean I should add m and n together?

Refer to your other post on the magnitude of a variable star for the discussion on the magnitude system.

What you want to do is convert your magnitudes to intensities, since the intensities of the two stars can be added to give the total intensity (or brightness or power) of the pair. This leaves the question of what to use for a basis. You can pick any reference magnitude, say, zero, and compute the intensity of each star relative to the intensity of a zero-magnitude star. You would then add the intensities of each star and now compare the total intensity to that of the zero-mag star to find the magnitude of the pair.

 

[Benzoate]

Refer to your other post on the magnitude of a variable star for the discussion on the magnitude system.

What you want to do is convert your magnitudes to intensities, since the intensities of the two stars can be added to give the total intensity (or brightness or power) of the pair. This leaves the question of what to use for a basis. You can pick any reference magnitude, say, zero, and compute the intensity of each star relative to the intensity of a zero-magnitude star. You would then add the intensities of each star and now compare the total intensity to that of the zero-mag star to find the magnitude of the pair.

Is the equation for intensity, f(n)/f(m)=100^(m-n)/5. for example , can I tlet my reference magnitude be 0 and magnitude of m(1) is 3 and for the second intensity, reference magnitude n is still zero and magnitude of m(2) is 4. Once i calculated the each of the intensities for the two stars , I proceed to add the two intensities of both stars?

 

[dynamicsolo]

Is the equation for intensity, f(n)/f(m)=100^(m-n)/5

I think your book or instructor is still using f from flux, but yes, that will work. (I just corrected a missing minus sign in my post in the other thread.)

 

[dynamicsolo]

can I tlet my reference magnitude be 0 and magnitude of m(1) is 3 and for the second intensity, reference magnitude n is still zero and magnitude of m(2) is 4. Once i calculated the each of the intensities for the two stars , I proceed to add the two intensities of both stars?

Somehow I got only the first line of this post when I went to reply to it... (?)

Yes, that is what I'm describing. You should get intensities which are between zero and 1, since they are the intensities relative to a brighter star...