# Homework Help: Apparent magnitude of binary star?

1. Jan 18, 2008

### samblue

[SOLVED] Apparent magnitude of binary star?

1. The problem statement, all variables and given/known data
A binary star has a total apparent magnitude of 15.00. One component star is twice as bright as the other.

a) Show that the apparent magnitude of the brighter star is 15.44.

b) The fainter star has an apparent magnitude of 4.50 . How far away is this binary star system? Express your answer in kiloparsencs.

2. Relevant equations

I think I should be using: m-M=5log10(D/10pc)

3. The attempt at a solution

I have done a little research and know that a binary star system is two or more stars orbitting a center of mass. I am not sure how I link this with the question. It says one component star is twie as bright as the other but is this apparent or absolule magnitude?

2. Jan 18, 2008

### Shooting Star

You have to use the relationship between ratio of their brightness and apparent magnitudes.

b1/b2 = 2.512^(m2-m1).

3. Jan 18, 2008

### samblue

Thankyou SO much. I have an exam tomorrow and this question seems to come up un all of the past papers but I just couldnt do it.

However I still cant do the question. if I put b1/b2=2 and then ssub in values and rearrange I get : m2-m1=-.7525.

Where do I go from here?

Last edited: Jan 18, 2008
4. Jan 18, 2008

### mgb_phys

You also need m = -2.5 log ( b )
you know b1 in terms of b2, you know the total apparent mag
Rememebr brightnesses just add, but magnitudes don't!

5. Jan 18, 2008

### Shooting Star

If the suffix 2 refers to the brighter star, then,

3/2 = 2.512^(m2 - 15). You get m2.