Apparent magnitude of binary star?

[samblue]

[SOLVED] Apparent magnitude of binary star?

Homework Statement

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.

Homework Equations

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

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?

 

[Shooting Star]

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

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

 

[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 couldn't do it.

However I still can't 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?

 

[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!

 

[Shooting Star]

Thankyou SO much. I have an exam tomorrow and this question seems to come up un all of the past papers but I just couldn't do it.

However I still can't 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?

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

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