What is the difference in magnitude between two stars with varying distances?

AI Thread Summary
The discussion centers on calculating the difference in apparent (m) and absolute (M) magnitudes between two stars with different intrinsic brightness and distances. One star is 100 times brighter than the other, but is located twice as far away. The relevant formula for determining the difference in magnitudes is m_2 - m_1 = 2.5 log(b_1/b_2), which connects apparent brightness to apparent magnitude. The challenge lies in applying the formula correctly, given the reverse scenario of known brightness rather than known magnitudes. Understanding this relationship is crucial for solving the problem effectively.
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Homework Statement


One star is intrinsically 100 times brighter than the other. If the brighter star is twice as far away as the dimmer star, what is the difference in their m values and their M values.



Homework Equations


None were given.



The Attempt at a Solution


The equation I've been using most frequently in this problem set is M + m = 5 - 5logd, but I'm not really sure how or even if I can apply it here, since this problem is reverse of what I've been given so far. Usually I have magnitudes and am asked to find the distance.

Any help you can offer will be greatly appreciated. :smile:
 
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The difference in magnitude between two stars given their brightness is thus:

m_2-m_1=2.5 \log(\frac{b_1}{b_2})

This relates to apparent brightness and apparent magnitude.
 
Thanks for your help!
 

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