What is the magnitude of a star that's 10 times brighter than a fifth magnitude star?

Question

asked Jul 4, 2019 235k views

1 Answer

Hanachronism · Answer 1 · 2019-07-10T13:22:11+0000

The apparent magnitude
m_i

of a star i measured with respect to the magnitude
m_(ref)

of another star is given by

$m_i -m_(ref)=-2.5 \log_(10)( (I_i)/(I_(ref)) )$
where
I_i

and

are the brightnesses of the two stars.

In our problem, the star used as reference has magnitude 5, so
m_(ref)=5

. We also know that the star i is 10 times brighter than the star of magnitude 5, so

(I_i)/(I_(ref))=10

therefore, we can rewrite the original equation as:

$m_i-5 = -2.5 \log_(10)(10)=-2.5$
And so, the magnitude of the star i is

m_i = 5-2.5 = 2.5