Answer:
Star A is brighter than Star B by a factor of 2754.22
Explanation:
Lets assume,
the magnitude of star A = m₁ = 1
the magnitude of star B = m₂ = 9.6
the apparent brightness of star A and star B are b₁ and b₂ respectively
Then, relation between the difference of magnitudes and apparent brightness of two stars are related as give below: [tex](m_{2} - m_{1}) = 2.5\log_{10}(b_{1}/b_{2})[/tex]
The current magnitude scale followed was formalized by Sir Norman Pogson in 1856. On this scale a magnitude 1 star is 2.512 times brighter than magnitude 2 star. A magnitude 2 star is 2.512 time brighter than a magnitude 3 star. That means a magnitude 1 star is (2.512x2.512) brighter than magnitude 3 bright star.
We need to find the factor by which star A is brighter than star B. Using the equation given above,
[tex](9.6 - 1) = 2.5\log_{10}(b_{1}/b_{2})[/tex]
[tex]\frac{8.6}{2.5} = \log_{10}(b_{1}/b_{2})[/tex]
[tex]\log_{10}(b_{1}/b_{2}) = 3.44[/tex]
Thus,
[tex](b_{1}/b_{2}) = 2754.22[/tex]
It means star A is 2754.22 time brighter than Star B.
