QQuestionAstronomy
QuestionAstronomy
How bright is a magnitude + 3.0 star compared to a magnitude + 4.0 star?
A. 4 / 3 (1.333) times brighter
B. 10 times brighter
C. 2.512 times brighter
D. 1 / 2.512 times as bright
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Answer
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Step 1:Let's solve this step by step using the magnitude brightness relationship.
Step 2:: Understand the Magnitude Brightness Scale
- $$m_{1}$$ and $$m_{2}$$ are their respective magnitudes
The magnitude scale is logarithmic. The relationship between brightness and magnitude is given by the formula: Where:
Step 3:: Calculate the Brightness Ratio
\frac{B_{1}}{B_{2}} = 10^{-0.4(3.0 - 4.0)}
Let's plug in the values:
Step 4:: Solve the Calculation
\frac{B_{1}}{B_{2}} = 2.512
\frac{B_{1}}{B_{2}} = 10^{0.4}
Final Answer
The magnitude scale is designed so that a difference of 1 magnitude corresponds to a brightness ratio of 2.512.
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