Questions: How many times brighter is a 1st magnitude star than a 6th magnitude star?

How many times brighter is a 1st magnitude star than a 6th magnitude star?
Transcript text: How many times brighter is a 1st magnitude star than a 6th magnitude star?
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Solution

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Solution Steps

Step 1: Understanding the Magnitude Scale

The magnitude scale in astronomy is a logarithmic scale used to measure the brightness of stars. A difference of 5 magnitudes corresponds to a brightness factor of 100.

Step 2: Calculating the Brightness Difference

To find how many times brighter a 1st magnitude star is compared to a 6th magnitude star, we use the formula: Brightness factor=10(m2−m1)/2.5 \text{Brightness factor} = 10^{(m_2 - m_1)/2.5} where m1 m_1 and m2 m_2 are the magnitudes of the two stars.

Step 3: Applying the Formula

Substitute m1=1 m_1 = 1 and m2=6 m_2 = 6 : Brightness factor=10(6−1)/2.5=105/2.5=102=100 \text{Brightness factor} = 10^{(6 - 1)/2.5} = 10^{5/2.5} = 10^2 = 100

Final Answer

100\boxed{100}

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