Question

problem 3
two stars have a magnitude difference of 0.97. how many times greater is the apparent brightness of the brighter star?
brighter star = 2.432 times brighter

Explanation:

Step1: Recall the formula

The relationship between the magnitude difference $\Delta m$ and the ratio of apparent brightnesses $b_1/b_2$ of two stars is given by $b_1/b_2 = 2.512^{\Delta m}$, where the brighter star is associated with $b_1$.

Step2: Substitute the value

We are given that $\Delta m = 0.97$. Substitute this value into the formula: $b_1/b_2=2.512^{0.97}$.

Step3: Calculate the result

Using a calculator, $2.512^{0.97}\approx2.432$.

Answer:

$2.432$