Question

Star A and Star B have different apparent brightnesses but identical luminosities. Star A is 10 light years away from earth and appears 36 times brighter than star B. How far away is star B?

Answer 1

intensity of a star is inversely depends on the square of the distance from the star

we can say it is given as

$\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}$

here we know that

$\frac{I_1}{I_2} = 36 times$

also we know that

$r_1 = 10 Ly$

now we will have

$\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}$

$36 = \frac{r_2^2}{10^2}$

$r_2 = 60 Ly$

so other star is at distance 60 Light years