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

`(I_1)/(I_2) = (r_2^2)/(r_1^2)`

here we know that

`(I_1)/(I_2) = 36 times`

also we know that

`r_1 = 10 Ly`

now we will have

`(I_1)/(I_2) = (r_2^2)/(r_1^2)`

`36 = (r_2^2)/(10^2)`

`r_2 = 60 Ly`

so other star is at distance 60 Light years