Question

Star A and star B appear equally bright in the sky. Star A is twice as far away from Earth as star B. How do the luminosities of stars A and B compare?

Answer 1

The answer to the question is

The luminosity of stars A is four times that of star B

Step-by-step explanation:

Flux (F) produced by a source of light is directly proportional to the brightness or Luminosity (L), and varies inversely to its distance d, that is
`F \alpha (L)/(d^2)`

Therefore if the two stars present the same flux then we have

`(L_1)/(d_1^2) = (L_2)/((2d_1)^2)` then crossing out like terms gives
`(L_1)/(1) = (L_2)/(2^2)` or 4·L₁ = L₂

The luminosity of star A is 4 times the that of star B