# 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

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?

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1 year 2021-09-04T13:08:45+00:00 1 Answers 32 views 0

The answer to the question is

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

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 $$F \alpha \frac{L}{d^2}$$

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

$$\frac{L_1}{d_1^2} = \frac{L_2}{(2d_1)^2}$$ then crossing out like terms gives $$\frac{L_1}{1} = \frac{L_2}{2^2}$$ or 4·L₁ = L₂

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