Two stars – A and B, with luminosities 0.5 and 4.5 times the luminosity of the Sun, respectively – are observed to have the same apparent brightness. Which star is the more distant, and by how...

Two stars – A and B, with luminosities 0.5 and 4.5 times the luminosity of the

Sun, respectively – are observed to have the same apparent brightness. Which star

is the more distant, and by how much?

Asked on by cfoster4

1 Answer | Add Yours

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e-devam | High School Teacher | (Level 2) Adjunct Educator

Posted on

Stellar flux is the stellar luminosity divided by the surface area of the imaginary sphere it is situated in.

`F_A=L_A/(4pid_A^2)`

`F_B=L_B/(4pid_B^2)`

Therefore,

`F_A/F_B=(L_Ad_B^2)/(L_Bd_A^2)`

Since both of them are of same apparent brightness,

`F_A/F_B=1`

`1 = (0.5/4.5)xx(d_B^2/d_A^2)`

So, `(d_B/d_A)^2 = 9`  

`d_B/d_A=3`

B must be three times farther away than A.

Sources:

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