Cepheid Variables and the Small Magellanic Cud

[Berdi]

Homework Statement

The Galactic Cepheid variable δ Cephei has a parallax of 0.0033 arcseconds. An astronomer locates another Cepheid, with the same period as δ Cephei, in the Small Magellanic Cloud (SMC). If this Cepheid appears 11.5 magnitudes fainter than δ Cephei, calculate the distance to the SMC.

Homework Equations

$$m-M=5\log(d)-5$$

$$L=4\pi R^2F$$

$$m_{1}-m_{2}=2.5\log( L_{2}/L_{1})$$

The Attempt at a Solution

Well, I know the distance to the first Cepheid, as it is 1/Parallax = 303pc. I understand that the same period means the same luminosity, and that 11.5 fainter will mean that the m will be actually 11.5 larger, But I'm unsure how this will help me. Unless you say that $$m_{1}-m_{2}$$ is 11.5 and change the L's for 1/d^2 ?

 

[mgb_phys]

The absolute magnitudes of the two variables are the same (same period)
If one appears 11.5 mag fainter then it's obvisouly further away.

The first equation tells you have far away an object would have to be to be less bright by (m-M) magnitudes compared to an object 1pc away.

Another way to think of it. Work out the relative apparent luminosity of the two stars, then if the second one was 1/4 as bright it would have to be twice as far away.