Cephid Variables: Finding Distance from Parallax & Magnitude

[Unto]

This one has me stumped:

A galactic Cephid variable has a parralax of 0.002 arcseconds. What is it's distance in parsecs? A second cephid variable with the same period is 20 magnitudes fainter. What is the distance to this second star?

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Now I worked out that the distance to the former is 500pc.

Then using a flux equation I learned in lectures, I gathered that since the difference in the maginuteds is 20, one of the the stars must be 1E8 times brighter. So if we denote the second star as flux 1, the first star has flux 1E8.

But how then would I work out the distance to the second star of flux 1?

 

[mgb_phys]

If a star is twice as bright it must be 4x nearer (since light spreads out in an inverse square)

The link between apparent magnitudes and distance is called the "distance modulus"

 

[Unto]

Thank you for your informative reply, but I don't want to jump into this just yet.

I have values (which are know exact but are representative) in fluxes. I understand that distances are usually correlated with luminosities and apparent magnitudes. Do I just jump the gun and say 'since this star is 1E8 times dimmer, it must be so-so further away?

And the question states that the two stars also have the same period, what does this tell me?

Is there anyway where I can get the magnitudes of the stars? I would be gratified for some more help as I really like astrophysics.

 

[mgb_phys]

I have values (which are know exact but are representative) in fluxes. I understand that distances are usually correlated with luminosities and apparent magnitudes. Do I just jump the gun and say 'since this star is 1E8 times dimmer, it must be so-so further away?

Pretty much
You don't need to convert the magnitude to fluxes since the 'log' in the distance formula effectively does that. Since one star is 10^8 times fainter than it must be 10,000 times further away (assuming they are the same brightness)

And the question states that the two stars also have the same period, what does this tell me?

The period of a of a cepheid depends on it's absolute magnitude - so the same period means the same power.

Is there anyway where I can get the magnitudes of the stars?

If you have the period - yes there is a formula

 

[Unto]

Alas I was not given the period.

Thank you for your help.