## How are Cepheids used to measure distances?

Hello,

I've read about this in four different textbooks and in several websites, but I still don't get it: how are Cepheids used to measure distances? I understand that Cepheids are stars whose brightness varies periodically; that the longer their period, the brighter they are; and that different Cepheids have different brightness and periods.

But, how is that used to measure distances?

Thanks,
M

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 Note that the longer the period, the higher their intrinsic brightness. So you measure the period, and then from the relation between period and intrinsic brightness, you now know their intrinsic brightness - that is how bright they really are. Then you measure their apparent brightness - that is how bright they appear. Because of the inverse square law, if we have two objects of the same intrinsic brightness at two different distances, the one further away will appear fainter, just like with two identical street lights - the one further away will appear fainter. So if I know the intrinsic brightness and the apparent brightness, I can calculate the distance. Mathematically, the relation between the two is given here: http://en.wikipedia.org/wiki/Magnitude_%28astronomy%29
 That explains nothing, mate. They would need a Cepheid close enough for parallax measurement to use as a standard first.

## How are Cepheids used to measure distances?

 Quote by Cryptonic That explains nothing, mate. They would need a Cepheid close enough for parallax measurement to use as a standard first.
In fact, for many years, this point was the weakest link in the astronomical distance scale, since no Cepheids were close enough to use parallax to measure their distance. So historically other methods were used to get the distance to the nearest Cepheids and calibrate the relationship. Uncertainties in the calibration of the Cepheid relationship led to several re-assessments of the size of the universe. Try reading this:

However, this is no longer an issue, since the Hubble space telescope was now able to measure the parallax of Delta Cephei, the prototypical cepheid. See this:

http://en.wikipedia.org/wiki/Delta_Cephei

Mentor
 Quote by Cryptonic That explains nothing, mate. They would need a Cepheid close enough for parallax measurement to use as a standard first.
And there now 273 such objects. There should be many more when Gaia launches.

 Thank you, phyzguy. I wish textbooks were as clear and concise as you are.