# How is distance measured to far away stars and galaxies?

What I need is an accurate description of the methods used to determine the distance to Andromeda. The Parallax method is for nearby objects as I presume. The red shift method applies, but how do you really determine a red shift? Maybe the radiation emanated from that object already has the wave lengths reach Earth? Or maybe it's travelling at a large speed from us? Or maybe its mass is greater than we think?

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The short--short versions is that we start with parallax and build outward finding new measures as we need them. Fun stuff. –  dmckee Nov 27 '12 at 17:37
Good luck, but my experience is that no amount of explanation, science or logic will make one bit of difference in the young Earth creationists literal belief in the bible. I know, I tried... –  FrankH Nov 27 '12 at 17:39
It's not clear to me that any of those are a perfect duplicate for this one or that we have a single all-singing all-dancing answer for this as yet (though this is isn't a bad stab at it). –  dmckee Nov 27 '12 at 17:56
You should start by taking a look at the (cosmic) distance ladder of standard candles: en.wikipedia.org/wiki/Cosmic_distance_ladder –  user12345 Nov 27 '12 at 22:25

There are several methods:

For closer galaxies you can use the cepheid variables as standard candles. There's a relationship between the periodicity and absolute brightness and from that you can find the distance.

For distant galaxies use redshift - you look for a known spectroscopic emission line e.g. the neutral Hydrogen hyperfine spin-flip transition at the famous 1420MHz. Measure the difference between the expected and the measured frequencies delta f - plug that into Hubble's law and it gives you the distance.

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You should start by taking a look at the (cosmic) distance ladder of standard candles: en.wikipedia.org/wiki/Cosmic_distance_ladder

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There doesn't seem to be a complete answer explaining redshift, I'll give it a go -

Redshift is the phenomenon where (in this context) light appears to be redder meaning it has a longer wavelength. This is related to the doppler shift but there are other ways that light can get redshifted.

This redshifting of light happens because of two reasons -

• The object under observation is moving away from us: This is because of the doppler effect. Since the object is moving away at some finite speed, the apparent wavelength of light is shifted by $$\frac{\Delta \nu}{\nu_{0}} = \frac{v_{obj}}{c}$$

where $\Delta \nu$ is the change in observed frequency of light, $c$ is the speed of light, $\nu_{0}$ is the original frequency of light, and $v_{obj}$ is the velocity of the object (relative to us).

• The universe is expanding : It is important to realize that this effect is not due to the doppler effect. The result is exactly the same viz., the wavelength of light is redshifted, but this is because spacetime itself is expanding. Even if the object is at rest relative to us (i.e., at any instant of time, where the rate of expansion of the universe is negligible) the light from it will still be redshifted, because of the expansion of the universe. Careful measurements of this effect yield numbers for Hubble's constant.

Now to answer how to determine a redshift : One is usually looking for a spectral line or a set of spectral lines to observe. Now, one can calculate and observe under controlled circumstances what the wavelengths of these spectral lines will be when they are at rest with respect to us, so we know what wavelengths to look for.

A kind of opposite of spectral lines are absorption lines (pictured). Absorption lines are what are used (to my knowledge) in astronomy. Now, one thing that you'll notice from the picture is that if one line is redshifted, then all the lines will be redshifted by the same amount. Therefore by measuring the relative spacing between the lines we can identify what species it is from our prior knowledge. And then by measuring by how much the observed spectral lines are offset from the expected values we can calculate the redshift of the object. Figuring out whether the observed redshift is due to the expansion of the universe or due to a doppler shift is a more subtle problem to tackle. But your question doesn't worry about that, so I'll leave it to curious people and Google to figure out.

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The parallax method is shorter than required for Andromeda and the red shift method is longer, than required for it.

The distance to Andromeda galaxy is measured by the method of standard candles: http://en.wikipedia.org/wiki/Standard_candle#Standard_candles

I think Cepheid variable starts are appropriate for Andromeda galaxy. The period of pulsing of those stars is related with it's maximal brightness, which allows to calculate the distance.