# How do you measure distance to stars within the galaxy?

I know that for close by stars (<50 LY) we can use the parallax effect. And for distant galaxies we use red-shift (& hubble's constant). So how do we measure how far is a star lets say 50,000 LY from the earth?

I know I am missing something, I just don't know what.

How can we assume there is a relationship between red-shift and distance when the stars

• act like a (turbulent) fluid within the galaxy and
• can be moving in any sort of different manner?

Edit: It is a physics question, because I really want to know what is the star velocity model within the galaxy in order to use red-shift. My instinct tell me that stars move like a swarm within the galaxy with an overall rotation about the galaxy center of gravity (In agreement to the edited horowitz answer).

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Good question, but I think it'd be a better fit on the astronomy site. I'm not going to close it here, though, because it does have something to do with physics, and we're not really supposed to migrate questions to beta sites. –  David Z Aug 27 '11 at 5:58
The parallax is good to several hundred light years. Indeed I believe the longest measurements go out past 1000 light years now, though the error bars on them are staggering. –  dmckee Aug 27 '11 at 6:03
Those measurements were probably made possible by satellite astrometry, like the new Hipparcos satellite, en.wikipedia.org/wiki/Hipparcos –  Benjamin Horowitz Aug 27 '11 at 13:24
Possible duplicates: physics.stackexchange.com/q/24927/2451 and links therein. –  Qmechanic Jul 18 at 18:56

There are numerous distance indicators used for within the galaxy. The most common way is by using intrinsic magnitude. By knowing how bright an object would be if we were close, we can determine how far away it is by how dim it is. There are many types of stars where we have a rough idea of how bright they should be due to characteristics of the star:

1. Cephied Variables: The original type of variable star that was used by Hubble to determine the distance to the Andromeda Galaxy.

2. RR Lyrae Variable: Like the Cephied variable, but usually dimmer.

3. Type 1a Supernova: These guys, unlike the first two, are cataclismic variables. Essentially a binary white dwarf slowly accretes matter from its binary till it reaches the Chandrashankar Limit, after which point it explodes in a very characteristic way (since the mass at the time of explosion is roughly constant).

4. Main Sequence Stars: Generally less accurate than the first 3, there are some types of main sequence stars which are used to find distances in a similar way.

There are a few other ways we can measure distances:

Perpendicular Movement: For example there is a "light echo" from SN 1987A which is essentially light from the supernova interacting with dust around the old star. Since this echo should be expanding at the speed of light, we can tell how far away the nova is by the angular velocity of the light.

Relative Velocity in a Moving Cluster: (see dmckee's answer)

Tulley-Fisher relation: A relationship between the luminosity of the galaxy and it's apparent width. Can be used as a decent distance calculator.

Faber-Jackson Relation: Similar to Tulley-Fisher, relates luminosity with radial velocity dispersion rate.

The whole relationship between redshift and distance was in fact established by Hubble by relating distance to Cephied variables (I believe) with redshift. Later on it was made more precise using supernova, which are brighter and can be seen from much father away (I think recent supernova can be occasionally seen around Z=2, while Cephieds are all Z<1). Within a galaxy, redshift cannot be used directs since the "peculiar velocity," the velocity within the galaxy, completely overshadows the effects of universe expansion on which Hubble's Law is based. Redshift within the galaxy is useful for certain other techniques.

EDIT: corrected a few minor errors.

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Thanks for the answer, and I am in agreement, although I still don't see how a typical main sequence star can be measured for distance accurately. In the answers I am not looking at how far galaxies are (Tulley-Fisher, Supernova, Cepheid, etc), but how do we know for example that HIP 11062 is at 1347.75 LY from us? –  ja72 Aug 27 '11 at 14:57
Supernova and Cepheid are used in our galaxy. HIP is an abbreviation for the Hipparcos Satellite's Catalog which uses trigonometric parallax. –  Benjamin Horowitz Aug 27 '11 at 15:59
Main Sequence Stars: iopscience.iop.org/0004-637X/673/2/864/pdf/63948.web.pdf –  Benjamin Horowitz Aug 27 '11 at 16:08
@Ja72: Luminosity is an easy measurement. So is the color of a star. Once you have these two things, there is a known relaiionship between the star's color and it's mass. And there is also a known relationship between the star's absolute luminosity and it's mass, verified by observations on stars that can be ranged with parallax. Then, it's just a matter of using $I=\frac{I_{0}}{4\pi r^{2}}$ to find the distance to the star, where $I$ is the intensity of starlight on Earth, and $I_{0}$ is the intensity of starlight at some fixed radius from the star. –  Jerry Schirmer Aug 27 '11 at 16:11
To expand on Jerry's comment. We don't just use stars in parallax distance to calibrate the HR diagram, we also use stars in globular clusters and nearby galaxies (this is important because there are relatively few bright stars). That's why you keep getting answers about finding distances to nearby bound objects that are either outside the galaxy or are on the fringes of the galaxy: ranging these objects was needed to understand the luminosities of stars in general. The "ladder of distance" actual has some backwards steps. –  dmckee Aug 28 '11 at 23:09

One neat trick for middle ranges requires a dynamically bound system whose components have measurable proper motions. There are a reasonable number of globular clusters that qualify.

If you project those motions across the sky, they will appear to come together (to some approximation) in two places (one forward and one backward), and the directions of those are the direction of the real motion. Combine that with the measured line-of-sight velocity (from Doppler shifts of spectral lines), and you know he total velocity and can compute the distance.

For more distant compound objects (clusters and galaxies) still too close to use the cosmological scale (we can't use the Hubble relationship on anything in our local group because the velocities arising from dynamic binding are larger than the cosmological relationship)), one can use Cephied variables and Type 1a supernovae as standard candles. Measuring the distance to clusters and near by galaxies (the Magelenic clouds in particular) for finding distances inside the galaxy because it increase the total population of star we can use to calibrate the HR-diagram.

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But that is the point, that within the galaxy there is no smooth relationship between distance and velocity. A star at 2000 LY might be moving away from us, where as a star at 2200 LY might be coming towards as. In general there is movement around the galaxy, but the individual star variation must be at least of the same order of magnitude. –  ja72 Aug 27 '11 at 14:45
When you have a measure of the actual velocity (find from Doppler shift plus the diretion) and the proper motion (angular velocity and known from direct measurement if the pointing trick is to work) finding the distance is a matter of trigonometry. –  dmckee Aug 27 '11 at 16:02