Measuring Distance

http://en.wikipedia.org/wiki/Hubble's_law

Scrolling down a bit, you´ll notice that the Hubble constant is part of a linear relationship between recession velocity (that is, the velocity that an object is moving away from Earth) and the distance to that object. There are various problems associated with measuring these distance.

Something you´ll probably get introduced to fairly early on is a problem astronomers had a while ago - when looking at distances close (in our part of the Universe anyway) to us - the recessional velocity of galaxies with respect to Earth is dominated by gravitational effects from other galaxies that are close by. In these instances (most notably in our effects is the Local Group of 36 galaxies, all of which are to an extent gravitationally bound) the galaxies are infact moving towards each other because the gravity is strong enough to overcome the velocity from Hubble´s law.

These velocities (due to gravitational, other effects) are known as, perhaps unsurprisingly as peculiar velocities.

The best galaxies to measure then may be the ones farthest away, there are several methods and various problems in measuring these distances. Cepheid variables as you correctly mention is one method - essentially Cepheid variable is just a name given to a particular type of star that - for reasons you may not have to worry about - have a varying luminosity - that is the amount of light the stars output changes. This pattern of change follows a strict relationship with a particular period.

We can use what we know about this variation to calculate how far away the star is. Also worth noting is that the name Cepheid Variable isn´t really in any way significant, it only comes from the fact that the first star of this type happened to be known as Delta Cephei.

 

Once you feel confident that you know the HUBBLE PARAMETER (and a couple of other parameters relating to what cosmological model you assume) then you can take the observed redshift of a distant object and just crank out the distance. There is a neat calculator that does this at Ned Wright's website.

But the catch is, you first have to determine a reliable value of the Hubble parameter!!! For that you need real nuts/bolts nittygritty ways to measure distance. Then you compare those known distances to redshift and determine Hubble parameter which means basically, in effect, that you are calibrating redshift as a distance scale.

But first, to determine Hubble, there have to be other methods

HERE IS WIKIPEDIA ABOUT cosmic distance ladder
http://en.wikipedia.org/wiki/Cosmic_distance_ladder
they start out with basic (trig etc.) tools and use the nearby more basic method to CALIBRATE the method used for the next step further out.

for distances within our galaxy and to nearby Local Group stuff such as Magellanic Clouds (almost within our galaxy roughly speaking)
there are some methods using some form of triangulation and the Herzsprung-Russell (H-R) diagram. (also called "main sequence" fitting)
I think Ned Wright lists these and gives a thumbnail sketch at his website.

the simplest is just PARALLAX
http://en.wikipedia.org/wiki/Parallax
but there is also OPEN CLUSTER METHOD where you use a cluster of stars like the Pleiades, one that is moving towards or away at a rate you can tell by Doppler, and then measure perspective angles changing over time and do some trig.
H-R diagram shows that during star's normal H-burning lifetime (before red giant and end of life stuff happens) there is a simple relation between intrinsic brightness and color the bluer ones are brighter.

these basic nearby methods are used to CALIBRATE CEPHEIDS which are then used in the next stage
clusters of all sorts are used in a logical strategem you could call "cluster reasoning" that for example goes like hmmmm the magellanic cloud stars are in a bunch suggesting they are all the same distance, so if I pick out all the Cepheids in that bunch and notice a pattern relating between their fluctuation frequency and their APPARENT
brightness that will also imply a relation between their frequency and their real intrinsic absolute brightness (if we could determine it). then if I can just find a nearby Cepheid that I can tell the distance to, and measure its frq and determine ITS absolute brightness that will calibrate the scale and I will know how far the magellanic Cepheids are.

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the newer more jazzy stuff is the EXTRAGALACTIC part of the distance ladder

for starters, you find Cepheids in other galaxies, like Andromeda

then there is "cluster reasoning" where you see a cluster of galaxies and your commonsense tells you they are probably all the same distance (whatever that unknown distance is) and so you look for PATTERNS relating a spiral galaxy physical appearence and its apparent brightness----there is one called the Tully-Fisher relation

and then there are the TYPE 1A SUPERNOVAS which are a recognizable kind of supernova that can be observed in distant galaxies and which are theorized to be all roughly the same brightness----so that can be a "standard candle" for measuring distance.

and quite recently a new method was invented by BONANOS and friends which is called the ECLIPSING BINARY method, where you find a pair of stars that orbit each other in such a way that one of them comes in front of the other

http://arxiv.org/abs/astro-ph/0610923
Eclipsing Binaries: Tools for Calibrating the Extragalactic Distance Scale
A.Z. Bonanos
Review in proceedings of IAU Symposium 240, Editors W. Hartkopf, E. Guinan & P. Harmanec; 10 pages

"In the last decade, over 7000 eclipsing binaries have been discovered in the Local Group through various variability surveys. Measuring fundamental parameters of these eclipsing binaries has become feasible with 8 meter class telescopes, making it possible to use eclipsing binaries as distance indicators. Distances with eclipsing binaries provide an independent method for calibrating the extragalactic distance scale and thus determining the Hubble constant. This method has been used for determining distances to eclipsing binaries in the Magellanic Clouds and the Andromeda Galaxy and most recently to a detached eclipsing binary in the Triangulum Galaxy by the DIRECT Project. The increasing number of eclipsing binaries found by microlensing and variability surveys also provide a rich database for advancing our understanding of star formation and evolution."