 Sloan Digital Sky Survey

The purpose of this survey was to understand the implications of the spectrums of stars and galaxies.  We gathered data from 5 stars and 5 galaxies, from the Sloan Digital Sky Survey database:

The collection of stars and galaxies that I used for this activity can be found here.

The first step of this activity was to determine the velocity of the given stars and galaxies relative to us, according to their red shift.  To do this, we applied the formula v = c*((1+z)2 - 1)/ ((1+z)2 + 1), where v is the velocity of the object relative to us, c is the speed of light, and z is the red shift of the object�s light.  This is a very straightforward calculation; its results are included in a table with the results from the next step.

The next step was to calculate the distance to each object from us.  The formula for this is v = Hor, where v is the velocity of the object, r is the distance to the object, and Ho is Hubble�s constant, 75 km/(sMpc).  A Mpc, or a mega-parsec, is a unit of distance, as is a km, so they cancel out (with a very large, but constant, conversion factor), leaving Hubble's constant with units of frequency:
Mpc = pc * 1000
pc = 3.26 light years (ly)
Mpc = 3260 ly

ly = 3*108 (m*year)/sec  *  31,536,000 sec/year
= 9.4608 * 1015 m

3260 ly * (9.4608 * 1015 m) / ly = 3.084 * 1019 m

75 km/(s*Mpc) * (1000 m)/km * Mpc/(3.084 * 1019 m) = 2.432 * 10-15 s-1

So Hubble's Constant, in terms of frequency, is 2.432 * 10-15 s-1.  Plugging this, along with the objects' velocities (determined earlier), into a variant of Hubble's Law (v/Ho = r) gives the following table:

Stars:
 z k r 1) -0.0006 -180 -7.402 * 1016 2) -0.0006 -180 -7.402 * 1016 3) -0.0004 -120 -4.935 * 1016 4) -0.0003 -90 -3.701 * 1016 5) -0.0001 -30 -1.234 * 1016

Galaxies:
 z k r 1) 0.1328 37215 1.172 * 1019 2) 0.1225 34514 1.419 * 1019 3) 0.0177 5263 0.2164 * 1019 4) 0.1000 28507 1.172 * 1019 5) 0.1000 28507 1.172 * 1019

The last two galaxies may well be opposite sides of an Einstein ring; they are very nearly identical, yet they are slightly separated in space.  I don't know what degree of similarity objects are prone to having, but four identical significant figures does seem a little improbable, especially given their proximity.

In answer to the last question for this assignment, it is possible to classify galaxies by their spectra.  The obvious classification scheme is by their red shift; this shift, as has been shown above, relates directly to their distance from us.  To choose a different classification scheme, just to make things interesting, I'll classify them by average variation from the standard spectrum.  Most galactic spectrums stay reasonably close to the standard spectral curve, though their curve is not always centered where we would expect because of red shifting.  But most galaxies do have many fairly dramatic spikes, and some even have regions where they don't seem to adhere to the curve at all; finding the standard variance from this curve could be a mechanism for classifying galaxies.  I don't have a mechanism at the present time for precisely calculating this area; at a rough estimate, I would give this chart:

 Galaxy Variance (1) Medium (2) Medium (3) Medium (4) Low (5) Low