Expert: Philip Stahl - 4/26/2006

Question
how fast do galaxies travel through space?

Answer
Hello.


Galaxies undergo a variety of motions, including rotation and recession (as part of galaxy clusters).

In the case of the latter (in what we call cosmological expansion), we are interested in how fast the galaxy-cluster is receding from us, according to Hubble's law. (Where the velocity of recession v = H d, H being the Hubble constant, and d the distance of the cluster).

We measure what is called the red shift (z), to find this out, where:

v (velocity) = c z

c = 300,000 km/s or the speed of light

For example, if the Hydrogen-alpha spectral line is found to redshift(e.g. displace toward the long wavelength end of the spectrum) by 20% from its normal position (at 6563 Angstroms, where 1 A = 10^-8 cm) we have:  z = 0.2

0.2 = v/c  or v =  0.2 c

In other words, its velocity of recession is two-tenths the speed of light, or 0.2 (300,000 km/s) = 60,000 km/s.

This means that galaxy A inside cluster B is moving away from us at that rate.

If the galaxy- cluster is found to be at great distances, a more complicated expression must be used - reflecting a redshift a lot higher. In this case, the velocity is:

v =  [(z^2 + 2z)/ (z^2 + 2z + 2)] c

For example, if the redshift z = 0.9 (e.g. the hydrogen line shifted 90% from its normal position) then,

v = 169,800 km/sec

or more than half the speed of light


Apart from the above motions, one can also examine the individual motions of galaxies, say as they occur within clusters. However, this entails very complex mathematics and determining the motion in particular planes - much as we do for the planets using celestial mechanics.

In general, however, one will assume some basic conservation principle first, then work from that. For example, assuming the total of kinetic and potential energy in the motion system is constant.

E.g.

H =  K  + V  =   p^2/ 2m   + V(x,y,z)


where K = p^2/ 2m is the kinetic energy (say for the galaxy or galaxies in the particular cluster) and V(x,y,z) is the potential energy for the same (x,y,z referring to 3-D space coordinates)

since the momentum p = mv

and v = v(x) + v(y) + v(z)   [defined in terms of components in differing space directions)

it then becomes possible to work these out for particular masses, m, and potential energies V.

One finds using this technique that the motions can range from perhaps 25 km/s to over 100 km/s. Again, the particulars must be worked out on a case by case basis - and the equations I have given represent only a simple sketch of what actually must be done.

For a much more exhaustive and detailed look, check out the chapter: 'Galactic Dynamics: The Dynamics of DIfferential Motions' in 'Principles of Stellar Dynamics', by S. Chandrasekhar, Dover Books.

Warning: this isn't for the mathematically "faint of heart"!

Unfortunately, the detailed study of galaxy motions is one that can't be divorced from quantitative treatments - since there is no one "generalized" motion, speed or behavior that applies uniformly to all galaxies.