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Top Document: [sci.astro] Galaxies (Astronomy Frequently Asked Questions) (8/9)
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```        Joseph Lazio <jlazio@patriot.net>

By 1925, V. M. Slipher had compiled radial velocities for 41 galaxies.
He noticed that their velocities were quite a bit larger than typical
for objects within our Galaxy and that most of the velocities
indicated recession rather than approach.  In 1929, Edwin Hubble (and
others) recognized the simple relationship that recession velocity is
on average proportional to the galaxy's distance.  (His distance
measure was the apparent magnitude of the brightest individually
recognizable stars.)  This proportionality is now called "Hubble's
Law," and the constant of proportionality is known as the "Hubble
constant," H (often written "Ho," i.e., H subscript zero).

The Hubble constant also has the property of being related to the age
of the Universe, which undoubtedly explains some of the interest in
its value.  It is a constant of proportionality between a speed
(measured in km/s) and a distance (measured in Mpc), so its units are
(km/s)/Mpc.  Since kilometers and megaparsecs are both units of
distance, with the correct factor, we can convert megaparsecs to
kilometers, and we're left with a number whose units are (km/s)/km.
If we take 1/H, we see that it has units of seconds, that is 1/H is a
time.  We might consider 1/H to be the time it takes for a galaxy
moving at a certain velocity (in km/s) to have moved a certain
distance (in Mpc).  If the galaxies have always been moving exactly as
they now are, 1/H seconds ago all of them were on top of us!

Of course the proportionality isn't exact for individual galaxies.  Part
of the problem is uncertainties in measuring the distances of galaxies,
and part is that galaxies don't move entirely in conformity with the
"Hubble Flow" but have finite "peculiar velocities" of their own.  These
are presumably due to gravitational interactions with other, nearby
galaxies.  Some nearby galaxies indeed have blue shifts; M 31 (the
Andromeda galaxy) is a familiar example.

In order to measure the Hubble constant, all one needs a distance and a
redshift to a galaxy that is distant enough that its peculiar velocity
does not matter.  Measuring redshifts for galaxies is easy, but
measuring distances is hard.  (See the next question.)  The Hubble
constant is therefore not easy to measure, and it is not surprising that
there is controversy about its value.  In fact, there are generally two
schools of thought: one group likes a Hubble constant around 55
(km/s)/Mpc, and another prefers values around 90 (km/s)/Mpc.

When converted to an age of the Universe, H = 55 (km/s)/Mpc corresponds
to an age of about 19 billion years and H = 90 (km/s)/Mpc is an age of
11 billion years (again if the velocities are constant).

A measure of how difficult it is to determine the Hubble constant
accurately can be seen by examining the different values reported.  A
search by Tim Thompson <tim@lithos.Jpl.Nasa.Gov> for the period
1992--1994 found 39 reported values for H in the range
40--90 (km/s)/Mpc.

The linear relation between distance and recession velocity breaks down
for redshifts around 1 and larger (velocities around 2E5 km/s).  The
true relation depends on the curvature of space, which is a whole other
topic in itself (and has no clear answer).  The sense, though, is that
infinite redshift, corresponding to a recession velocity equal to the
speed of light, occurs at a finite distance.  This distance is the
"radius of the observable Universe."  Nothing more distant than this can
be observed, even in principle.

```

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