The Expansion of the Universe:

(The Hubble Law)

Key Concepts:
1.  All galaxies beyond the Local Group are moving AWAY from us.
    Their spectra are all REDSHIFTED 
(c.f. the Doppler Effect).
2.  More distant galaxies are speeding away from us faster than nearby galaxies
           (THE HUBBLE LAW).

3.  Facts #1 and #2 imply that the Universe is expanding.

4.  There is NO CENTER to the expansion:  the Universe is infinite, AND is expanding everywhere.

5.  These facts imply that the expansion started a finite time ago -- roughly 14 billion years ago,
     in what has been dubbed THE BIG BANG.
6.  Asking what happened BEFORE the Big Bang is kind of like asking what is south of the south pole:
     time as we know it was not a linearly increasing quantity then.
7.  Given the Hubble Law, we can derive the distance to any galaxy, if we have a spectrum of it.

Still, astronomers ask the questions:
"Where did we come from? How did the universe begin?  Where are we going?  Why is the universe the way it is?  The questions are clear and deceptively simple, but the answers have always seemed well beyond
our reach -- until now."
                            --- Stephen Hawking, see Stephen Hawking's Universe

 The distances to galaxies can be found using "Standard Candles"
   A Standard Candle is any object we can identify whose ABSOLUTE MAGNITUDE or LUMINOSITY is known.
   So, if we can measure it's APPARENT MAGNITUDE, we can calculate it's distance.

   We've already talked about two
      (1) Cepheids  (pulsating stars, period of pulsation --> luminosity)
       (2) Type Ia Supernova (except for a small correction easily made from measuring how fast they dim, they are standard candles).
             The book calls Type Ia Supernovae "white dwarf supernovae" since they are not the kind of supernovae that ressult directly from massive star evolution, they are the type where a white dwarf accretes material from a stellar companion.

   There are a few other techniques, described in the text, E.G. the Tully-Fisher Relation, where you measure the velocity spread in the disk of a spiral galaxy and from that derive the luminosity of the galaxy.

2.  The HUBBLE LAW states that the Doppler Shift of a galaxy is proportional to its distance.

Virtually all galaxies have spectra which are redshifted, that all the galaxies are moving away from the Milky Way.

Hubble made the following plot, now known as the Hubble Law:



v = Ho  d

where v  =  the speed of the galaxy moving away from us
          d  =   the distance to the galaxy
        Ho =   a constant number, called the Hubble Constant.

Here's the best version of this plot, Published in The Astrophysical Journal, Volume 553, Issue 1, pp. 47-72, 2001.
Note how much further in Distance the X-axis goes.

3.  Hubble's Law means that the Universe is Expanding.

(Image from

See Interactive Figure 1.16

Key Concepts:
The distant galaxies are all moving away from us.
However, we are NOT at the center of expansion.
Every galaxy sees all other galaxies moving away.
The expansion of the Universe has no center.
The galaxies are not really moving, the Doppler Shifts are the result of the expansion of space.  Sometimes the spectral shifts are referred to as "cosmological redshifts" since they result from space expanding.

We assume that the Universe is infinite, it has no edge.  However, it is expanding.

YOU are not expanding, however, since you are held together by electromagnetic forces.  
The Milky Way, Local Group, Clusters of Galaxies -- are not expanding, they are bound by gravity.

I like to visualize this with M. C. Escher's drawing:

The galaxies are at the cubes, and the rods between them are expanding.

4.  If you play the movie backwards, space was infinitely small at a point in the past.  The expansion started in an event called THE BIG BANG.

The Big Bang occured 13.7 billion years ago.

What came before the Big Bang?  That's like asking what's south of the South Pole.  At the time of the Big Bang, time was not the nice, linear quantity we know it to be today.

5.  Since the Universe has a finite age, there is a cosmological horizon.

We can't see farther than 13.7 billion light years, since light from a galaxy farther than that has not had enough time to reach us.

However, we assume that the Universe is infinite, and that what we see is a fair sample of the Universe.

6.  Having trouble believing the expansion?  You're not alone!   

                             Hubble                                                            Einstein

Einstein's Theory of General Relativity predicts that the Universe should expand.   Einstein recognized this, long before Hubble found the Hubble law.  Expansion of the Universe seemed so implausible to Einstein that he added an arbitrary constant, called the cosmological constant, to his equations so that the Universe would not expand.  After Hubble found that the Universe is expanding, Einstein called the cosmological constant, "the biggest blunder of my life".

 Einstein at Mt. Wilson, visiting the telescope used to find the Hubble Law.