The Local Group

Our Milky Way galaxy has a number of neighbors -- other galaxies which are relatively nearby (compared to most). There are roughly 40 galaxies in our Local Group. Of these, the biggest are

our Milky Way
the Andromeda Galaxy, aka M31, is about the same size as the Milky Way, or maybe even larger
M33 is a spiral galaxy somewhat smaller than the Milky Way or M31

How close are these major galaxies to each other? Very, very far apart, of course, but, in one respect, not as far as you might think. Using this worksheet , you can compare the spacing of major galaxies in our Local Group to the spacing of stars in the Milky Way.

But most of the galaxies are much smaller; we call them dwarf galaxies, by comparison with the Milky Way (which sets the standard). Some of these dwarfs orbit the big galaxies:

Large Magellanic Cloud at a distance of about 50 kpc, used to be considered our nearest neighbor
Small Magellanic Cloud orbits our Milky Way, currently at a distance of about 80 kpc. It is classified as a dwarf irregular galaxy.
M32 a dwarf elliptical which orbits the Andromeda Galaxy. It looks pretty darn elliptical.
NGC 205 is another dwarf elliptical companion to the Andromeda Galaxy.

Other dwarfs in the Local Group are not as clearly orbiting one of the bigger galaxies:

Leo I is a dwarf spheroidal, about 250 kpc away from us, and may be orbiting the Milky Way. Note the color of its stars: mostly blue. That means they must be young. We believe that many of these stars are "only" 3 billion years old, which is younger than those in most galaxies.

In 1994, several astronomers were measuring the motions of stars in the Milky Way. They noticed that in one direction -- almost directly towards the center of the Milky Way -- there were a whole bunch of stars with very similar speeds and directions. When they looked very, very closely, they were able to determine that these were actually stars which belong to a galaxy never noticed before: the Sagittarius Dwarf Galaxy. It is really close to the Milky Way -- in fact, it is inside the Milky Way! That's one of the reasons that it was so hard to notice.

At about the same time, a group of Dutch astronomers were making a survey of the plane of the Milky Way with a radio telescope called "Dwingeloo". They noticed a patch of strong emission in 21-cm radio waves, due to neutral hydrogen. When they looked very closely with infrared and optical telescopes, they discovered a galaxy, now called Dwingeloo 1 It's a bit outside the Local Group (about 4 Mpc away), but still much closer than most galaxies. We just didn't notice it earlier because it was hidden by the dust clouds and stars in the disk of the Milky Way.

The Local Group as a Laboratory

Because galaxies in the Local Group are bound to each other by their mutual gravitational attraction, we can use them to measure the masses of galaxies. In fact, we can measure the mass of our own Milky Way by carefully analyzing the motion of several of its companions. Here's how:

Suppose that there's a big, massive object, with a smaller, less massive object orbiting around it. The speed of the small object in its orbit depends on two things:

its distance from the big object, R. Large distances mean weak gravitational force, which means a slow orbital speed
the mass of the big object, M. A big mass means a strong gravitational force, which means a fast orbital speed

If you know that a small object is moving in a circular orbit around a big object, and you can measure the distance of the small object from its big massive neighbor, and the speed with which it moves in its orbit, then you can calculate the big object's mass:

                   v^2  *  r
           M   =  ----------- 
                      G

    where

           M       is the mass of the big object
           v       is the orbital speed of the satellite
           R       is the distance between the two objects
           G       is the gravitational constant

One can put this into a form convenient for use in galactic situations:

                                 2
           M   =  (2.3 x 10^5)  V   *  R
             

    where

           M       is the mass of the big object in units of solar masses
           V       is the orbital speed of the satellite in km/s
           R       is the radius of the orbit in kpc

We can measure the distances and speeds of several dwarf galaxies which are (very probably) in orbit around the Milky Way. For example, the Large Magellanic Cloud has

           V   =  210 km/s
           R   =   50 kpc

which yields a mass for the Milky Way of about

           M   =    5 x 10^(11)   solar masses

The Leo I dwarf galaxy has

           V   =  180 km/s
           R   =  250 kpc

which yields a mass for the Milky Way of about

           M   =   16 x 10^(11)   solar masses

Hmmm. Why are those numbers different? It may be due to the fact that the Milky Way actually extends out beyond the LMC; instead of being only, say, 30 kpc in diameter, our galaxy may have a dark halo which extends out to 50 or 100 kpc or even 200 kpc. Why do we call this a dark halo? Because we don't see any light from material at these large distances from the Milky Way. If there were ordinary stars out at those distances -- we'd see them.

This is another piece of evidence for dark matter in the universe: many galaxies (though not all) have gravitational forces which indicate more mass than one can see directly as ordinary stars.

Other resources:

SEDS description of the Local Group
George Lake's article on the Local Group describes how to use the galaxies to detect the mysterious "dark matter".
A 3-D view of galaxies around our Milky Way