QUESTION: 
How do astronomers estimate or try to count the number of stars
in the Milky Way? 

ANSWER from Jim Sweitzer on 27 October 1995: 
This is an interesting question because the same method is used to measure
the mass of our earth and sun. Astronomers don't actually count the stars
in the galaxy, they really just try and figure out how much matter there
is in the galaxy. Then, from studying how many stars are of different
types, they can guess what the average mass is for a typical star in the
galaxy. Dividing the average mass into the total mass for the galaxy gives
a rough idea of how many stars there are. 
 
The most important thing is to get the mass of the galaxy. How is that
done? Well, have you ever spun something on a string around in a circle?
If you have, you probably know that the faster you spin the object, the
stronger you feel the string pull on your hand. If you've never done this,
you should try it by tying something attaching a small rubber ball to a
few feet of string and giving it a whirl. 
 
Well, the faster the ball moves in a circle, the stronger the force you
should feel on the string. Basically the same thing happens with stars
orbiting in our galaxy. The stars are like the ball and the "string"
holding the stars in the galaxy is the gravity of the rest of the stars in
the galaxy. The same thing happens with the Space Shuttle orbiting the
earth, but in this case, it is the earth's gravity that keeps it from
zooming off into space. 

The circle the whirling ball travels in is the same thing as an orbit.
It's just that for stars in the galaxy, the orbits are enormous. Where it
takes a fraction of a second for the ball on the string to whirl around
your head, it takes about ninety minutes for the space shuttle to orbit the
earth. For a star that orbits the galaxy out where we live, it takes about
250 million years! And the radius of our sun's orbit in the galaxy is
about 600,000,000,000,000,000 miles! 

The law of gravity says that the amount of force that keeps something in
orbit depends on how much mass is pulling on the star and how far the star
is from the center of all this mass. I won't go through it here, but when
astronomers work backward from the orbit of the sun and its speed in the
galaxy, they know that there needs to be about 100,000,000,000 times the
mass of our sun to keep it on a steady orbit. 

They also know that the sun is a pretty average star. So, if you divide
the mass of the sun (=1 in these units) into the number above, you get
that there are about 100,000,000,000 stars (or 100 billion). Now this
answer is very, very approximate, but is certainly accurate to within a
factor of ten either way. 
 
At one time McDonalds resturants used to list how many hamburgers they
have sold. I remember one time seeing one that said 100 billion sold and I
thought of the number of stars in our galaxy. Now I think they just say,
"billions sold." 

I hope all this makes some sense. Thanks for asking.