The calculation begins with estimating the mass of the Milky Way. This is done by using the following argument:
In a stable circular orbit, like that of the Sun around the center of the
Milky Way, the velocity of the Sun (V) and its mass (m) are related to the radius of its orbit
(R) and
the mass of the Milky Way (M) interior to its orbit by:
2 M m
m V = G ------
R
with a little bit of algebra you see than 'm' cancels, and you get the Milky
Way's mass inside the orbit of the Sun as
2
V R
M = -----------
G
so that for R = 8,800 parsecs and V = 250 kilometers/sec you get
2
M = (250x 100000) ( 8800 x 3 x 10^18 centimeters)
------------------------------------------
-8
6.6 x 10
44
or M = 2.6 x 10 grams.
Since the mass of the Sun is 2 x 10^33 grams, this works out to 120 billion
times the mass of the Sun. Now, this would be the number of stars in the
Milky Way if the most common stars had the mass of the Sun. But they don't.
For every star equal to the mass of the Sun, there are many more stars with
1/2 the mass, and even more 'dwarf' stars with 1/4 the mass. A proper
accounting of how many stars there are for each 'solar' mass of material
would get you about 2 - 10 stars. So, to our above estimate we have to multiply
it by a factor of 2 - 10 to get the total number of stars, or about 240 - 1200
billion stars. Also, the above mass
estimate is low by possibly a factor of two because we have not accounted for
the mass OUTSIDE the orbit of the Sun, and the mass of the 'dark halo'
population which we think is out there. The 'actual' stellar population
in the Milky Way could be as high as several trillion stars or more
by some estimates. Most astronomers usually carry around the ball-park
estimate of 250 billion stars. At the present time, what counts is the amount
of mass in the galaxy, not exactly how many stars contribute to it. It is the
total mass that influences the gravitational field, and which determines
the details of how the Milky Way behaves as a system.
A survey of various books yields the following estimates:
Book Year Mass Stars ----------------------------------------------------------------------- Astrophysical Quantities 1976 140 Billion suns .......... Introductory Astronomy and Astrophysics 1973 150 billion suns ............. Horizons: Exploring the universe 1991 ................. 200 billion Discovering the Universe 1990 600 billion suns ............. Survey of the Universe 1970 140 billion suns .............. ------------------------------------------------------------------------