Astronomy Masterclass
Wednesday, 17th march, 2004
The Number of Stars in our Galaxy
1. Introduction
We live in a ‘spiral galaxy’ called the Milky Way, made of a central ‘bulge’ of stars,
surrounded by spiral arms. The Sun is located in one of the spiral arms, about 30,000
light years from the galaxy centre. Our galaxy contains a huge number of stars- so many
that it is not practical to try and count them all. However, we can estimate the total
number of stars using photographic images of the Milky Way, and a simple model for the
shape of our galaxy.
2. Method
We see more stars when we look towards the centre of the Milky Way than when we look
away from the centre. This is because there are many stars in the central bulge of the
galaxy, and only a few on the outer edges of the spiral arms.
To estimate the total number of stars in the galaxy we can count the number of stars in
small regions looking towards the galactic centre, and looking away from it. We can then
use the average number of stars we count to estimate the total number.
Using the photographic Plates
Astronomers can study the positions of stars using detailed photographs of the night sky,
called ‘plates’. We can use photographic plates of the Milky Way to count stars. The
plates are negative exposures, so the stars appear as black dots, and are easier to see.
a) On the photographic plate looking towards the galactic centre, place the 1mm
square over a region and count the number of stars contained within the square.
b) Record the number of stars you count in the table below.
c) Place the 1mm square over another region of the plate, and count the number of
stars again.
d) Repeat this until you have recorded the number of stars at least 6 times.
e) Calculate the average number of stars you have observed in the 1mm region.
f) Repeat the entire procedure with the plate looking away from the centre of the
Milky Way, using the 3mm square, and calculate the average number of stars you
counted.
Results table
Number of stars towards
the galactic centre (1mm square)
Average number:
Number of stars away from
the galactic centre (3mm square)
Average number:
3. A simple model of our galaxy
Once we have calculated the average number of stars in the small region on the plate, we
can use these results to work out the number of stars in the entire galaxy. We can do this
by constructing a simple model of the galaxy and working out its volume. We can also
calculate the volume that contained the average number of stars we counted on each
plate. We will obtain our final answer by using these results.
The simple model galaxy is made from a sphere of radius 2 kiloparsecs (a parsec is a
distance equal to 3.6 light years), and a disk of radius 15 kpc and height 700 pc (0.7 kpc).
We can calculate the total volume by finding the volumes of these two shapes.
Calculate the volume of the model galaxy
a) First calculate the volume of the central sphere. The volume of a sphere is given
4
by πr 3 .
3
b) Calculate the volume of the disk, given by πr 2 d , where d is 700 parsecs.
c) Add these volumes together to find the total volume.
€
Volume of sphere
(parsec3)
Volume of disk
€
(parsec3)
Total volume
(parsec3)
Calculate the volume of the regions on the photographic plates
The stars you counted on the plates were not all at the same distance, and in fact were
distributed through space up to a distance of around 3 kpc (about 10, 000 light years). We
cannot see many stars more distant than this because most of them are hidden by dust and
gas in the Milky Way (an effect called ‘extinction’).
When you look at a square region on the plate, you are actually looking at a volume of
space in the shape of a square-based pyramid, with the top point at your eye. So all the
stars you counted are in a volume equal to that of a square-based pyramid of height 3 kpc,
which is how far you can see.
The size of the square base of the pyramid depends on the size of the square on the plate.
A 1mm square has sides of 1 parsec, and the 3mm square has sides of length 3 parsecs.
With this information you can work out the volume of space contained in the 1mm and
3mm squares on the plate.
a) Calculate the volume of the square-based pyramid with a base length of 1 pc, and
1
a height of 3 kpc. The volume of a pyramid is given by base x height. Record
3
your result in the table below.
b) Repeat the calculation for the 3mm square, which has a base length of 3pc and a
€
height of 3 kpc.
Volume of pyramid for 1mm square
Volume of pyramid for 3mm square
The density of stars in the regions towards and away from the galaxy centre is given
simply by dividing the average number of stars in the region, by its volume. Use the
results you have already obtained to find out the number of stars per parsec in the 1mm
and 3mm squares you looked at, and record your results in the table provided.
1mm square
3mm square
Average number of stars
Volume of region (parsec3)
Number of stars per parsec3
Estimate the number of stars in the Milky Way
Now that you have worked out the number of stars per parsec, you can apply these values
to the simple model we looked at earlier. To find the total number of stars in the sphere,
simply multiply the volume of the sphere (in parsec3) by the number of stars per parsec3.
This will give you the total number of stars in the central sphere. We know that there are
more stars towards the centre of the galaxy than towards the edge, so use the number of
stars per parsec3 you obtained for the 1mm square for the sphere. Repeat the calculation
for the disk, using the number of stars per parsec3 you obtained for the 3mm square.
1mm square (sphere)
3mm square (disk)
Number of stars per parsec3
Volume of model in parsec3
a) sphere
b) disk
Total number of stars in
a) sphere
b) disk
a)
b)
a)
b)
Add the two results together for the total number of stars in the sphere and the disk, and
you will have estimated the total number of stars in the Milky Way.
An accurate estimate of the total number of stars in the galaxy is around 100 billion stars.
It is unlikely that your result is exactly the same as this, and is probably a smaller
number. What reasons can you think of that might explain why there is a difference
between your result and a more accurate estimate? Do you think your model could be
improved? How accurately were you able to count the number of stars on the plate
images?