How many stars is it possible to see in the night sky?
This project introduces the concept of star counts and develops a theory that enables us the answer the question "How many stars can we see?" By using this theory and making some simple measurements, we will then determine how many stars we can see from our observing location.
Sonoma State University
Astronomy 231
Dr. Gordon Spear
One of the questions often asked by beginning students in astronomy is "How many stars are there in the sky?" Under ideal conditions, an observer in the northern hemisphere can observe nearly 8000 stars with the naked eye. A few of these stars are very bright and are easy to see even through the glow of city lights. But most stars are faint and can only be seen under dark sky conditions away from city lights and with no moon in the sky. Thus, the number of stars that can be seen depends upon how faint one can see from a specific observing location.
Suppose you wanted to know how many rain drops fall in your backyard in an hour during a rain storm. Clearly it is not practical to actually count all the individual drops. However, imagine that it is raining outside and you place a glass on the ground and count the number of raindrops that land in the glass each minute. If you know the (collecting) area of the glass and the area of your yard you can determine the number of drops that fall on your yard since
raindrops in glass / raindrops on yard = collecting area of glass / area of yard
or
raindrops on yard = raindrops in glass X (area of yard / area of glass)
This same method was used by William Herschel over 200 years ago to estimate the number of stars in the sky. By counting the number of stars in a small area of the sky and knowing what fraction of the sky this represents, an estimate of the total number of stars can be determined.
Next, imagine placing a large funnel above the glass in your yard so that the rain collected by the funnel is poured into the glass. Clearly, more raindrops will fall into the glass each minute when using the funnel than without using the funnel.
Think of starlight as raindrops of energy (technically, photons) and the pupil of your eye as the glass. A pair of binoculars or a telescope is analogous to the funnel. Photons are collected and concentrated so that the eye sees a much brighter view of the sky. Using binoculars or a telescope enables an observer to see much fainter stars because more light can be collected and "funnelled" to your eyes. Increasing the collecting area of the optical system is like using a larger funnel. You will collect more rain drops (see more and fainter stars).
Imagine looking at the sky through a cardboard tube. This tube will define an area of the sky. If you place your eye at the back end of the tube and point the tube toward the sky, and if the tube has a length L and a diameter D, then the angular field of view of the tube is given by
FOV = 57.296 D/L (degrees)
For comparison, the field of view for a normal healthy human is about 150 degrees, while the apparent angular size of the full moon (and the sun) is about 1/2 degree (30 minutes-of-arc).
If this angle is small in comparison to 360 degrees, we may approximate the area involved by assuming a flat surface (rather than a section of the surface of a sphere). Then we may determine the area of the sky as viewed through the tube as
For comparison, the angular area of a sphere (like the celestial sphere) is approximately 41254 square degrees.
Now imagine that we count the number of stars visible through the tube. It must then be true that
stars counted / total observable stars = area examined / total area of sky
Now, if we let N represent the total stars counted, T* represent the total observable stars, and As represents the total angular area of the sky, we may write
Here n represents the number of areas of the sky sampled with the tube to produce the total count N. That is, if you only observe one area of the sky then n=1, but if you observe 6 different regions of the sky then n=6. Of course, N is the total number of stars counted in all the areas observed.
It may ultimately be shown that
This equation may be used to predict the total number of observable stars based on observations of the total number of stars counted through a tube pointed to n different locations on the sky.
a. Measure the length and diameter of your cardboard tube. Compute the angular field of view (FOV) for your tube in degrees.
b. Count the number of stars seen through 5-10 randomly chosen regions of the sky. For each region selected record the approximate altitude, azimuth, and count. Of course, also remember to record the date and the approximnate time you make your observations. Also indicate the approximate constellation for each chosen region. Finally, make certain to record a description of the general conditions of the sky while you were making your observations. Was the moon visible? Was there much indication of light pollution?
c. Compute an estimate of the total number of stars visible to the unaided eye from your observing location. Show all calculations.
d. Repeat your observations and calculations for a different observing location. If possible, also try to repeat your observations on a different night.
e. Summarize all your important results in a table.
f. Some questions to consider for your summary and conclusions:
Are your results in agreement with the expected results? Comment on the effects of observing conditions and light pollution on your results. Are there regions of the sky which appear to have decidedly greater or fewer numbers of stars that other regions? Comment on the possible reasons for this phenomenon.