Project 2: Number of stars visible to the naked eye Purpose: To demonstrate how
ID: 1409831 • Letter: P
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Project 2: Number of stars visible to the naked eye Purpose: To demonstrate how the total number of stars visible to the eye is estimated from samples, and to investigate how that number changes when the Moon is visible. You will need: One paper towel tube (or similar tube) about 30 cm long Calculator One clear, dark night and once clear night with bright moonlight Procedure: To estimate how many stars a person could see without a telescope, we can use a statistical method called sampling, in which the number of stars in some known fractions of the sky's area are counted; then that number is "scaled up" to give an estimate of the number that would be visible across the entire sky. Almost as important as this total number is its uncertainty, which can be calculated from how closely the results from different sampled locations agree with each other. The length of an observer's tube is L, and its inner diameter is D, so the area of the open end of the tube is (D/2)2. If the observer moves the tube in all directions across the sky, the tube would eventually cover the surface of an imaginary hemisphere centred at the observer's head (see the image below). Nstars Image copyright: Wadsworth Group The radius of this hemisphere would be the length L of the tube, so the surface area of the hemisphere (half-sphere) would be (4L2)/2. So we have: (Area of hemisphere of sky)/ (Area of end of tube) = [(4L2)/2]/[(D/2)2] = 8 L2/D2 Lastly, we make an assumption: that stars are strew evenly across the night sky. If that is true, then the more area we sample, the more stars we should see. What this means as a formula is that: (Total number of stars in hemisphere of sky)/(Number of stars in projected spot) = = (Area of hemisphere of sky)/ (Area of end of tube) = 8 L2/D2 Finally, combining the last two formulas, we have: The total number of stars in a hemisphere of sky = (8 L2/D2) x (average) number of stars in a projected spot Carefully measure L and D for your tube, to better than 1 mm. Then calculate the factor (8 L2/D2). Observations: On a clear night (no Moon visible), go outside (to a relatively dark location). Allow your eyes some time to adjust to low light levels - at least 5 minutes. Then, looking through your tube, count the number of stars you can see in each of at least ten parts of the sky. Then your average number of stars in a projected spots will be Nav= (N1 + N2 + ... + N10)/10 where Ni (i=1,..,10) is the number of stars measure in each part of the sky. Calculate a scatter (uncertainty) in your average number using standard deviation: sigma where n is Nav. Because the total number of stars visible to the naked eye is Nstars = (8 L2/D2) x Nav the uncertainty in the total number is (8 L2/D2) x sigma. Repeat your observations (and calculations) on a clear night when the Moon is visible and bright. Take samples from all around the sky, but take care not to look right near the Moon. Questions: How does Nstars and its uncertainty compares compare for the two different nights (with and without the Moon's presence)? How do you think your results would be affected if you used a tube of different length or diameter to take your sampling?
Explanation / Answer
The dark night (without moon) is better to make the experiment. Just because of the better contrast you will see more stars (the dimmer starts may be observed in thiese conditions).
In a bright (with moon) night, lesser starts will be observed. The dim starts will be blurred by the moonlight.
If about the number of starts that can be observed and the type of night: a clouded night will give the less visibility.
The length of the tube does not have any influence on the result, but the diameter, yes: you'll get a larger number of stars when performing the experiment with a larger tube diameter.
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