Astronomy 101
Homework #1
B.Margon - Winter 1996

This homework asks you to make comparisons between two different samples of stars. The bright star table was selected on the basis of apparent brightness NOT the luminosity of the stars. The near star table is all stars within 5 parsecs (about 15-16 lightyears) from the sun.

1. The first thing an astronomer does when faced with a pile of data is gaze at it, contemplates it, and wait for inspiration. Look over the two lists of stars and compare them to the star we know best, Our Sun:
• a) Characterize the average properties of stars in the "Near Star List" as compared to the Sun. (mention Luminosity, color, and temperature.) "Nearby stars tend to be...."
• b) Characterize the average properties of stars in the "Bright Star List" as compared to the Sun. (mention Luminosity, color, and temperature.) "Apparently bright stars tend to be...."
Plot log(L_Star/L_Sun) versus Temperature for both the lists of nearest stars and brightest stars on the attached graph. Use constrasting colors or symbols so that the two samples of stars are clearly distinguished. The plot you have made will be an HR diagram. Label the region of the diagram where the main-sequence stars, Red Giant stars and White Dwarf stars are found.
2. In a brief sentence or two, comment on the differences in location on your plot of these two groups of stars.
3. Capella has approximately the same temperature as the Sun, yet it is 140 times as bright as the Sun. We know that the luminosity of a star is L_Star/L_Sun = (R_Star/R_Sun)^2 (T_Star/T_ Sun)^4 . Knowing this, can you propose an explaination for the higher luminosity of Capella?
4. Using this formula, (R_Star/R_Sun)^2 = (L_Star/L_Sun) / (T_Star/T_Sun)^4 and the lists, find the radius of the hot main-sequence star Vega, the very hot main-sequence star Hadar and the cool main-sequence star Ross 614-A as ratios of the radius of the Sun.

        R_Vega / R_Sun  =    

        R_Hadar / R_Sun  =   

        R_Ross 614-A / R_Sun  =

5. From the above calculation, do you see any trend between the size of a main-sequence star and its temperature? If so, what is it?
6. For each list of stars, the nearest stars and the brightest stars, count the number of stars that fall into each of these temperature ranges: 3000 or less; 3001 to 5000; 5001 to 7000, 7001 to 10,000; greater than 10,000. Make a histogram for each set using the second diagram. Again, use constrasting colors for the two samples so they can be easily distinguished from one another.

Note: some star systems have more than one star in them; count each star in the system individually. For example the 40 Erid system is made of three stars, each of different temperature.

7. Comment briefly on the differences between two samples of stars on the histogram you have drawn.
8. We are not able to catalog all the stars in our Galaxy. However, if we assume that the Sun is situated in a typical piece of Galaxy, we should be able to assemble a sample of stars which accurately reflects the population of the whole Galaxy (e.g. when pollsters want to find out the President's approval rating, they don't ask ALL Americans, but rather they assemble a sample of ~1000 typical Americans and assume that this sample accurately reflects the whole population.)

 
9. Which list (the bright star list or the near star list)would best be a representative of the total population of the Galaxy? Explain why!

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