Astronomy 209 Lab Assignment 4 – Summer 2023
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Astronomy
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Dec 6, 2023
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Astronomy 209 Lab Assignment 4 – Summer 2023 Working out stellar diameters Introduction:
We can measure stellar mass relatively easily as long as we have two stars orbiting each other. The diameter is near impossible to determine by direct observation. We can make a first order approximation of the diameter though if we know the star's distance, apparent magnitude and temperature. In this lab you will be given some basic observational data. You will then use that data to come up with estimates of the diameters of some selected stars to a first order approximation. THERE ARE NOTES FOR THE MATH ON D2L IF YOU GET STUCK!
Data:
Table 1: Solar data Distance Diameter Flux at Earth Apparent Magnitude Sun 1.50x10
11
m 32 arc minutes 1300 W/m
2
-26 Table 2: Stellar data Star Apparent Magnitude parallax (mas) Peak emission (nm) Spectral Class Alpha Ori 0.42 4.55 840 M2I HIP 66840 9.75 40.45 723 M0V CD-74 898 10.19 0.41 191 B5V CU Tuc 9.86 3.97 451 F0V HD 56200 6.76 19.14 445 F4II HD 166620 6.40 90.13 593 K2V Calculations:
Solar reduction: You now need to work out some required information for the Sun, specifically the solar radius, luminosity, and Absolute magnitude.
Table 3: Results of solar analysis Solar diameter (m) Solar Radius (m) Solar Flux (W/m
2
) Solar luminosity (W) Absolute Magnitude Solar diameter can be worked out with the small angle formula (1.1 on the formula sheet). Radius is half of diameter. Check your units before doing the calculation! Solar flux can be worked out using the inverse square law of light (2.3), the distance to the Sun, the flux at Earth, and the solar radius. Solar luminosity is the solar flux times the surface area of the sun (work out from solar radius). Solar absolute magnitude can be computed from the distance to the Sun and its apparent magnitude using the absolute magnitude/distance modulus relation (2.5). Again remember to convert units! Stellar reduction: It is now time to do the data reduction for the stars. You can put the results of your calculations in Table 4. Report your results to 3 significant digits, though keep all your numbers through each calculation! You many find it easier to do this in a spreadsheet to start. First we will work out the distance to the various stars from the reported parallaxes using formula 3.1. Remember that the formula wants the parallax in arc seconds and the numbers reported are milli arc seconds, that is 1/1000 of an arc second! Next we will work out the temperature of the stars from their peak emissions (2.6). Remember to covert nm to m. Now you will need to compute the absolute magnitude using the given apparent magnitudes (2.5). Now you will compute the star's flux using formula 2.7. Now use formula 2.4, the magnitude luminosity relation, solved for l
2
, to work out the luminosity of the star. Use the solar absolute magnitude for m
1
, the star's absolute magnitude for m
2
, and the Sun's luminosity for l
1
. If you get stuck solving for l
2
, ask for help.
The surface area of the star will be the star's luminosity divided by its flux. The radius in metres can be calculated by solving the formula for the area of a sphere for radius.
Finally the radius in solar radii can be determined by dividing the star's radius by the Sun's radius.
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Table 4: Stellar Calculated Data Star Distance (pc) Temperature (K) Absolute Magnitude Flux (W/m
2
) Luminosity (W) Surface Area (m
2
) Radius (m) Radius (R
sol
) Alpha Ori HIP 66840 CD-74 898 CU Tuc HD 56200 HD 166620
Analysis:
1. Compare the temperatures and radii of the main sequence stars (those with a "V" in their spectral class). What pattern do you see? What do you think this pattern suggests? 2. There are two non-main sequence stars in the sample. How do their radii compare to the main sequence stars of the same spectral class (e.g. M with M)? What does this tell us about stars off the main sequence? 3. What does the process you did to compute the radii of the stars tell you about how we work out the physical characteristics of far away objects? What would error in one of our measured quantities do to our final result and what implication does this mean for what we know about interstellar/intergalactic objects?
Marking rubric:
For calculations (9 total) Mark Standard 9 All calculations correct and to the correct significant digits 2-8 Varying amounts of correct calculations. Significant digits may be correct or not. 1 One or two calculations correct or to the correct significant digits. For analysis: Question 1 and 2 (3 marks each): Mark Standard 3 Answer describes pattern seen and provides insight into what the patterns tell us. 2 Answer describes patterns seen. Some insight into the patterns' meaning. 1 Some description of a pattern present Question 3 (3 marks) Mark Standard 3 Answer shows insight into the implications of the method used, what error can do to our conclusions as well as the implication on our understanding of astronomy. 2 Some insight into the process that provides us with our information. May or may not mention error and its implications. 1 Little insight into the process or error.
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