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Black Hawk College *

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102

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Astronomy

Date

May 12, 2024

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pdf

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8

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Astronomy 102 Construction of an H-R Diagram Name Semester Purpose The purpose of this exercise is to make a Hertzsprung-Russell diagram and to demonstrate how to make the measurements that are used to find the quantities that are plotted in an H-R diagram.. Material You will need a sheet of graph paper which can be printed out from the file on the Canvas page. Also you will use a scientific calculator. The H-R diagram An H-R diagram is essentially a plot of luminosity vs. temperature for a group of stars. For convenience, these quantities are usually converted into other terms. Because stellar luminosities can extend over a huge range, we will plot the logarithm of the ratio of the luminosity of the star to the luminosity of the Sun. This is more easily expressed in a mathematical function: log(L/L Sun ). Instead of plotting temperature directly, spectral type is usually listed. Finding the spectral type is usually done by a detailed analysis of the spectrum from a star. We will use a simplified procedure in a sample calculation. The temperature of a star cannot be directly measured from Earth. We can, however, directly measure the spectrum emitted. We can get an idea of the spectral class by finding the wavelength of the peak in the thermal radiation curve. See the graph in figure 5.19 and Mathematical Insight 5.2. The temperature is found from the peak wavelength using the following equation: T = 2,900,000/ max , where T is in Kelvins, and max is in nanometers. After you have found the temperature, the spectral type can be estimated using Table 15.1 in your text. The luminosity (L) of a star is the energy per unit time that it emits. Luminosity is found by measuring the apparent brightness of a star and its distance. Apparent brightness (B) is the energy per unit time per unit area that reaches the earth. The luminosity is found by multiplying the apparent brightness by the area over which the energy is distributed. This energy is distributed over a spherical area with a radius equal to the distance (d) from the star to the Earth. Since the area of a sphere is equal to 4 *(radius) 2 , we can write L = B*4 *d 2 . If B is measured in Watts/m 2 and d is measured in meters, L will be measured in Watts.
The distance (d) to a star can be calculated from its parallax angle (p). The equation is d = 1/p, where d is measured in parsecs and p is measured in arcseconds. This distance can then be converted to meters for use in the formula above. Measurements Suppose you observed a star over time and made the following measurements: wavelength of peak thermal radiation = max = 360 nanometers parallax = p = 0.128 arcseconds apparent brightness = B = 5.42 x 10 -8 Watts/m 2 Find the temperature of the star using the formula T = 2,900,000/ max and record your answer below T = K Look in Table 15.1 in your book and determine the spectral type of the star. Spectral type Find the distance to the star in parsecs using the formula d = 1/p, using the value of p given above. d = pc Convert this distance to meters by multiplying your previous answer by 3.08 x 10 16 meters = 1 pc. d = meters Now calculate the luminosity using the formula L = B*4 *d 2 , using the value of B given above and the value of d in meters that you just found. L = watts The luminosity of the Sun is 3.8 x 10 26 watts. Find the ratio L/L Sun by dividing your answer above by the luminosity of the Sun. L/L Sun = Calculations similar to these are used to find the quantities listed in the appendices of your book. However, we are not taking into account some possible complications. For example, factors such as light absorption need to be considered in finding the luminosity. We will not be concerned with details like these here.
Preparing the Table for the Nearest Stars Use table F.1 in Appendix F of your book to fill in the following information about the nearest stars to our solar system. The first two have been filled in for you. For the last column, find the logarithm of L/L Sun for the star. To do this you must use the "log" key on your calculator. On some calculators, you will type in the number and simply press the "log" key. On others, press the "log" key, then type the number, then press the "Enter" key. Please let me know if you have any problems. Star name Spectral Type Luminosity Class log(L/L Sun ) Sun G2 V 0 Proxima Centauri M5.5 V log(0.0006) = -3.22
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