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Astronomy 120 HOMEWORK - Chapter 13 The Stars as Suns Use a calculator whenever necessary. For full credit, always show your work and explain how you got your answer. Be careful about units! Please CIRCLE or put a box around your final answer if it is numerical. 1. Zeilik Study Exercise 13.1 In the winter sky, you see the following stars: Capella (yellowish), Betelgeuse (reddish), and Sirius (bluish). List these stars in order of increasing surface temperature. Estimate the surface temperature of Betelgeuse and of Sirius. 2. Zeilik Study Exercise 13.9 Jupiter is about 5 times as far from the sun as the earth is ( 5 A.U.’s compared to 1 A.U. ). By how much less is the sun’s flux at Jupiter compared to that at the earth? 3. Zeilik Study Exercise 13.3 What limits the accuracy of ground-based heliocentric parallax measurements? 4. Zeilik Study Exercise 13.4 Refer to Figure 13.15 to answer the following questions. (a) Capella and the sun have roughly the same surface temperature. Which star is larger? (b) Regulus and Capella have about the same luminosity. Which star is larger? (c) Vega and Sirius have about the same surface temperature. Which star is more luminous? (d) Which star would appear redder, Vega or Pollux? 5. Zeilik Study Exercise 13.6 What procedure does an astronomer follow to find out a star’s density? Hint: Divide mass by volume to get density. 6. Zeilik Study Exercise 13.7 Consider a binary star system that does not eclipse and in which one star is much brighter than the other. Then the absorption lines from the fainter star do not appear in the spectrum, but those of the brighter one do. Describe how the Doppler shift would appear from the orbital motion of the stars. 7. Zeilik Study Exercise 13.8 The star Regulus has a mass about five times that of the sun. Use the mass-luminosity relationship to estimate the luminosity of Regulus. 8. Zeilik Study Exercise 13.2 Consider stars with the following spectral types: M I, G III, and A V. Which star is the largest? Which is the most luminous? 9. The Sun produces energy primarily via the proton-proton chain. We can figure out how much energy one such reaction will release by using the famous Einstein relation: E mc 2 where E is the energy in Joule's m is the mass in kilograms c is the speed of light in meters per second c 2.9979 108 m s The mass in this equation refers to the difference in mass between 4 protons 4 electrons 6.694 10 27 kg , and a helium nucleus ( 2 protons 2 electrons ) 6.644 10 27 kg . a) Find the difference in mass and then the energy released. b) if the Sun emits 3.9 10 26 Joules per second, how many of these reactions must occur per second? 10. The flux we receive from the Sun is about 1370 Watts per square meter. (A watt is a unit of power which is equivalent to 1 Joule per second). Sirius sends us a flux of about 1 10 7 W m 2 . Luminosity is related to flux by the following equation: L 4r 2 F where L is the luminosity in Watts r is the distance in meters F is the flux in W/m2 a) The Sun is 1.49598 x 1011 m away, what is the Sun's luminosity? b) Sirius is 8.8 ly away (1 ly = 9.46053 1015 m ). What is Sirius' luminosity? c) If Sirius had a surface temperature of 15,000 K, what would its luminosity be then? We need to remember that flux has a temperature dependence through the equation.... F Teff 4 where Teff is the "effective" or surface temperature and is the Stefan-Boltzman constant. 56697 . 108 W 2 4 . Assume Sirius has a radius of 8 10 8 meters - this is where m K the flux is measured. 11. Stellar parallax allows us to find the distances to stars using simple trigonometry. The figure below shows the geometry. Earth R p Sun d tan p R d so that d R tan p but the tangent of small angles is approximately equal to the angle itself in radians. So.... d R , p if R is in A.U.'s and p is in arcsec's, then d is in parsec's and 1 pc = 326 . ly . See Focus 13.2 (Zeilik, p. 286). the smallest detectable parallax is about 0.001 arcsec; how far would a star with this parallax be? 12. The relationship between the apparent and absolute magnitude of a given star is expressed as: m M 5log d 5 where m is the star's apparent magnitude, M is the star's absolute magnitude and d is the distance to the star in parsec's. If the star in problem #11 had an apparent magnitude of 5, what would its absolute magnitude be? 13. On the Hertzsprung-Russell (HR) diagram on the back of this page, plot points representing the Luminosity and Surface Temperature of each of the 16 brightest stars (in the northern hemisphere) on your list. (The values of luminosity (in units of the Sun's luminosity) and the surface temperature are given in your list of stars.) Write the name of each star next to its location on the HR diagram. 14. Invent a new mnemonic for spectral classification. O-B-A-F-G-K-M (e.g. Oh boy, a furry gorilla kissed mom!). HERTZSPRUNG – RUSSELL DIAGRAM 106 105 104 103 102 10 1 10-1 30 25 20 15 10 9 8 7 6 SURFACE TEMPERATURE (103 K) 5 4 3 2 16 BRIGHTEST STARS (VISIBLE FROM NORTH OF THE TROPICS) ___________________________________________________________________________ STAR DISTANCE APPARENT LUMINOSITY Tsurf(oK) TYPE (light years) BRIGHTNESS (Sun = 1) (Compared to the sun if it were 32.6 ly distant ___________________________________________________________________________ 1. Sirius 8.7 310 38 9,700 (white main sequence) 2. Arcturus 36 86 200 4,600 (orange-red giant) 3. Vega 26.5 80 97 10,000 4. Capella 45 76 170 5,250 900 74 120,000 11,700 5. Rigel 6. Procyon 7. Betelgeuse 11.3 520 59 7.59 6,670 57 110,000 3,100 (white main sequence) (yellow giant) (blue-white super giant) (yellow main Sequence) (red super giant) 8. Altair 16.5 41 12 7,940 9. Aldebaran 68 39 500 4,150 10. Spica 220 34 9,000 22,000 11. Antares 520 35 20,000 3,200 (blue-white main sequence) (red super giant) 12. Pollux 35 29 53 4,850 (orange-red giant) 13. Fomalhaut 22.6 28 20 9,000 1600 26 110,000 9,200 (white main sequence) (white super giant) 15. Regulus 87 24 410 13,000 16. Castor 45 20 53 10,000 14. Deneb (white main sequence) (orange-red giant) (blue-white main sequence) (white main sequence)