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Unformatted text preview: Ch. 45 Page 1 CHAPTER 45 Astrophysics and Cosmology Note: A factor that appears in the analysis of energies is e 2 /4p = (1.60 10 19 C) 2 /4p(8.85 10 12 C 2 /N m 2 ) = 2.30 10 28 J m = 1.44 MeV fm. 1. Using the definition of the parsec, we find the equivalent distance in m: D = d / ; 1 pc = (1.50 10 11 m)/[(1.000 )/(3600 /)(180/p rad)] = 3.094 10 16 m. From the definition of the lightyear, we have 1 pc = (3.094 10 16 m)/(3.00 10 8 m/s)(3.16 10 7 s/yr) = 3.26 ly. 2. We find the distance from D = 1/ = [1/(0.38 )](3.26 ly/pc) = 8.6 ly . 3. We find the distance from D = 1/ = [1/(0.00019)(3600 /)](3.26 ly/pc) = 4.8 ly . 4. ( a ) We find the parallax angle from D = 1/ ; 36 pc = 1/ , which gives = 0.028 . ( b ) We convert this to degrees: = (0.028 )/(3600 /) = (7.7 10 6 ). 5. We find the parallax angle from D = 1/ ; (55 ly)/(3.26 ly/pc) = 1/ , which gives = 0.059 . The distance in parsecs is D = (55 ly)/(3.26 ly/pc) = 17 pc . 6. We find the distance in lightyears: D = (35 pc)(3.26 ly/pc) = 114 ly. Thus the light takes 114 yr to reach us. 7. The star farther away will subtend a smaller angle, so the parallax angle will be less . From D = 1/ , we see that D 1 / D 2 = 2 = 2 / 1 , or 1 / 2 = ! . 8. ( a ) The apparent brightness of the Sun is = 1.3 10 3 W/m 2 . ( b ) The absolute luminosity of the Sun is L = A = (1.3 10 3 W/m 2 )4p(1.5 10 11 m) 2 = 3.7 10 26 W . 9. The apparent brightness is determined by the absolute luminosity and the distance: L = A = 4p D 2 . If we form the ratio for the apparent brightness at the Earth and at Jupiter, we get E / J = ( D J / D E ) 2 ; (1.3 10 3 W/m 2 )/ J = (5.2) 2 , which gives J = 48 W/m 2 . Ch. 45 Page 2 10. The diameter of our Galaxy is 100,000 ly so the angle subtended by our Galaxy is Galaxy = d 1 / D 1 = (100,000 ly)/(2 10 6 ly) = 0.05 rad = 2.9. The angle subtended by the Moon at the Earth is Moon = d 2 / D 2 = (3.48 10 6 m)/(3.84 10 8 m) = 9.06 10 3 rad = 0.52....
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 Spring '08
 ROSS
 Physics

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