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Unformatted text preview: Astronomy 160: Frontiers and Controversies in Astrophysics Homework Set # 6 Solutions 1) a) Faint “browndwarf” stars have absolute magnitudes of around 17.5. How many times fainter than the Sun are these stars? M BD = 17 . 5 M sun = 5 17 . 5 5 = 5 2 log b 1 b 2 12 . 5 × 2 5 = log b 1 b 2 5 = log b 1 b 2 10 5 = b 1 b 2 So brown dwarfs are 10 5 fainter than the sun. b) If one observes a nearby galaxy at a distance of 1 Mpc ( = 10 6 parsecs) what is the apparent magnitude of Sunlike stars in that galaxy? distance = 10 6 parsecs m M = 5 log D 10 pc m 5 = 5 log 10 5 m 5 = 25 So the apparent magnitude of Sunlike stars at a distance of 10 6 parsecs is 30. c) The magnitude of the full Moon is around 14.5. How much brighter does the Sun appear than the Moon? The apparent magnitude of the full moon is 14.5. So we can use the brightness equation along with the apparent magnitude of the sun (27) to find the ratio in brightnesses. 27 + 14 . 5 = 5 2 log b 1 b 2 12 . 5 × 2 5 = 5 = log b 1 b 2 b 1 b 2 = 10 5 The sun is 10 5 times brighter than the full moon. d) The brightest stars are around 10 5 times brighter than the Sun. If the apparent magnitude of these bright stars in some galaxy is 22.5, how far away is the galaxy? First we need to find the absolute magnitude of the bright stars. M 1 5 = 5 2 log 10 5 M 1 = 5 2 × 5 + 5 = 12 . 5 + 5 = 7 . 5 Now use the distance equation and the given apparent magnitude to find the dis tance. 22 . 5 ( 7 . 5) = 5 log D 10 pc 1 22 . 5 + 7 . 5 = 30 = 5 log D 10 pc D 10 pc = 10 6 so D = 10 7 parsecs e) White dwarfs are 10 4 times fainter than “Atype stars”. the nearest example of which is Sirius. Sirius has a distance of 3 parsecs, and an absolute magnitude of M = 1 . Sirius is orbited by a white dwarf known as Sirius B. What is the apparent magnitude of Sirius B (note that you can assume that the two stars in the Sirius system are at the same distance from Earth)....
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 Spring '08
 MarkSaltzman
 Hubble, absolute magnitude

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