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Homework 5 solutions
•Q4.  Spectroscopic parallax.  (Apparent) magnitude = 5.4 for an O6 V star.  How far away is it?  First need to get an absolute magnitude.  Can estimate it several ways (H-R diagrams, mass-luminosity relation).  I used M = -5.6.  So:
•d (pc) = 10 (m-M+5)/5 = 103.2 = 1585 parsecs
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•Q5. If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.)
•d (pc) = 10 (m-M+5)/5 = 108.2 = 1.6x108 pc x 1Mpc/106pc = 160 Mpc
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•Q6.  The “Blade Runner Question.”  A star that burns half the lifetime of the sun does not burn twice as bright.  How bright (luminous) is it?
•  Lifetime in solar units = M-2.5 (solar m)
• 0.5 = M-2.5
• M2.5 = 2
• M  =  (2)1/2.5 = 20.4= 1.3 solar masses
• L in solar units = M3.5 (solar units)
• Luminosity = (1.3)3.5 = 2.6 solar
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