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
• 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
• 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