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SOLUTIONS TO EXERCISE 8
(a) Since a Megaparsec is about 3.1 * 10^22 m, this burst's luminosity is
L = 4 * pi * r^2 * F = 4 * 3.14 * (3000 * 3.1 * 10^22 m)^2 * (5 * 10^-10 W/m^2)
= 8.7 * 10^43 W or 8.7 * 10^43 Joule/sec
For a 90 second period, the total energy release was
E = (8.7 * 10^43 Joule/s) * (90 s) = 7.8 * 10^45 J.
(b) The luminosity of a galaxy is usually about equal to the luminosity of all
its stars put together. Since the Milky Way has about 10^11 stars, if we use
the Sun as a typical star then our galaxy's luminosity is
L = 10^11 * (4 * 10^26 W) = 4 * 10^37 W.
The luminosity of the gamma-ray burst is
(8.7 * 10^43 W)
--------------- = 2.2 million times greater than an entire galaxy!
(4 * 10^37 W)
(c) The energy released by the burst was (7.8 * 10^45)/(10^44) = 78 times
greater than that of a typical supernova.
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