Dl/l = v/c

In astronomy, the Doppler shift is a very powerful tool from which
can lead us to know not only how fast something is moving, but also
how far away from us it is. Between 1912 and 1925, Astronomer
V.M. Slipher at the Lowell Observatory first measured the radial
velocities of galaxies using the Doppler shift. He discovered that
they all seemed to be moving away from us...the Universe was
expanding! By 1929, Edwin Hubble at the Mt. Wilson Observatory
determined the distances to galaxies for which velocities had been
measured and found that these two parameters were proportional to each
other. This relation is now known as the Hubble law. It can be written
as v = Hr, where r is the distance, H is the constant of
proportionality called the Hubble constant, and v is the velocity. The
Hubble constant is currently believed to be between 60 and 75 km/s per
million parsecs.

What do the redshifts (which astronomers define as Dl/l) have to do with GRBs? Try this:

In a few cases, shortly after the detection of a GRB, high-powered
ground- and space-based observatories were able to detect the
afterglow of the event. These observations provided scientists with
the data to determine the host galaxy of the event and obtain a
redshift measurement of that galaxy. Redshift measurements allowed a
determination of the distance to the source of the GRB!

• Examine the table below. Use what you have learned about
redshift to determine the velocities and distances of the galaxies
which appear to host the GRB events. Perform these calculations with
both the minimum and maximum Hubble constant values. HINT: The
material associated with GRBs is moving very, very fast — so the
simplified version of the Doppler shift equation cannot be used.

__Burst__ | __Redshift__ |

970508 | 0.835 |

971214 | 3.418 |

980703 | 0.966 |

990123 | 1.6 |

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• Given your knowledge of how fast gamma-rays travel, how long has it taken them to reach us from such a distance?

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• What does this tell us about the age of the Universe?

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• What must have happened in the Universe already in order for a GRB to occur?

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