How Far, How Powerful?
Getting from here to there

A detector records a gamma-ray burst. We measure the amount of energy that falls on this detector near Earth. How powerful was the event that we measure?
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First, we'll review how light falls off with distance. As we move away from a source of light, the energy we measure decreases.
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Next, we'll review Hubble's Law and the expansion of the universe. The further an object is from Earth, the faster it is moving away.
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We'll then see how fast a gamma-ray burst is moving away from us by measuring the Doppler shift of lines in its spectrum. From this, we'll find its distance from the Earth.
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Knowing the distance to the gamma-ray burst, the energy we measured, and the rate at which the universe is expanding, we'll find the power emitted in the event.