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Imagine that you are a particle physicist, and you have come up with a theory that...

Imagine that you are a particle physicist, and you have come up with a theory that some gamma-ray bursts come from the decay of a new and exotic sub-atomic particle that you think might exist.

You calculated that if this particle really does exist and decay as you predict, the decaying particles would need to be about 100 astronomical units away from the Earth, to give the observed typical fluence of the gamma-ray bursts.

Unfortunately, you've just found out that you made a mistake in your prediction. The energy put out when one of your particles decays is actually a factor of 17.3 greater than you originally thought.

How far away (in astronomical units) must the typical decaying particle be now, to give the fluences observed?

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