How Far from a Gamma Ray Burst to Match Solar Radiation at Earth?

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SUMMARY

The discussion revolves around calculating the distance from a gamma ray burst required for its average power to match the solar radiation at Earth, quantified as 1300 watts/m². The energy released by the sun if it were to vaporize is approximately 2.7 x 10^47 joules, derived from the equation E = mc². Participants emphasize the need for a formula that relates energy to distance, particularly focusing on the concept of energy dispersal across a spherical surface. The conversation suggests using the formula for surface area of a sphere to derive the necessary distance.

PREREQUISITES
  • Understanding of E = mc² and its implications for energy calculations
  • Familiarity with the concept of solar constant and its measurement (1300 watts/m²)
  • Knowledge of the surface area formula for a sphere (4πr²)
  • Basic principles of energy dispersion in physics
NEXT STEPS
  • Research the relationship between energy, power, and distance in the context of gamma ray bursts
  • Study the implications of energy dispersal across a spherical surface
  • Explore the concept of instantaneous energy release and its effects on surrounding space
  • Learn about the calculations involved in astrophysical phenomena related to gamma ray bursts
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Astronomy enthusiasts, astrophysicists, and students studying energy dispersion and gamma ray bursts will benefit from this discussion.

Stephen_D
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Given the energy if sun were to instantly vaporize (using E = mc^2) = 2.7 x 10^47 J
( E = (mass of sun) * c^2)

how far would one have to be from a gamma ray burst in order for the average power from it to be equivalent to the average power from the sun's radiation at the Earth (solar constant, 1300 watt/m^2)

I understand the problem, but I can't seem to find a formula that would solve for distance using units of the solar constant. The only thought I have is using the potential energy formula, but that is joules. Any hints on what formula to use? or solving it could also be helpful :-)

thanks


Oops, this is my first post, didn't notice the homework section, sorry about that!
 
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Well, the power spreads out across the surface of an imaginary sphere centered at the sun. This gives you some figure in Energy/m^2. And since you're considering a 1 time explosion of the sun, might as well say it lasts just one second, for comparison's sake.
 

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