Calculating Distance for Equivalence of Gamma Ray and Solar Radiation Power

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SUMMARY

The discussion centers on calculating the distance from a gamma ray burst required for its average power to match the solar constant of 1300 watts/m², given the energy released if the sun were to vaporize, calculated as 2.7 x 10^47 J using E = mc². Participants clarify that the energy radiates evenly in all directions, suggesting the use of spherical surface area to determine distance. A key insight is that if the vaporization occurs instantly, it implies infinite power due to Δt being zero. The final energy considered for the calculation was adjusted to 5 x 10^46 J over a duration of 120 seconds.

PREREQUISITES
  • Understanding of E = mc² and its application in energy calculations
  • Familiarity with the concept of solar constant and its significance
  • Knowledge of spherical geometry and surface area calculations
  • Basic principles of power and energy over time
NEXT STEPS
  • Research the formula for calculating power from energy over time
  • Explore the implications of instantaneous energy release in astrophysical contexts
  • Learn about the effects of gamma ray bursts on surrounding environments
  • Investigate the relationship between energy distribution and distance in spherical radiation
USEFUL FOR

Astronomy enthusiasts, astrophysicists, and students studying energy dynamics in astrophysical phenomena 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 is 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
 
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This is weird, I don't think the problem is solvable as written.

I guess the idea here is that the energy would be radiated evenly in all directions. So at a distance r from the sun, the energy is spread evenly over a spherical surface of radius=r.

However, if the vaporization takes place "instantly", that implies Δt is zero hence infinite power.
 
ahh yes sorry, I miss read the question but your technique is correct. I ended up getting the solution, the energy was 5 * 10^46 and it lasts for 120 seconds.

I didnt get around to editing the post, sorry about that.
 

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