Calculating Distance for Equivalence of Gamma Ray and Solar Radiation Power

[Stephen_D]

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

 

[Redbelly98]

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.

 

[Stephen_D]

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.