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Say we can collect all the energy from the sun's output and all the particles from the solar wind. If we had an energy to mass converter and turned everything into say, carbon, how many kilograms of new material would we be able to "create" each year?

If it matters, assume we're collecting everything at one AU.

Edit:

It's been ~10 years since I've done physics. I think I know the basic process I'd need to calculate this ($E = mc^2$), but I'm not confident I know the right units and unit conversions to use. Plus I have the vague thought that $E = mc^2$ is just a simplified formula of what I should actually be using. Finally, there are a few specific pieces I'm not sure of:

  1. Does the distance from the sun matter? I was thinking no, but presumably some energy would get absorbed elsewhere. Possibly easiest to calculate this if we collect inside of Mercury's orbit?
  2. I'm sure I could find an estimate for the sun's energy output in Joules/year, but I'm not sure how I'd tell if that was just solar/photon output or if it also included the solar wind.
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  • $\begingroup$ Are you looking for what you need to solve this or are you asking us to do the math for you? $\endgroup$ – Jim Jan 28 '15 at 20:01
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    $\begingroup$ I've done the boring part for you: Solar power is about 3.8e26 Joules/s and the solar wind ejects about 1e9 kg/s. There are about 3.2e7 seconds per year. $\endgroup$ – lemon Jan 28 '15 at 20:07
  • $\begingroup$ @Jim: either/or. I editted the question to add some clarifications on where I'm at. This is related to world-building and not homework, if that helps. $\endgroup$ – Dan Smolinske Jan 28 '15 at 20:10
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    $\begingroup$ Dyson sphere going on here? $\endgroup$ – Carl Witthoft Jan 28 '15 at 21:00
  • $\begingroup$ @Carl - Yes. Either a full one or a partial that's harvesting energy/solar wind to grow. I'll have to decide how efficient the energy -> mass conversion is, then I can calculate how long it will take to finish building itself. $\endgroup$ – Dan Smolinske Jan 28 '15 at 21:09
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According to @lemon's data, the energy output of the sun per year is 3.8e26*3.2e7 J. Dividing that by $c^2$ you find that the sun is losing about 1.3e17 kg/year of matter - so if you collected all that energy and converted it back to matter, that's the amount of material you would get. Add to that the solar wind, which contains another 3e16 kg/year, for a total of $$1.6\cdot10^{17} \mathrm{kg/yr}$$

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    $\begingroup$ By comparison, there is a total of about $10^{19}$ kg of carbon on Earth. $\endgroup$ – lemon Jan 28 '15 at 21:02
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    $\begingroup$ @lemon - thanks for that. It puts into perspective how enormously large the sun is... $\endgroup$ – Floris Jan 28 '15 at 21:05

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