How close could a satellite get to the sun, and how much energy could it harvest?
September 4, 2011 8:02 PM Subscribe
If some future civilization decided that they should tap solar energy at the source for industrial purposes, how close to the Sun could they site their energy collection facilities without having them burst into flames/die from radiation degradation, and how much energy could they harvest? Just to keep things simple, say they use photovoltaics or some other technology we have access to.
I originally started thinking about this issue while playing with a NaNoWriMo sci-fi novel idea, and stumbled over my notes on the project a couple days ago and am considering picking it up again - and, frankly, I'm just plain curious. I've had trouble trying to find information on the Web - probably because sticking a satellite near the Sun isn't really a priority right now, for energy generation or otherwise.
I originally started thinking about this issue while playing with a NaNoWriMo sci-fi novel idea, and stumbled over my notes on the project a couple days ago and am considering picking it up again - and, frankly, I'm just plain curious. I've had trouble trying to find information on the Web - probably because sticking a satellite near the Sun isn't really a priority right now, for energy generation or otherwise.
Tough question to answer, authoritatively, for a couple of reasons.
But, as a first cut, consider the surface temperature of Venus, which goes as high as 460° C, partly due to its proximity to the Sun, and partly due to its strong greenhouse gas atmosphere. So it seems even a partial Dyson sphere civilization would have to construct their energy gathering structure at something greater than Venusian orbital distance, just for basic materials to survive temperatures created by average radiation flux (or they'd have to re-radiate excess energy out to space really, really effectively, for the structure to survive long term).
The other big problem with our Sun, and perhaps most other stars, as energy sources, is that they generate, almost at random, large flares of high energy radiation, from which it would be really hard to shield energy gathering structure. We're it not for the Earth's magnetic iron core, and resultant strong Van Allen belts, we'd be regularly hosed by such eruptions, and life itself might never have gotten very far on Earth.
posted by paulsc at 8:23 PM on September 4, 2011 [1 favorite]
But, as a first cut, consider the surface temperature of Venus, which goes as high as 460° C, partly due to its proximity to the Sun, and partly due to its strong greenhouse gas atmosphere. So it seems even a partial Dyson sphere civilization would have to construct their energy gathering structure at something greater than Venusian orbital distance, just for basic materials to survive temperatures created by average radiation flux (or they'd have to re-radiate excess energy out to space really, really effectively, for the structure to survive long term).
The other big problem with our Sun, and perhaps most other stars, as energy sources, is that they generate, almost at random, large flares of high energy radiation, from which it would be really hard to shield energy gathering structure. We're it not for the Earth's magnetic iron core, and resultant strong Van Allen belts, we'd be regularly hosed by such eruptions, and life itself might never have gotten very far on Earth.
posted by paulsc at 8:23 PM on September 4, 2011 [1 favorite]
Best answer: I can't answer the "how close" but the "how much" is easy to calculate on the back of an envelope:
* peak solar flux around the equator on earth is roughly 1 kW/m^2
* in high orbit you get 150% of that due to no atmospheric gasses blocking: 1.5 kW/m^2
* modern solar panels are around 15% efficient (less, but we're rounding) and maximum theoretical efficiency from our current understanding of PV is 30%; so for ideal cells, you'd actually extract 0.45 kW / m^2
* radiation goes down as 1/r^2
So if you moved your solar power station to halfway between the earth and sun you'd get 4 times the power, or 1.8 kW/m^2. Half again as close would net you 7.2 kW/m^2. And so on. Of course, the thing wouldn't be perfectly an inverse square law, but it would be very close.
posted by introp at 9:33 PM on September 4, 2011
* peak solar flux around the equator on earth is roughly 1 kW/m^2
* in high orbit you get 150% of that due to no atmospheric gasses blocking: 1.5 kW/m^2
* modern solar panels are around 15% efficient (less, but we're rounding) and maximum theoretical efficiency from our current understanding of PV is 30%; so for ideal cells, you'd actually extract 0.45 kW / m^2
* radiation goes down as 1/r^2
So if you moved your solar power station to halfway between the earth and sun you'd get 4 times the power, or 1.8 kW/m^2. Half again as close would net you 7.2 kW/m^2. And so on. Of course, the thing wouldn't be perfectly an inverse square law, but it would be very close.
posted by introp at 9:33 PM on September 4, 2011
Post on the limits of potential energy production.
posted by jeffamaphone at 9:58 PM on September 4, 2011
posted by jeffamaphone at 9:58 PM on September 4, 2011
Best answer: Also, note that temperature (radiating what you don't convert) isn't a huge issue if your power plant isn't a Dyson sphere and you have lots of resources. The shadow of a solar panel provides an infinite amount of shading if you're willing to build out away from the sun. Radiant cooling isn't fantastically efficient at those temperatures but looking into deep space is mighty cold.
(If that doesn't make sense, imagine putting a radiator sticking out of the back of your solar panel like a tee. Want to almost double the radiation cooling? Just stick another radiator adjacent to the first, farther away from the sun. Of course, you run into scaling issues eventually, but we're being sloppy here.)
Okay, I'm bored, so a rough pass (disclaimer: late-night math):
Where R is 1/r in AU (so halving the distance to the sun would be R = 2) and radiator_area_factor is the ratio of radiator size to panel size (2 m^2 of radiators per 1 m^2 of panel means radiator_area_factor = 2):
. flux_in = power_at_earth_orbit * R^2
. flux_converted = efficiency * power_in
. flux_delta = (1 - efficiency) * power_in ... this is how much you have to radiate to keep your panel temperature constant
. flux_from_radiators = radiator_area_factor * stefan_boltzmann_constant * T^4 ... note T is in degrees kelvin
so pick a steady-state temperature Tmax for your solar panels, some radiator_area and compute:
R = sqrt( radiator_area_factor * sigma * Tmax^4 / (1 - efficiency) / 1500 W/m^2 )
Let's say Tmax = 100 C (373.15 K), radiator_area_factor = 1 (say we just radiate off the back of the solar panel), efficiency = 30%
R = 1.02 .. so pretty much Earth's orbit, which is fairly reasonable. We're probably within an order of magnitude.
This shows the idea that as you get closer to the sun you need to start building cooling systems as R^2.
posted by introp at 10:08 PM on September 4, 2011
(If that doesn't make sense, imagine putting a radiator sticking out of the back of your solar panel like a tee. Want to almost double the radiation cooling? Just stick another radiator adjacent to the first, farther away from the sun. Of course, you run into scaling issues eventually, but we're being sloppy here.)
Okay, I'm bored, so a rough pass (disclaimer: late-night math):
Where R is 1/r in AU (so halving the distance to the sun would be R = 2) and radiator_area_factor is the ratio of radiator size to panel size (2 m^2 of radiators per 1 m^2 of panel means radiator_area_factor = 2):
. flux_in = power_at_earth_orbit * R^2
. flux_converted = efficiency * power_in
. flux_delta = (1 - efficiency) * power_in ... this is how much you have to radiate to keep your panel temperature constant
. flux_from_radiators = radiator_area_factor * stefan_boltzmann_constant * T^4 ... note T is in degrees kelvin
so pick a steady-state temperature Tmax for your solar panels, some radiator_area and compute:
R = sqrt( radiator_area_factor * sigma * Tmax^4 / (1 - efficiency) / 1500 W/m^2 )
Let's say Tmax = 100 C (373.15 K), radiator_area_factor = 1 (say we just radiate off the back of the solar panel), efficiency = 30%
R = 1.02 .. so pretty much Earth's orbit, which is fairly reasonable. We're probably within an order of magnitude.
This shows the idea that as you get closer to the sun you need to start building cooling systems as R^2.
posted by introp at 10:08 PM on September 4, 2011
Typo typo typo: all the above that say power_in should read flux_in. My brain was swapping.
posted by introp at 10:13 PM on September 4, 2011
posted by introp at 10:13 PM on September 4, 2011
You might be interested in NASA's Solar Probe Plus scheduled to launch in 2015. It will approach to within 8.5 Solar radii of the Sun which is closer than any probe yet.
posted by euphorb at 10:30 PM on September 4, 2011
posted by euphorb at 10:30 PM on September 4, 2011
This is a strange question, since one of the conveniences of solar is placing it at the point of use. The truth is that there is more energy than we need on the planet right now, it's more a matter of capturing it or converting it to a useful form.
A lot of the math for this sort of question has been done in terms of stuff like the Dyson sphere, but they also rest on the positing of a civilization that must needs expand infinitely, a consumer civilization that eats and burns everything in sight until the end of time or, I guess, the sun burns out. Other approaches to civilization might not be so rapacious.
As for figuring what you need to protect your solar satellites if they get too close, you can throw in any sort of unobtainium to serve this purpose. Niven used "GP hulls" for his indestructible spaceships, for instance.
posted by dhartung at 11:37 PM on September 4, 2011
A lot of the math for this sort of question has been done in terms of stuff like the Dyson sphere, but they also rest on the positing of a civilization that must needs expand infinitely, a consumer civilization that eats and burns everything in sight until the end of time or, I guess, the sun burns out. Other approaches to civilization might not be so rapacious.
As for figuring what you need to protect your solar satellites if they get too close, you can throw in any sort of unobtainium to serve this purpose. Niven used "GP hulls" for his indestructible spaceships, for instance.
posted by dhartung at 11:37 PM on September 4, 2011
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posted by jet_silver at 8:23 PM on September 4, 2011