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Short-duration flights (Vostok, Voskhod, Mercury) use several-kWh batteries. Space stations use photovoltaic cells for their high power-to-weight ratio.

The longest mission duration accomplished with a fuel cell seems to be a few weeks: Gemini 7 (13 days 8:35:01), Apollo 17 (12 days 13:51:59) and STS-80 (17 days, 15:53). (Soyuz 7K-LOK would have used fuel cells for its moon landing mission, as well.)

Soyuz and Shenzhou both use PV cells. SpaceX Dragon is the first American transport vehicle to use solar arrays.

What advantage do fuel cells have over solar for 12-18 day missions, and why didn't Gemini, Apollo, and STS use PV instead?

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    $\begingroup$ Because the PV cells available in the 1960s (a pretty new technology back then) were much less efficient (and heavier) than those available today? The early solar-powered communications satellites were very low-power devices: the original Telstar's PV cells generated a mere 14 watts. $\endgroup$ – jamesqf Feb 22 '15 at 5:32
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    $\begingroup$ @jamesqf: the Apollo contemporary Soyuz 1 (1967) had solar panels, however. $\endgroup$ – Jacob Krall Feb 22 '15 at 19:11
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    $\begingroup$ If I remember correctly, before Saturn the Russian boosters could launch more weight. So it was probably an engineering decision based on lots of factors, with a balance tilting in favor of solar as they developed. $\endgroup$ – jamesqf Feb 23 '15 at 19:31
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The high power levels of Shuttle and its need to return to an aerodynamic configuration would have necessitated a very large array that would need to be deployed and retracted each mission. This would have complicated the design considerably. reduced the maneuverability of the Shuttle, and introduced other failure modes.

Although I am not as familiar with them, I imagine some of the same considerations apply to the other vehicles you mention.

Incidentally, Discovery's maiden flight, STS-41-D, deployed a large solar array for test purposes.

enter image description here

enter image description here

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    $\begingroup$ From a design perspective, that solar array is a clear predecessor of the ISS solar array elements. Nice photos! $\endgroup$ – dotancohen Feb 22 '15 at 14:05
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    $\begingroup$ Yeah, it was a test of the mast/blanket technology. IIRC there were only a few working cells on it. $\endgroup$ – Organic Marble Feb 22 '15 at 14:10
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    $\begingroup$ So solar only becomes competitive once the fuel for the fuel cells weighs a LOT more than that giant solar mast! Awesome answer, thanks. $\endgroup$ – Jacob Krall Feb 22 '15 at 18:23
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    $\begingroup$ If you get a chance to see the old IMAX movie The Dream is Alive, there is footage of this mast being retracted around 16:30 into the film. It's pretty awesome in IMAX. $\endgroup$ – Organic Marble Feb 23 '15 at 19:15
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    $\begingroup$ @Sean IIRC nothing significant. There may have been some cells hooked up to a test circuit, but I'm not even sure about that. The objective was to test the deployment system. $\endgroup$ – Organic Marble Jul 10 '19 at 21:27
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Fuel cells produce water. The output of the Apollo fuel cells (PDF on Apollo power supply system design) was used as drinking water and as a coolant in the environmental control system.
If you use solar cells, you need rechargeable batteries to supply the spacecraft when it's on the night side of the planet.
I suspect the choice came down to the total weight of the alternatives: fuel cells + H2 and O2 tanks versus solar cells + batteries + drinking water.

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    $\begingroup$ Shuttle fuel cells created water too, and it was used for the same purposes. They made so much water that before ISS it had to be dumped out into space regularly (later they gave it to ISS). I started to put this in my answer, but I think it was really more the complexity of deploying and retracting the array that ruled it out for STS. $\endgroup$ – Organic Marble Feb 24 '15 at 14:40
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The issue with solar panels is the mass and complexity of such a system. Firstly, any meaningful solar array is going to need to be big. But you can't launch with solar panels extended, that would result in a stupid looking and unaerodynamic fairing (or in the case of the American Space Shuttles (STS) panels breaking) So, you need somewhere to stow them.

In standard spacecraft such as the Apollo CSM, this isn't so much a problem, they can be stowed out of the service module. But for the shuttles, they would have to be stowed inside the shuttle, among the OMS fuel and the OMS oxidiser, reducing the space for said fuel and oxidiser.

That's not the only problem, also the batteries needed for the dark side of orbit very heavy for the energy they store, and in the end, for the distance these are going, (to the Moon and back at most) it won't take too much time so therefore the fuel cells and fuel are cheaper and smaller. And they can be put anywhere convenient. Sure, solar power and batteries are best for interplanetary travel but for short flights, fuel cells are lightest, thus needing less fuel.

THE BOTTOM LINE: Fuel cells are the lightest for journeys within Earth's gravitational field, and solar power with batteries is lightest for interplanetary missions.

And the ISS uses solar power because it's up to stay and doesn't need to change its orbit (save for the odd bit of space junk) and fuel cells on the ISS would need resupply missions every day or so.

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    $\begingroup$ "...and in the end, for the distance these are going..." is it really distance, or is it time that's important here? Consider three days in orbit vs three years in orbit - isn't it really the total energy you need - $current \times voltage \times time$? Solar is renewable for years or decades while fuel cells or storage batteries run out. $\endgroup$ – uhoh Apr 9 '17 at 11:53
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    $\begingroup$ Not only weight and size, but to avoid structural stresses, you'd have to stow the arrays when burning the engines, which is exactly when you want both your batteries and panels providing independent supplies of electricity.. $\endgroup$ – Innovine Apr 9 '17 at 19:24
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    $\begingroup$ solar panels are useless for interstellar missions, there isn't enough light out there. solar panels function only as far out as jupiter/saturn, beyond that they generate so little power that they are not worth the weight. Might change if the technology improves but that's todays situation. $\endgroup$ – Innovine Apr 9 '17 at 19:26
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    $\begingroup$ I suppose it is time that is more important, even though it is kinda linked to distance. Improving answer based on feedback! $\endgroup$ – TDplay Dec 25 '17 at 17:46
  • $\begingroup$ And the Soyuz uses solar because it used to stay in orbit for weeks at a time, well beyond the length of time fuel cells would be capable of providing power for. $\endgroup$ – Vikki Jul 10 '19 at 21:29

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