concentrating starlight with mirrors for photovoltaics in deep space

would it be feasible to use mirrors to concentrate starlight in order to produce efficient solar panels in interstellar space? could we produce enough electricity to provide ongoing propulsion?

At first about concentrating sunlight. The Sun is a star like many others, but it is very close to Earth.

The maximum distance of Pluto to the Sun is about 50 AU, that is 50 times the distance of Earth to the Sun. You would need a mirror with an area of 2500 square meters to receive the same energy from the Sun as a solar panel of 1 square meter receives in Earth orbit.

But Pluto is just in the backyard of our solar system. The mirrors needed for interstellar space would be incredible huge and should be aimed to the Sun very precisely. Outside the Oort cloud at a distance of about 200,000 AU, that is the border to interstellar space. The mirror size would be 40,000 square kilometers, 200 by 200 kilometers to get only the power to a square meter at 1 AU distance.

Now about the concentration of starlight.

Starlight is extreamly weak, at the Earth about 100 million times weaker than Sunlight. But a mirror with an area of 100 square kilometers would not help. Starlight is not from a single tiny spot but from incredible many stars spread over the full sky and could not be concentrated by a huge mirror. Only a very small area of stars may be concentrated by an optical mirror to a small solar panel.

Solar concentrators have been used on spacecraft, for collecting sunlight. More info below.

Until now, no mission outside Jupiter's orbit has used solar panels. The first solar-powered Jupiter mission (Juno) used large solar panels instead of combining concentrators with a smaller solar panel.

Saturn orbits at ~10 AU. So with the current state of the art, sunlight at 10AU is not bright enough to make solar panels (with or without concentrators) cheaper than an RTG. At Saturn, sunlight is 2.5 million times brighter than starlight.

The tradeoff between solar panels and RTG is mainly because of weight constraints, I suspect: to launch a spacecraft to e.g. Saturn requires a large amount of delta-V which translates into an expensive launch that puts a tiny spacecraft atop the most powerful rocket we can find.

This makes mirrors a hard sell: you'd have to build a good mirror that is lighter than a solar cell. If mirrors and solar panels are the same wight, you can either carry 2 solar panels or 1 solar panel and 1 mirror of the same size as the panel.

Starlight is more or less isotropic. When you add a mirror to a solar array, you also block the light from the stars behind the mirror.

Deep Space 1 used solar concentrators for sunlight:

Deep Space 1 used an ion engine, so this array "produced enough electricity to provide ongoing propulsion".

Other missions (e.g. Dawn, which used the same type of ion engine as DS1) have used ion engines without solar concentrators. As you can see, the concentrators add a lot of material, so it may be cheaper to just install a bigger array.

• Why did Deep Space 1 use solar concentrators? – uhoh Feb 10 '19 at 10:17
• Do you have an example about concentration of starlight using mirrors instead of lenses? Your example is about sunlight and lenses. – Uwe Feb 10 '19 at 11:00

sources:

numbers:

            visual magnitude     irradiance
The Sun           -26.7            1361      W/m^2
Sirius             -1.5            1.132E-07 W/m^2


You can calculate that quickly;

• Sirius is 25 magnitudes dimmer than the Sun.
• Every 5 magnitudes is a factor of 100
• Sirius is 100^5 = 10,000,000,000 times dimmer than the Sun
• To collect the same power as 1 square meter of solar panel at 1 AU, you'd need 100,000 x 100,000 meter square collection area (100 x 100 kilometers).
• Since stars are so far away, it would be independent of distance to our sun.

If your farthest reflector is 50 kilometers away from your 1 meter solar panel and you want to illuminate your panel uniformly for good electrical performance, you'll have to have all your reflectors pointing with an accuracy of a microradian, or about 0.2 arcseconds, which is mind-bogglingly difficult.

Here are two ways to address that:

1. You could make your panel 10 x 10 meters and run at 1% of solar intensity (which I think is still doable for some kinds of photovoltaics) and then have a pointing accuracy of 2 arcseconds, but going much farther pushes the limits of efficiency. If you are far from the Sun and other sources of heat, the cold will help the efficiency.

2. You can go to non-focusing optics to re-concentrate the light from a larger circle of confusion.

• +1 for quantifying the effects of magnitude. In the general interstellar case there is no need to think in terms of a particular target star and so the pointing problem disappears at the expense of having a fainter background all around. – Puffin Jan 12 at 18:03
• @Puffin diffuse sources of light can not be concentrated. For example imagine using a magnifying glass to focus sunlight, it works well. Then imagine trying to concentrate blue sky; nothing happens. Conservation of etendue = Conservation of phase space It's the "paralleness" of rays from a single star that allows us to concentrate it. So yes, optics demands that we think in terms of a particular star, and the pointing problem does not disappear. – uhoh Jan 13 at 1:22
• good point, I wasn't really "concentrating", ha ha. Actually the motivation from my comment didn't come from any thought of using concentrators; instead I just assumed that the hemispherical starlight would exceed that available from a single bright star. – Puffin Jan 13 at 9:51
• @Puffin ha! :-) taking this further, perhaps caffeine-doped silicon could concentrate better. On the practical side, the problem with photovoltaics is that their efficiency plummets in low light levels. That might be partially ameliorated by the very low temperature they will be at so far from the Sun, but then they might not work at all at such low temperatures. A concentrator will help bring up the current density to allow higher efficiency, and the waste heat will keep the material warm enough to have a decent carrier concentration. I'm no expert on the topic; these are just guesses. – uhoh Jan 13 at 10:57
• ok, got it. I'll refrain from reading up about superconductivity opportunities! – Puffin Jan 13 at 17:11