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JanKanis
JanKanis
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Sure. Well, mostlyalmost.

Sure. Well, mostly.

Sure. Well, almost.

fix/clarify calculation
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JanKanis
JanKanis
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The disk of the sun has an angular diameter of about 32' (arc-minutes) in the sky. If we cover the near side of the moon with adjustable flat mirrors, the reflected beam from each mirror would also have a beamwidth of 32'. If we aim all the mirrors at the same spot on earth, those mirrors from earth look just as bright as the sun (assuming 100% reflective mirrors). The disk of the moon is about the same angular width as that of the sun, so during full moon this produces the same amount of lighting. In that area it would be like day. The spot on earth that the 32' wide beam from the moon illuminates is some 3500 km wide. (Which happens to be the same as the diameter of the moon, as the moon and the sun look the same size in earth's sky.)

Of course this only works when the moon is in the sky at night, which isn't always the case. There is one happy accident which is that the illuminated part of the moon's disk is always the same as the dark part of earth's disk as seen from the moon, so if you want to illuminate the dark part of earth uniformly (at 7.4% of daylight illumination) the moon's phase nicely cancels out. If the moon is at, say, first quarter, then the earth as seen from the moon is at last quarter, so only half of the visible earth disk is in nighttime and needs illuminating, so we can focus the mirrors on the moon only at that area of earth. It doesn't work perfectly, as the spots we can work with are 3500 km wide, but it works to a first approximation. If you want at least 25% of daylight illumination, well, you need at least 25% of the moon's disk to be in sunlight.

The disk of the sun has an angular diameter of about 32' (arc-minutes) in the sky. If we cover the near side of the moon with adjustable flat mirrors, the reflected beam from each mirror would also have a beamwidth of 32'. If we aim all the mirrors at the same spot on earth, those mirrors from earth look just as bright as the sun (assuming 100% reflective mirrors). The disk of the moon is about the same angular width as that of the sun, so this produces the same amount of lighting. In that area it would be like day. The spot on earth that the 32' wide beam from the moon illuminates is some 3500 km wide. (Which happens to be the same as the diameter of the moon, as the moon and the sun look the same size in earth's sky.)

Of course this only works when the moon is in the sky at night, which isn't always the case. There is one happy accident which is that the illuminated part of the moon's disk is always the same as the dark part of earth's disk as seen from the moon, so the moon's phase nicely cancels out. If the moon is at, say, first quarter, then the earth as seen from the moon is at last quarter, so only half of the visible earth disk is in nighttime and needs illuminating, so we can focus the mirrors on the moon only at that area of earth. It doesn't work perfectly, as the spots we can work with are 3500 km wide, but it works to a first approximation.

The disk of the sun has an angular diameter of about 32' (arc-minutes) in the sky. If we cover the near side of the moon with adjustable flat mirrors, the reflected beam from each mirror would also have a beamwidth of 32'. If we aim all the mirrors at the same spot on earth, those mirrors from earth look just as bright as the sun (assuming 100% reflective mirrors). The disk of the moon is about the same angular width as that of the sun, so during full moon this produces the same amount of lighting. In that area it would be like day. The spot on earth that the 32' wide beam from the moon illuminates is some 3500 km wide. (Which happens to be the same as the diameter of the moon, as the moon and the sun look the same size in earth's sky.)

Of course this only works when the moon is in the sky at night, which isn't always the case. There is one happy accident which is that the illuminated part of the moon's disk is always the same as the dark part of earth's disk as seen from the moon, so if you want to illuminate the dark part of earth uniformly (at 7.4% of daylight illumination) the moon's phase nicely cancels out. If the moon is at, say, first quarter, then the earth as seen from the moon is at last quarter, so only half of the visible earth disk is in nighttime and needs illuminating, so we can focus the mirrors on the moon only at that area of earth. It doesn't work perfectly, as the spots we can work with are 3500 km wide, but it works to a first approximation. If you want at least 25% of daylight illumination, well, you need at least 25% of the moon's disk to be in sunlight.

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JanKanis
JanKanis
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Sure. Well, mostly.

There are lots of answers here saying why that would be a bad use of your resources, which is certainly true, but not answering the question. So I'll do that here.

The disk of the sun has an angular diameter of about 32' (arc-minutes) in the sky. If we cover the near side of the moon with adjustable flat mirrors, the reflected beam from each mirror would also have a beamwidth of 32'. If we aim all the mirrors at the same spot on earth, those mirrors from earth look just as bright as the sun (assuming 100% reflective mirrors). The disk of the moon is about the same angular width as that of the sun, so this produces the same amount of lighting. In that area it would be like day. The spot on earth that the 32' wide beam from the moon illuminates is some 3500 km wide. (Which happens to be the same as the diameter of the moon, as the moon and the sun look the same size in earth's sky.)

Now, the earth is bigger than that, so that 3500 km wide spot won't cover the entire earth. The diameter of the earth is some 12000 km, which is 3.67 times the diameter of our spot. The angular area of the earth's disk as seen from the moon will be 13.45 times as large as the area of our spot. To distribute that light evenly over the whole disk, it will be 13.45 times dimmer, so your solar panels will only work at 7.4% of daylight output. But if you are willing to make some compromises such as not illuminating oceans or Antarctica, you should be able to get your percentage up over 25% for a large part of the time, and at some times closer to 100%.

Of course this only works when the moon is in the sky at night, which isn't always the case. There is one happy accident which is that the illuminated part of the moon's disk is always the same as the dark part of earth's disk as seen from the moon, so the moon's phase nicely cancels out. If the moon is at, say, first quarter, then the earth as seen from the moon is at last quarter, so only half of the visible earth disk is in nighttime and needs illuminating, so we can focus the mirrors on the moon only at that area of earth. It doesn't work perfectly, as the spots we can work with are 3500 km wide, but it works to a first approximation.

This plan assumes you will cover the entire visible side of the moon in mirrors. That will give you an illumination of 7.4% of the sun if you want to cover the entire night side of Earth, up to 100% if you are happy with a 3500 km wide spot. If you are happy with a 3500 km wide spot and 25% of daytime illumination, you only need to cover 25% of the moon's surface with mirrors. The most economically effective (well, least ineffective) place would be the center of the moon's near side. Or if you want to make as much as possible from the crescent moon, cover a band over the moon's equator on the near side.

As for light pollution, that depends on your definition. The moon will look as bright as the sun, depending on how you point the beams. Is that light pollution or is that just extended daytime? It surely will wreak havoc on the day-night rhythm of plants and animals, but with a bit of environmental care many species could probably adjust.

But if your goal is energy production it is much better to put those solar panels themselves on the moon. A lot of the light reflected to earth won't end up on a solar panel after all. Or even better, put the panels in space where they don't suffer from nighttime. Or just put them on earth and invest in some kind (any kind) of energy storage, that will be much cheaper than putting stuff on the moon or in space.