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The Emperor of the World wants there always to be a full moon. His Scientific Advisor (the SA) comes up with a plan.

He plans to cost out the venture, hand it over to the Keeper of the Treasury who then has the unpleasant job of explaining to the Emperor how much it will cost.

The SA's plan is to to cover the entire surface of the moon with a network of LEDs, solar panels and rechargeable batteries.

The sunny side of the Moon will charge the batteries and the dark part of the moon will be lit up with the LEDs. Detectors will make sure that only the dark parts of the Moon facing the Earth are lit.

Ignore the exorbitant cost, not to say the virtually impossible task of transporting the materials - those difficulties will be presented to the Emperor by the unfortunate Keeper of the Treasury.

Question

In theory, given unlimited resources and using 2018 technology could the SA ensure that there was always the equivalent of a full Moon in terms of brightness. Are there any insurmountable technical problems?


Side Note - Not part of the question but the emperor wants a picture of his face to flash on and off when a New Moon coincides with his birthday. Eventually he would like the Moon to act as a colour TV screen for propaganda.

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    $\begingroup$ Is the emperor also going to keep these panels clean from dust? $\endgroup$ – NofP Nov 30 '18 at 0:42
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    $\begingroup$ Assassinating or otherwise convincing the emperor to "stop it" are much cheaper solutions. However, the army of needed maintenance techs would at least get to live on the moon and the kick to space tech would have an interesting societal impact. $\endgroup$ – Gary Walker Nov 30 '18 at 3:05
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    $\begingroup$ @NofP There's no atmosphere on the moon, how dusty does it get? Occasional meteors? $\endgroup$ – Xen2050 Nov 30 '18 at 4:28
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    $\begingroup$ The LED plan seems to miss an obvious problem: the moon orbits the Earth, and so is visible (even if only illuminated by Earthshine) only half the time. Better to cover the actual moon with ultra-black panels so it can't be seen, and build an inflatable faux moon (a larger version of the early Echo satellites) in geostationary orbit. $\endgroup$ – jamesqf Nov 30 '18 at 6:50
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    $\begingroup$ @jamesqf - I like it. $\endgroup$ – chasly from UK Nov 30 '18 at 9:01

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Sure it is possible (in theory).

Moon's albedo is 12%

Photovoltaic panel efficiency is around 19% (commercially available) and can go up to 40% with more exotic technologies.

Assuming Moon gets the same amount of solar radiation as Earth, surface receives 1367 watts per square meter, 42% of which is visible light, which gives us 574 watts per square meter to play with. LEDs should beam back 69 watts. Assuming that we are using commercially available LEDs with 50% efficiency, 1 square meter should house 138 watts of LED power. This is a lot, but our bulbs will cover only a fraction of surface. The rest can be used for solar panels. Solar panels, on the other hand, will give us 229 watts per square meter.

During lunar day, panels will be baking in sunlight, converting it to electricity, which would be stored in batteries (do we have enough lithium on Earth? Hmm...) during the night, the bulbs will turn on, creating illuminated Moon face.

Also note that while solar panels can cover 100% of Moon surface, LEDs need to be installed only on the visible side, which should double the energy balance in our favor.

P.S. Calculations above assume that lunar LEDs work just like the Moon's surface, i.e. their emission is omnidirectional. Our efficiency can be improved A LOT is we are allowed to beam light only in Earth's direction.

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    $\begingroup$ Why not place the solar panels on the dark side of the moon, since the "Dark side" is not dark but lit up during the times where the moon is not full (And when the moon is not full, well you dont need the solar panels) $\endgroup$ – Magic-Mouse Nov 30 '18 at 9:13
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    $\begingroup$ I was going to suggest much the same as @Magic-Mouse - you only want to light up the area of the moon in shadow too - you could literally wire the solar panels to LEDs directly opposite to each other - big savings on batteries, as you don't need to store the power - you do need a lot of cables however (can be reduced by shared power lines with data transmission to determine with LEDs to light) but then again, with co-located panels and LEDs, you'd need batteries that would last with each cycle being an entire month. $\endgroup$ – Baldrickk Nov 30 '18 at 9:36
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    $\begingroup$ I suggest skipping the batteries entirely. "Just" transfer the power across an ultra-high voltage lunar electricity grid. After all - half the moon is always receiving the power you need. $\endgroup$ – Windlepon Nov 30 '18 at 9:54
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    $\begingroup$ Wouldn't a huge solar farm effectively reduce the lunar albedo for that area, as the energy is getting absorbed by the panels instead of being reflected? $\endgroup$ – Kyyshak Nov 30 '18 at 10:38
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    $\begingroup$ @Kyyshak: The moon’s surface is actually very black/dark. The solar panels probably reflect more light than the moon’s natural surface. $\endgroup$ – Michael Nov 30 '18 at 13:10
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I wouldn't touch the actual moon, it's 384,400km away, it seems much cheaper & within reach to make your own "equivalent" using an array of satellites (maybe only 320km - 600km away) with very bright lights, maybe in a geosynchronous orbit (approximately 35,786 km away) to keep them at least visible every night, using each one like a single pixel in a very large "display screen".

Either individual satellites just close enough together to look right, or tethered together with cables or filaments, or an extremely large single array or framework of bright lights.

So you end up with a virtual LED display in space. Perfect for displaying messages, or depending on the density of lights, even any picture or video.

With unlimited resources & energy, powering them should be within reach today with either solar power & batteries, or nuclear, or maybe even a Tesla-esque wireless power transmission from earth. Taking the "unlimited resources" more literally, then the pixel-satellites could even be brighter than the actual moon, so a "sky television" could even be seen during the day.

Some satellites are already visible from the earth now (and I'm pretty sure they don't even have any purpose-built lights aimed at the earth). Here's an image of some from How to See and Photograph Geosynchronous Satellites:

enter image description here

Just imagine a few million of them, tied together in a giant "screen" array, with unlimited energy for bright colours, and you've got your emperor's face, and propaganda, and a moving zooming or even exploding image of the moon, or Mars, or Jupiter, or anything really.

Here's a hopefully poor example using 160 computer keyboards (each with maybe 100 led lights), but it should give an idea of what's possible with even just 160,000 lights (from here, video here or directly on YouTube):

enter image description here

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Numbers, numbers

  • The actual Moon surface is quite dark; the albedo of the Moon is 0.136. This means that the Moon reflects only 13.5% of the sunlight it receives. Moreover, the reflection is diffuse, that is, the reflected light goes all over the place, not only towards Earth.

    In order to move light from the far side of the Moon to the near side in the form of electric power, we need to (1) capture the energy of the light and convert it to electric energy, (2) transfer the electric energy to the near side, and finally (3) convert the electric energy into light. The overall efficiency of the process must at least match the 13.6% achieved by the Moon rocks through reflection.

    Can this be done?

  • The efficiency of a decent photovoltaic panel is about 20%, meaning that the panel converts 20% of the incoming light energy into electric energy.

  • The efficiency of a white LED lamp is currently around 15%, but 20% efficient lamps exist; the theoretical maximum luminous efficacy of a white LED is about 40%. Let's say that the emperor's scientists have achieved the capacity to make white LEDs with 30% luminous efficacy.

  • Let's put the efficiency of electric power transmission at 90%.

  • Overall this gives 20% (light-to-electricity conversion) × 90% (transmission) × 30% (electricity-to-light conversion) = 5.4% overall efficiency. This means that, at best, the artificially illuminated new moon will have about 40% of the luminosity of the full moon; in photographic terms, that's a difference of about 3.5 stops of exposure; in astronomical terms, this is a difference of one magnitude.

    How visible is the difference in luminosity? Here is an image showing a normally exposed full Moon and a copy with the luminosity reduced to 40%.

The Moon with normal and 2.5 times smaller luminosity

The photograph of the Moon on the left is exposed so that the highlights are close to the maximum value, without exceeding it. The Moon on the right is the same image, digitally manipulated to make the Moon have 40% of the luminosity. Own work.

  • But what about the phases of the Moon? Won't there be a marked difference in luminosity between the naturally lit and the artificiall lit parts? Yes, there will be a one-magnitude, or 3.5 stops, difference; visible, but hey, it very much better than the current situation.

  • But what about the non-uniform illumination of the photovoltaic panels? True, the Moon is spherical, and the conversion efficiency of the photovoltaic panels on the far side will vary between the theoretical maximum when the Sun is up in the sky to zero when it is on the horizon; this will bring the available power down a factor of two, and make the artificially illuminated part even darker. Actual calculation remain as an exercise for the reader; however, overall we can confidently say that we can build a decent artificial lunar illumination system for our glorious and much beloved emperor.

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  • $\begingroup$ Check out my answer and see if why I disagree with you (I claim, now, that it can be done) is wrong. LED efficiency isn't particularly useful until you normalize lumens. I'm curious to know if my analysis was bad. $\endgroup$ – JBH Nov 30 '18 at 3:08
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    $\begingroup$ Why would you not aim the LEDs so that they point to the earth. An directional lighting would be much more efficient in terms of lighting up our planet. $\endgroup$ – Gary Walker Nov 30 '18 at 3:10
  • $\begingroup$ Hmm this does make me wonder how much we would be allowed to get away with faking it would it be allowed for example to essentially turn the uniluminated portion of the moon facing Earth into effectively a giant LED display that simply displays the image of the moon that would be visible if illuminated. If so we can get better results for less power by focusing the light from each point more closely onto the 2 degrees of sky containing Earth than the 178 degrees of sky conspicuously lacking any presence of Earth. $\endgroup$ – MttJocy Nov 30 '18 at 3:11
  • $\begingroup$ @JBH: We both say that it can be done. This calculation is made without batteries, just moving electric power from the illuminated (but invisible) side to the visible (but not illuminated) side. The rest is just a difference of values for efficiencies, which are anyway best guesses. $\endgroup$ – AlexP Nov 30 '18 at 4:02
  • $\begingroup$ Don’t forget the fact that transmission lines are nowhere close to efficient at long distances. $\endgroup$ – dalearn Nov 30 '18 at 16:57
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Much cheaper option:

Every evening, send a large LED panel into the upper troposphere, e.g., with balloons and haul it down every morning. Since the panel is a lot closer to the ground, it can affordably be a lot smaller in cross section than the moon.

Plus side:

You can then rig the LED panel like a normal TV or monitor.

Minus side:

  • It will always remain in the same place.
  • There will normally be two "moons" in the sky.
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    $\begingroup$ But will it always stay in the same place? There's a lot of weather up there softschools.com/facts/weather/troposphere_facts/2202 $\endgroup$ – chasly from UK Nov 30 '18 at 14:21
  • $\begingroup$ @chaslyfromUK: Normally, with a balloon (or blimp) supporting expensive technology, you'd have it tethered in place. But what I meant above, was that the screen wouldn't move across the sky like the actual moon. $\endgroup$ – nzaman Nov 30 '18 at 15:04
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EDIT: It can be done, see my second edit below.

Fundamentally can't be done. This issue was parodied at XKCD. The gist of the problem is this: you can't duplicate the firepower of the sun, especially if you're using a solar-based power system that isn't 100% efficient. Even if it was. It would need to acquire 100% of the solar energy that would hit the moon during a full moon, transfer that power perfectly (100% efficiency... the engineer within is starting to weep) to LEDs, which can emit the collected power as photons with 100% perfect conversion (oh, the pain!).

Can't be done without serious power. Serious. Check out the link. Serious.


Edit:

Also, remember that where there's solar panel, there isn't LEDs. You can hide the batteries underground and put the panels on the backside of the moon (it's tidally locked), but that means you must capture and store enough power to illuminate all those buka-watt LEDs for each night. Serious.


Edit:

OK, Shadoweze has piqued my curiosity. Lunar albedo for a full moon is 0.12. Albedo is the ratio of energy received to energy reflected. The sun bathes the moon in 1kw/m. So the reflection, what we need to achieve, is 0.12kw/m.

The full-moon lunar surface is 1013 m2. That means we need to generate 1.2E12 watts or 1.2 terrawatts. The most efficient solar panel in 2018 has a 22.2% efficiency. That means for every kw of solar energy we'll actually have only .222 kw to work with. That's twice-ish what we need, so far so good.

Average lunar light is about 0.015 foot-candles or about 0.0019 lumens per m2 for 0.016 lumens-per-watt of lunar emittance. 2018's most efficient LED is 105 lumens-per-watt. Good news! We don't need to cover every inch of the earth-side of the lunar surface!

Better news is that for each pass of the moon in front of the sun, there isn't a commensurate "full-moon" pass for the earth. The moon varies from a new moon (100% LED use) to a full moon (0% LED use). I'm absolutely wrong with the assertion I'm about to make, but to keep this from becoming a full dissertation, let's assume we only need to store 50% of the power needed to hold a full moon all the time and there's enough space between the LEDs that we can use detectors to shut off the LEDs we don't need during each phase of the moon. (And I'm ignoring the fact that we only need to turn the LEDs on when the emporer is in the night cycle. Who cares what the peons see, right?)

OK, I'm convinced. Shadowzee's right. It can be done. It might need enough battery mass to shift the moon's orbit... but it can be done.

Why is the XKCD no longer relevant? It's emitted light from the earth reflecting off the moon. That takes a ton more power, and I'd ignored it.

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    $\begingroup$ Just add a massive solar array on the far side of the moon so that it is never seen from earth. Unlimited resources is an amazing thing for solving problems. $\endgroup$ – Shadowzee Nov 30 '18 at 0:53
  • $\begingroup$ @Shadowzee, you're timing was perfect. I just commented on that. I'm thinking you'd change the mass of the moon with the batteries needed to pull this stunt off. I'm still claiming it fundamentally can't be done. But, given enough Clarkean Magic.... $\endgroup$ – JBH Nov 30 '18 at 0:54
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    $\begingroup$ I know what you mean... but unlimited resources...unlimited..resources. I'm a strong believer of Throw enough engineers, scientists and money at a problem and its going to disappear. $\endgroup$ – Shadowzee Nov 30 '18 at 1:25
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    $\begingroup$ @Shadowzee, meh. Given enough Clarkean Magic everything is possible. That's boring. Half the fun of a story involving this concept is the weaknesses that make it imperfect. Achieving "good enough" is realistic. $\endgroup$ – JBH Nov 30 '18 at 2:10
  • $\begingroup$ @Shadowzee... wait... why is this an unlimited resource? The back side of the moon only faces the sun half the time. It has a limited surface. You can't gather more than 100% of the sunlight in energy. LEDs are brighter per-unit than reflected light off the surface, but you can't collect, store, transfer, and convert energy with 100% efficiency. My engineering spidy sense says this can't work unless the reflectivity of the lunar surface really stinks. Time for some research. $\endgroup$ – JBH Nov 30 '18 at 2:27
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Are there any insurmountable technical problems?

Not really, unless you are under some time constraint. Moon reflectivity is around 0.12, and considering directed reflectivity that goes down to around 0.02. In other words, less than 2% of the incident solar light gets reflected towards the Earth.

So it's possible to cover the Moon with laser LED arrays and solar panels; even with very low efficiency and transmission losses, the Sun will supply energy enough to power a virtual moonlight beam.

Of course most of the material will need to be mined in situ. This means replacing copper with aluminum and magnesium wherever possible. On the other hand, vacuum refinement of silica would be easier than on Earth. Solar panel fabrication would be an ongoing project, because the solar wind might age panels faster than normal.

The Moon has a visual radius as seen from Earth of around 16 arc-minutes, so it covers 800 arc-minutes squared. The best resolution the human eye is capable of is around .7 arc-minutes; make that 0.5 and you have a radius of 32 pixels, requiring around 3220 beam emitters. The "image" thus obtained will be indistinguishable from the Moon by the naked eye. You do not need to cover the whole Moon with LED panels (or solar panels).

The total visible light from the Moon towards the Earth has been plausibly calculated by the Internetz at 1/436000 of the Sun, the latter being 550 W/m^2 in the visible range.

So we can assume the total output required of each beam emitter to be around 50 MW. Solar panels can supply around 200 W/m^2, requiring a minimum of 25-50 hectares of solar panels for each tower, or 160,000 hectares in all. We may actually need up to about three times that to cover the new moon stage (when the whole 3220 emitters are powered by a ring of solar farms just beyond the terminator, with equivalent power transmission line lengths of 2800 km in length and losses thereof approaching 20% for aluminum-magnesium lines).

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As already stated - lighting up the surface of the Moon with LED's to mimic a full one can't be done with just solar panels and LED's.

"Possible" other options?

  • Nuclear power to provide the electricity - @Gary Walker pointed out the amount of Thorium on the moon to use for fuel. Benefit of not being limited by incoming sunlight
  • Earth based generators beaming power to the moon via microwaves?
  • Network of giant mirror satellites to reflect sunlight onto the moon when it's behind earth
  • During non-full moons, fly a massive plane/drone equipped with a giant LED screen between the Emperor's location and the moon, to mimic the appearance of a full moon. Added bonus of being able to display messages
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    $\begingroup$ How is nuclear a problem? The technology has been available since world war 2 $\endgroup$ – Shadowzee Nov 30 '18 at 1:17
  • $\begingroup$ I meant in terms of scale and providing fuel - technologically it's probably fine. Will edit $\endgroup$ – Chromane Nov 30 '18 at 1:19
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    $\begingroup$ The mirror satellites strike me as the best idea, simply because they have the fewest moving parts (aside from faking it with earthbound aircraft). Getting maintenance technicians up to fix objects in orbit, let alone on the moon, is a nontrivial task. $\endgroup$ – Cadence Nov 30 '18 at 1:29
  • $\begingroup$ @Chromane Plenty of Thorium on the moon. Even have a good ore location, so you could use local sourcing. You also have to develop LFTR tech, but that is a drop in the bucket for this project. Solar cells have to be replaced frequently too and require much more infrastructure, esp. considering the huge batteries or electrical grid need to work during the 2 week long nights. $\endgroup$ – Gary Walker Nov 30 '18 at 2:58
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Aiming makes a huge difference with LEDs

This adds to several answers which do the heavy calculations to duplicate the moon's albedo with LEDs. But the LEDs don't need to work nearly that hard.

The only light that matters is the light that's aimed at the Earth.

Since LEDs only emit about a 140-160 degree wedge of light, they lend themselves to aiming with lenses, which are extremely efficient. You narrow its radiant angle to just cover the earth. This dramatically reduces the energy required, by a factor of very roughly 99%, and that makes this a whole lot more practicable.

Since the moon is in synchronous rotation, you will only need to aim the LED once, you don't need heliostats to track the Earth.

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Recently a Chinese company had proposed plans to put fake moon into orbit.

This is a direct Quote from BBC

According to the People's Daily state newspaper, officials at a private aerospace institute in Chengdu want to launch this "illumination satellite" in orbit by 2020, and say it will be bright enough to replace street lights.

Why i pointed to this concept/idea?

Because in this scenario you do not need solar panels and leds which i think will cut costs and "EMPEROR" highness would be pretty much happy. No major capital burning here!

When and How ?

The satellite would be put to orbit by 2022 or so and would be known as the "Illumination Satellite", which would have reflective panels to reflect sunlight similar to putting a gigantic mirror in space. It would be in a geostationary orbit roughly 37,000km from Earth.

This is not the First of its kind mission (Quote from same BBC article)

In 1993, Russian scientists released a 20m-wide reflector from a supply ship heading to the Mir Space Station, which was orbiting at between 200km and 420km.

Znamya 2 briefly beamed a spot of light about 5km in diameter to Earth. The light marched across Europe at 8km/hr, before the satellite burned up on re-entry.

Side-effects / Disadvantages :

  • May affect natural sleep cycle in Humans.
  • Nocturnal creatures would be affected drastically.
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This is impossible for a multitude of reasons.

First of all, the moon doesn't really receive enough sunlight to power LEDs covering half of its surface. The amount of energy a single square inch of modern solar panel produces in an hour is only about 0.1 watts, whereas the amount of energy required to power a single modern LED for an hour is 6 watts. That means that an 8"x8" solar panel would be required to constantly power an LED that takes up a fraction of a square inch of space. Area-wise, the bright side of the moon just isn't big enough to power its opposite half.

Second, there is the issue of transporting the power you get to the LEDs. Every cable that we have loses power for every foot that it travels, which is a natural limit on how far power can be transported. Even with fiber optic -- the most efficient path we could use with 2018 technology -- the power loss experienced over the hundreds of miles of the moon's diameter would be too great for anything to reach the other end.

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  • $\begingroup$ We don't need 6 watt LED bulbs. They should only produce as much light as illuminated Moon surface. $\endgroup$ – Alexander Nov 30 '18 at 1:10
  • $\begingroup$ @Alexander, according to this XKCD, sunlight bathes the moon in 1Kw/m. Modern square LED panels aren't much different in size to the old round LED bulbs, r~=4mm including the base or 5.026e-5 m^2. That's basically 18,967 LED per square meter for 52.7mW per LED. You're right, we don't need a 6w LED, unless you need a lot of space between the LEDs (like detectors to turn off LEDs when bathed in sunlight, overly big ones. This is a government operation, after all). $\endgroup$ – JBH Nov 30 '18 at 2:25
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I can't put this in the original question because it might invalidate some answers. Therefore I'll put it as an 'answer' to my own question.

White Solar Panels

It’s being touted as a ‘revolution in renewable energy architecture’ – the world’s first white solar panel with no visible cells or connections.

https://www.energymatters.com.au/renewable-news/white-solar-panels-em4579/

Using these we could cover the side of the moon facing us and immediately get a much brighter moon. This would also make the unlit side somewhat visible. The LEDs could be inserted through holes on the panels and any stray illumination from them would also be reflected.

This is incomplete but it would supplement answers by those who have assumed solar panels must be black.

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Note: this answer was thought of before noticing the stipulation of "needs 2018 technology". I'm still including it because it would be exactly the kind of thing an worldwide emperor who wants a permanent full moon would approve of.

Move the moon to the L2 Sun-Earth Lagrange point

the L2 Sun-Earth Lagrange point is one of the 5 points in an orbital pattern where you can place objects in a relatively stable location relative to the 2 larger objects in the pattern. It is located about 1 million miles away from Earth in the opposite direction from the Sun. Moving the moon there means it should always be full moon.

Moving a gigantic natural satellite like this is impossible with our current tech. It would also have an absolutely massive impact on Earth's ecosystem: tides would change, no more lunar cycle for nocturnal animals, it would break the Earth-Moon Lagrange points and it would forever remove the possibility of solar eclipses.

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Ring Roads Around The Moon

There have been several Answers regarding photovoltaics and LEDs, which have missed a crucial point : no single device both creates and ingests light. If you have static devices on the lunar surface, you would need to alternate them on the Lunar ground, generating a fraction of the possible light. Directionality might improve that fraction.

Another possibility is to have moving devices. Imagine a large number of rings around Luna, built of railroads. Each ring is covered in rail cars that either receive light (photovoltaics) or creates light (LEDs). Electricity is transmitted through the rail, suitably insulated or through super-conductivity. Luna's synodic period is about 27.3 days, and Luna's circumference is 6786km, so the fastest rail at the equator needs to travel at 248km per day, or about 11km an hour.

Never stopping moving, with different LED cars set to different colors / brightnesses to emulate the ground underneath them.

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  • $\begingroup$ I'm concerned that the energy required to drive the rail cars would outweigh the advantages. Also, to emulate what's underneath them they would have to illuminate the ground because they are in the dark. Wouldn't they just see railway tracks? $\endgroup$ – chasly from UK Nov 30 '18 at 21:14
  • $\begingroup$ Imagine that the PVs or LED panels are set on wide panels held over head over the railroad cars, and that their edges are very close. Perhaps better to overlap with differing heights, so they don't run into each other as we go over terrain. Imagine that these panels are very large (kilometers across). $\endgroup$ – Christopher Hostage Nov 30 '18 at 21:21
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    $\begingroup$ As for emulating, we can show anything we want through the LEDs. The original Lunar surface as appropriate for the current orientation of Luna and Sol, for instance. $\endgroup$ – Christopher Hostage Nov 30 '18 at 21:22

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