If there were humans on the Moon - would we see the settlement lights from the Earth? For instance during a thin crescent Moon - could we see the lights of civilization in the parts of the Moon in darkness? 

It's a fun question to answer I think, so let's give it a go.

We can work it out backwards from the brightness of the full Moon.

Looking out on the lunar surface from inside a Moon city, frame from the 1965 Russian film Luna

(You can get this article as a kindle ebook)

AREA OF MOON NEAR SIDE NEEDED FOR SAME ILLUMINATION AS SIXTH MAGNITUDE STAR

First the Moon is –12.92 in Apparent magnitude.

The way this works is back to front from what you might expect. Bright stars are around zero magnitude, the very brightest like Sirius have negative magnitude - and the dimmest stars you can see with the naked eye in a dark rural site on a clear night go down to sixth or seventh magnitude for an experienced keen eyed observer.

So then, a sixth magnitude star is 18.92 magnitudes fainter than the full Moon. The other bit of information we need is that with each increase in magnitude, the stars are dimmer by a factor of 2.512 (this is just a number astronomers have settled on for historical reasons).

The brightness ratio between the Moon and a sixth magnitude star, therefore, by this formula for magnitudes, is 2.512^18.92.

I'll indent the rest of this calculation so you can skip it easily if you want.

So, the area of patch of the illuminated Moon equivalent to sixth magnitude star is 

π * (MOON'S RADIUS)² / 2.512^18.92

Note - we can treat the moon as a disk here. Of course it really is a sphere - but it turns out that this makes no difference, as it happens to have pretty much uniform brightness over its surface as seen from Earth. The illuminated Moon has no limb darkening. 

So, the first thing to do is to find out what size of a patch at the centre of the Moon as seen from Earth will have the same brightness as a sixth magnitude star.

Let's call the radius of that patch r, then
πr² =  π * (MOON'S RADIUS)² / 2.512^18.92

So, r =  (MOONS RADIUS) / sqrt(2.512^18.92)

The moon's radius is 1737400 meters

So our patch's radius is 1737400 / sqrt(2.512^18.92), or 285.57 meters.

So our patch's width is around 571 meters.

It's area is π * (285.57)² or about 256,000 square meters.

Let's try the patch widths for other magnitudes also. With each magnitude we increase the radius by sqrt (2.512).

See "Astronomical magnitude scale" from the International Comet Quarterly) - of course what you see depends a lot on your eyesight as well as your location. In very dark skies some people may see stars as dim as seventh magnitude.

So, looking at the last row in that table, if you could illuminate a roughly 9 kilometer diameter patch of the Moon as brightly as the sun does, it would shine in our sky as brightly as Arcturus, as bright as one of the brightest stars in the sky.

Let's look though at sixth magnitude - that's just visible to a keen observer in a very dark location.

CONVERSION TO "100 WATT" LIGHT BULBS

A hundred watt bulb has 2.6% efficiency Incandescent light bulb - so only puts out about 2.6 watts of light energy.

Each square meter of the Moon is illuminated with about 1000 watts - but - the albedo of the lunar soil is 0.12, it's actually quite dark - so only 120 watts is reflected back. 

So, each square meter reflects back light equivalent to about 46 of the "100 watt" light bulbs. So our 571 meter diameter, 256,000 square meters area of illumination of the Moon is equivalent to about about 11 million light bulbs shining on the Moon.

WOULD WE SEE A CITY?

First, there is no way we could send a million people to the Moon with present day technology. But this may not be so far into the future, with some emerging technologies. For instance, the British Skylon, which is currently not much more than an innovative engine and a great design, is on course to fly some time in the 2020s. If this works out, it may get us into space almost as easily as we cross oceans. There are other technologies in the wings that could do the same. We have about three billion person flights per year, and several million every day, in over a hundred thousand planes a day. If just a small proportion of those are able to fly to the Moon instead, we could have cities on the Moon easily. See my article Projects To Get To Space As Easily As We Cross Oceans - A Billion Flights A Year Perhaps - Will We Be Ready?

If you had a concentrated city of over 5 million people on the moon - and each of them had spill into space of about two 100 watt light bulbs per person into the sky - then you might just spot it as a sixth magnitude star in ideal conditions during lunar eclipse or with a thin crescent moon.

This assumes the habitats are on the surface. And also close together - if you had the combined light of a sixth magnitude star - but spread over a large area of the Moon in lots of smaller settlements, you wouldn't see it, because of low surface brightness.

A complication though is - that on the Moon - you would cover all the habitats with several meters of regolith for shielding from cosmic radiation.

Probably like this:


JSC lunar base concept, 1989

Also, I rather expect that human habitats would have few windows, and the windows all tiny, as in this Bigelow mockup.

Bigelow moon base mockup

At most you might have occasional larger ones like the Cupola on the ISS but they would be rare, surely - that's because windows are really hard to construct when you have to hold in ten tons per square meter of outwards atmospheric pressure.

Unless we develop some way of making amazingly strong transparent material (like the Star Trek "Transparent aluminum") they would surely rely on view screens to see the outside surface, or for that matter to display movies and scenes from Earth - but probably not much by way of windows as such, just one or two as special features like the Cupola.

Classic scene from Star Trek IV "The Voyage Home" about Transparent Aluminum - sadly we don't have anything like this to build our windows of our space habitats yet.

So - chances are even if they are on the surface - that hardly any light would escape from the human habitat. 

Here is a rather fine Russian video about a lunar city from 1965. It is from the second, science fiction, part of the film Luna directed by Pavel Klushantsev. Sadly I don't speak Russian.

The full movie, in restored colour, with machine translation subtitles for part of it (but sadly not this section).

Human habitats could also be underground, for instance in lunar caves. 

Hadley Rille photographed by Apollo 15, probably example of a large collapsed lava tube on the Moon. 

If so, then it may originally have been a huge hollow cavern. If so, what about lava tubes that are not collapsed, underground?

A study in spring 2015 found that they could be stable up to ten kilometers wide in the much weaker lunar gravity. If so, there may be caves on the Moon large enough to house entire cities, and if humans lived in them we'd see no trace of them from the Earth.

And, we wouldn't see solar panels, not when the habitats are in the lunar night - or anything reflective, as there would be nothing for them to reflect.

All in all, I don't think we have much chance of spotting human habitats in the areas of darkness on the Moon, at night, not for a long time to come, not directly.

WOULD WE SEE GREENHOUSES?

Greenhouses are more promising. They would be large very strong spherical or hemispherical buildings - if on the surface. They'd be made of some material far stronger than e.g. the plastic of "polytunnels" as they have to withstand several tons per square meter outwards pressure - but would probably be transparent to let in the daylight during the 14 day "day".

And if used for growing vegetables would need to be illuminated with close to full daylight for growth during the lunar night - probably in 12 hour day / night cycles so as viewed from Earth, they would blink in and out of sight every 12 hours.

Of course the light would be directed downwards onto the plants. But the plants themselves absorb only part of the light that is shone on them, and reflect the rest back.

Using albedo for green grass, 0.25, then diameter needed to see it from Earth is 571/sqrt(0.25/0.12) = 395 - or about 400 meters for the diameter of the greenhouse. Area about 126,000 square meters. Or about 31 acres. That's not that large for an agricultural field.

So, we wouldn't see a small greenhouse. But if you had greenhouses the size of a very large field - of order half a kilometer in diameter or so, seems that we would see the largest greenhouses in ideal conditions if fully illuminated to equivalent to daytime sunlight.

A very large field, perhaps half a kilometer in diameter or more, if fully lit up with artificial light equivalent to the sun, on the Moon, would be as bright as a sixth magnitude star. This is a photo I took myself, so copyright Robert Walker.

It is of the corner of a field in the Scottish Borders - not sure of its acreage. 

That is - unless they optimized the light for vegetation so that it supplies almost no green light, then the plants might look much darker.

WHAT ABOUT AN ICE SKATING RINK OR SKI SLOPE

Let's not bother with the practical details - do they go ice skating in spacesuits? (The ice or snow would be continually evaporating into space in that case, so would need to be replaced constantly) Or do they have a very thick polymer covering able to hold in ten tons per square meter? Or low pressure atmosphere?

But - just suppose we have ice, high Albedo, exposed on the surface, could we see it?

If it was, say, fresh snow - or perhaps an ice rink, then to see it from the Earth as a sixth magnitude star, it needs to have a diameter of 571/sqrt(0.8/0.12) or about a 220 meters diameter patch. Or about 9.4 acres.

A standard skating rink of 40 by 60 meters is not nearly large enough to see from Earth with the equivalent of full sunlight illumination.

A larger area - say, a fully illuminated giant slalom slope for low gravity skiing in spacesuits - that could be visible from the Earth. Length 400 meters, width 30 meters, so still nowhere near big enough. 12,000 square meters. We need ten times that to be as bright as a sixth magnitude star.

Olympic Super-G - sadly you couldn't see a Super G ski slope on the Moon - unless lunar slalom ski slopes are ten times wider or longer than on Earth.

Also that assumes they are lit at similar levels to full sunlight. But they would probably be lit at much lower light levels than that, at night.

So, the answer is no, we wouldn't see ice rinks or Olympic ski slopes on the Moon from the Earth, not unless the ski slopes are much larger than on Earth.

We'd see a complete enclosed ski resort easily though. The largest ski resorts are thousands of acres. If we had a fully developed ski industry on the Moon - if low gravity skiing really took off, they would only need to cover 10 acres or so to be visible as a sixth magnitude star from Earth. Or 25 acres for a fourth magnitude star, or 62.5 acres for a second magnitude star, or 157 acres for a zero magnitude star. That is, if lit to be as bright as daylight, and if it has a transparent cover, which may be a big "if".

STREET LIGHTS ON THE MOON

Would you have street lights on the lunar surface? Would you have roads for that matter? Or is it more a matter of cars and people in spacesuits carrying their own lights?

Anyway, whether they would use them or not, we can still work out if they would be visible from Earth.

NIGHT LIGHTS OF CHICAGO

For a ballpark figure to get stared, I found a couple of figures here. The city of Chicago with 2.7 million inhabitants had 175,000 street lamps in 2000, and upgraded them from 90 to 250 watts. So, that's equivalent of 437,500 of our hundred watt bulbs.

For another set of figures, also for Chicago, this time in 2007, then the street lights come to a total of 73,710 kilowatts, or 737,100 of our hundred watt bulbs.

We needed eleven million of them for equivalent of a sixth magnitude star.

Chicago has about 2.7 million inhabitants. In terms of stellar magnitudes, the difference in magnitude is log(ratio of brightnesses) / log (2.512) = log(11000/737.1)/log(2.512) = 2.934 magnitudes fainter.

So that rough calculation suggests the street lights of the city of Chicago on the Moon would be equivalent to a 9th magnitude star in brightness. So you'd need powerful binoculars to see them from a dark site on the Earth, and a small telescope to see them from a brighter site from the astronomical magnitude scale. That is assuming all the light is directed downwards to illuminate the streets, and that all that light is then returned back into space - in practice, it would be reduced further by the albedo of the surface. If it illuminated lunar soil, it would be reduced in brightness by an extra 2.3 magnitudes, to over 11th magnitude.

We could do more detailed calculation - for larger cities, and take account of other forms of light escaping from cities - but that's enough to see that even large cities are not going to be bright enough to be visible by street lights on the Moon.

SO - DON'T EXPECT TO SEE EARTH CITIES FROM THE MOON

So, what about in the other direction, could we see Earth cities from the Moon? The answer would seem to be, no, from our Moon calculation.

Earth lights as seen from space - from the Earth observatory. Our calculation suggests these lights are not visible from the Moon to naked eye, and similar lights on the Moon would not be visible from Earth. Which is backed up by direct observation by the Apollo observations

Back at the time of Apollo, our cities weren't as bright. But we do have direct observational evidence, that they didn't see the Earth cities from the Moon during the Earth nights. Even when they saw the Earth in total darkness from orbit around the Moon, with the Moon also in eclipse, they didn't see any cities.

We have a short video of this event here, of the sun going behind the Earth, as seen by the Apollo 12 crew, Conrad, Gordon and Bean, on their journey back to Earth from the Moon.

(click to show on youtube, this frame is 18 seconds into the video).

The video is very poor quality, but shows no sign of any cities on the Earth. And they didn't report seeing any city lights on Earth from the Moon.

ACTIVE ATTEMPTS BY LUNAR INHABITANTS TO MAKE THEMSELVES VISIBLE

What though if the inhabitants of the Moon are actively trying to make themselves visible to us? That should be easier.

FIRST - TRY A NUCLEAR EXPLOSION ON THE MOON?

If you wanted to create a light bright enough to be visible from the Earth, you could set off a nuclear explosion on the Moon. Though it's a very expensive way to make a bright light that lasts for a fraction of a second.

"By the time a 1-Mt fireball is near its maximum size, it is a highly luminous ball of more than 1 mile (1.6 kin) in diameter. At 0.9 second after detonation begins, it is at its brightest. Its surface, which masks the much hotter interior of the fireball from the surroundings, still radiates two and a half to three times more light and heat than that of a comparable area of the Sun's surface."

"By taking into account atmospheric attenuation (12-mile [about 19.3-km] visibility), at a distance of 6 miles (about 9.7 km), it would be 300 times brighter than a desert Sun at noon; and at 9 miles (about 14.5 km), it would still be 100 times brighter. Thus, extensive fire ignitions would accompany such an airburst over an urban/industrial area."

From the Medical Implications of Nuclear War.

Using those figures, at 9.7 kilometers it is 300 times brighter than the Sun - which has magnitude -26.74. By inverse square law, the Moon is 384,400 km away, so a one megaton explosion on the Moon would be 300 * (9.7/384,400)^2 times as bright as the sun, then converting that to magnitudes, log(300*(9.7/384,400)^2)/log(2.512) = 16.67 magnitudes less bright. So it would have magnitude -10 approximately. Far brighter than Sirius and approaching the brightness of the Moon itself at -12.74. In fact, as bright as an 8% illuminated crescent Moon.
This is an 8.1% illuminated crescent Moon



From: Moon Phase and Libration 2015 (NASA).

So, a one megaton explosion on the Moon would be about as bright as this, and far brighter than Venus. You'd see it easily. But only for a fraction of a second - you would have to be looking at the Moon at just the right moment to see it.

BRIGHT LASERS ON THE MOON POINTED AT EARTH

Now, if you had very bright lasers on the Moon pointed at Earth that's another matter. Most of the light from the lunar fields or the ice rinks etc spreads out in all directions and comes nowhere near the Earth.

If it was your aim to create a light on the Moon visible from the Earth, well for the sixth magnitude star, it was 126,000 square meters, its 120 watts of light reflected per square meter, so 30,720,000 watts (we don't need to take account of the 2.6% inefficiency of a "100 watt" light bulb here). 

But instead of spreading those 30 million watts in all directions, we can just focus a much smaller amount of light directly at the Earth.

A very rough calculation again, the Moon subtends 0.2 square degrees. And diameter of earth / diameter of moon = 3.671 so from the Moon, Earth subtends 0.2*3.671^2 = 2.7 square degrees approximately. A whole sphere has 41,573 square degrees. So, just for a very rough, back of the envelope, order of magnitude type calculation: our laser would just need to be about 30,270,000*2.7/(41,573/2) watts or about 3.9 kilowatts equivalent, not that much power, tightly focused enough for all its light to fall on the Earth if directed straight at it, and with the intended viewers in the center of the beam.

A one watt laser is very powerful and we need 3,900 of them. Or to be as bright as Arcturus, six magnitudes brighter, about 62,000 of them. Or about 31,000 of these 2 watt lasers.

At about $100 per watt, you could make a light on the Moon bright enough to be visible globally for about $390,000 worth of lasers, or a star as bright as Arcturus as seen from the Moon for about $3,100,000. Of course you have the problem then of getting them to the moon.

So, seems that 31,000 lasers on the Moon could create a "star" visible from Earth as bright as Arcturus. And 3,900 lasers would just about be visible as a sixth magnitude star from Earth, if all pointed at Earth.

If we can do this, it seems we could also shine laser lights to the Moon and they would be seen by any astronauts there if we can get together enough lasers and point them all at the Moon.

Here is someone else did a similar calculation, they found out that to be just barely visible from the Moon, you'd need ten of those one watt lasers, but need to focus them all within a 400 kilometer spot on the Moon. Since the diameter of the Earth is about 300 times larger than that, with intensity going down as inverse square of patch width, our 62,000 watts just focused on the Earth to be seen globally on Earth from the Moon is roughly consistent with it.

But we don't need to depend on calculations here. Someone has actually tried a rather similar experiment - though not as far as the Moon of course as we don't have anyone there to look at us.

Amateur astronomers in 2012 managed to create a bright spot large enough to be spotted on the ISS using just a one watt blue laser (plus two white spotlights - but the spot was also easily visible just using the blue laser). It was visible from the ISS as a greater than zeroth magnitude spot, so as brighter than Arcturus, very bright star.

Amateur astronomers flash the space station (another story about it)

The Moon is more than a thousand times further away than the ISS. So you would need more than a million of these lasers to be seen from the Moon, a lot more than our estimate of 62,000 focused on a patch the size of the Earth. So - seems it would actually be a lot brighter than Arcturus as seen from the ISS. Brighter than magnitude -6, brighter than Venus at its brightest. Doesn't actually say how bright it was, so could it be as bright as that?.

That's very rough, just figures happen to have to hand. But it's enough to give a ballpark idea. And given that you can see a 1 watt blue laser from the ISS as a negative magnitude star, you can surely shine lasers from the Moon to the Earth to be visible from Earth - the main question is just now many of them you need. If you have got nice ideas about how to work it out, do say, or have a go at working it out yourself :). 

LIGHTING UP THE MOON FROM EARTH

We could also try lighting up the Moon from the Earth. Much like our street lights but using lasers we can light the Moon even from the distance of the Earth.

Most of the light reflected from the Moon will spread in all directions and not come back to Earth. So, even using lasers, the amount of light you'd need to shine on the Moon to see a spot on the Moon from Earth is the same amount as you'd need for streetlights - except - that if it is a visibly extended patch, covering much of the Moon, you get the issue that celestial objects that produce enough light to be visible as a single spot can become invisible to the naked eye if spread out, say, as a galaxy, over an extended area of the sky because of low surface brightness.

In short, this way around, it is very hard. If you could focus the lasers right down to a single city on the Moon - it could be useful perhaps, as a way to provide "street lighting" from Earth but if you did that, then as for our street lighting calculation, for even a large city the resulting spot won't be bright enough to be seen from Earth.

There's an entertaining discussion here of the question "If every person on the Earth aimed a laser pointer at the Moon at the same time, would it change colour?" and a physics forum discussion of whether you could paint a spot on the Moon visible to the eye using laser pointers from Earth.

ADS ON THE MOON?

Shining laser light from the Moon to the Earth seems rather pointless, except perhaps for advertising. Asimov has a rather fun short story about that idea set on Jupiter, "Buy Jupiter". More examples here: Space Advertising (wikipedia)

The lasers would need to be spread over thousands of kilometers of the lunar surface to make a logo you could recognize from Earth, it's a mega project. There would be much easier ways to advertise. You could have big mirrors in space, in LEO, in the shape of your logo, to reflect light down to Earth - far brighter than the ISS. Because they are closer to Earth, they wouldn't need to be nearly as bright, so cost far less to construct. Put in a near polar low Earth orbit, and everyone on Earth would see your logo fly over at some time or another.

I don't think there is anything in international law to prohibit this, in the Outer Space Treaty. But surely we'd have legislation to stop it if it became practical. Well I'd vote to prohibit it anyway - would anyone except the advertisers themselves vote for it?

Hopefully if it ever becomes practical, illuminated signs on the Moon bright enough to be seen from Earth are not going to be permitted in the future :).

Sky writing and Aerial advertising is legal though, just not used that much, maybe because of the expense, see Aerial advertising (wikipedia). The only examples I can think of are blimps and hot air balloons carrying messages, have seen those sometimes .

And - you can put logos and advertising on the spacecraft and habitats themselves of course. So if this becomes a matter for legislation, I expect the laws will be quite complex, what you can and can't do by way of space advertising - and it would need international agreement world wide - a tricky thing to manage with space issues.

WHAT DO YOU THINK?

As I said in the article, not sure how likely any of this is. The fields seem the most likely in a way - but there are a lot of "if"s there - if the future Moon has extensive fields of 32 acres or more illuminated brightly with lights as bright as the sun, with the light being broad spectrum so including green light for the plants to reflect, and with the greenhouses not covered up at night? 

Or off- piste skiing?

As for deliberately shining a light on Earth - yes they could do it, but one wonders why anyone would attempt it. Even with advertising, it would probably be made illegal, and if not, there are much easier ways to advertise for much less expense.

What is your best bet for some form of lighting on the Moon that might in the future be visible from Earth if we had large scale settlement there?

SHOULD WE BUILD LARGE CITIES ON THE MOON

This is just a fun calculation, and not meant to answer either way whether we should build such cities. With the Moon, then it's much easier for planetary protection than, say, Mars. But it does have a few issues.

This may mean we need some caution even for small numbers of astronauts living there and some of these will need serious thought if we ever have large populations even on the Moon. It certainly needs to be talked over, and not something that should just be "left to the scientists" to decide, as it is an ethical rather than a scientific decision.

• The very thin lunar atmosphere, or exosphere. For instance, does the Moon have a water cycle? Does it get any water from the Earth also? As soon as you have rockets going back and forth to the Moon carrying astronauts, the thin atmosphere will get overwhelmed by the exhausts from the rockets, making these studies impossible. Just one large landing by astronauts would change the entire atmosphere, it is so thin.
• There is no risk of Earth life replicating on the Moon but a landing by humans will leave spacecraft and human waste products locally around the lander, from their air, rocket fuel, and also from their own wastes. A city with millions of people would of course have a huge wastes problem on the Moon though probably most of it would be recycled.
• A footprints and tracks problem. If you have millions of people there, eventually the entire surface around every settlement would get covered by tracks and footprints, which would not be erased by natural processes, even after millions of years. We have never explored a place quite like that before. So what would we do if the Moon gets really popular? Keep humans to special tracks, or sweep the surface after you walk or drive over it, or what?
• At present anyway it is much more expensive to live anywhere else outside of the Earth - so seems people on the Moon or elsewhere would be supplied mainly from Earth. Still, with a population of rising to perhaps 11 billion people on Earth, and the Moon so close, once transportation to the Moon gets as easy as present day transportation to another continent - you might well get millions of people on the Moon as tourists, even with it costing far more to live on the Moon than on Earth. And where you have millions of visitors, probably get a few hundred thousand people at least living there permanently.
• Ice mining on the Moon. There are millions of tons of ice probably, so it seems you could mine a lot of it without impacting on scientific studies. But they are in rather limited regions around the poles in permanently shadowed craters - could this be done in a way that has low impact on the science we'd surely want to do studying those craters and the history of the solar system? Would need to find a way to mine the ice without adversely impacting on the unmined ice.  

So, anyway that's not the main focus of this article, whether or not we ever have big cities on the Moon, just fun to work out what we could see from the Earth with the naked eye.

But it's interesting to note, that even the Moon, is not without some planetary protection issues as well, and ethical issues to discuss, if you have large numbers of people visiting it.

ORIGINAL QUESTION - ON QUORA

This came up on quora a while back, as "When we colonize the moon, will people on earth be able to see the settlements' lights on its surface facing us even during a crescent moon?"

The anonymous questioner continues: "In other words, say it was a crescent moon, but there was a well-lit civilization on the part of the moon we wouldn't normally be able to see in the sky that night. Would we be able to see those lights from Earth? Would they light the surface well enough for us to see the surface (like a full Moon) as well?"

PLEASE COMMENT IF YOU HAVE ANY IDEAS, THOUGHTS, CORRECTIONS ETC

Please say in the comments if you spot any errors however minor, including typos and interested in any ideas or thoughts on any of this. Thanks.

OTHER ASTROPHYSICS "WHAT IF" SCENARIOS

You might also like my

• Can A Planet's Moon Be As Bright As Its Sun?
• Could A Star Orbit A Planet? - Just For Fun
• Could Another (small) Satellite Orbit The International Space Station?
• So You Thought You Knew What Planets Look Like? ... Shapes Of Rapidly Spinning Planets
• Can Moons Have Moonlets? Or Rings? Moonlets Of Pluto's Moons?
• Is It Possible To Build A Spacesuit Or Spaceship To Travel Through The Sun With Future Tech? - Just For Fun.

Some of them are also available as kindle books

HOW TO GET THIS ARTICLE AS A KINDLE EBOOK

You can get it here:

Could You See Moon City Lights or Greenhouses from Earth?

• More kindle books from me (articles turned into ebooks)