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So I'm working on a sci-fi setting, a scorching hot desert planet where colonists live in canyons. The problem is, canyons are naturally formed by water- something this desert planet is very lacking in.

So that got me to thinking of ways of making an artificial canyon. I don't wanna go with nukes, asteroid bombardment seems difficult- but I was thinking about masses of orbital mirrors, focusing their reflected light on the ground, like a magnifying glass. Concentrated sunlight, carving channels around the surface of a planet like epic scrimshaw.

My question is: is it actually feasible that this could be used to dig deep canyons? Like, 500 meters + deep?

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    $\begingroup$ Wait, this makes no sense. 1. Canyons are not cool - they are hot. The bottom of Grand Canyon is hotter than its rims. It is scorching hot during the summer. 2. If the mirrors work perfectly, you get molten rock. Molten rock is very difficult to dig through. It is a lot easier to dig through normal rock than it is to dig through molten rock. Do colonists have houses with air conditioners? If they have interstellar travel, they must have houses with air conditioners. Those are easier to build than canyons, and unlike canyons, they actually work. $\endgroup$
    – void_ptr
    Jun 22 at 5:42
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    $\begingroup$ Rift valleys do not need water. The Vallis Marineris is a nice, big example. If you wanted to have a story in a canyon, start with one of those. maybe you live at the bottom because the atmosphere is thicker. If you have no want to make shade, use mirrors to reflect the light into the sky. Live in the shade under the mirror. Add solar cells. Much easier. Unless you have a huge mining project for another reason, and the canyon is just a by-product. $\endgroup$
    – Richard Kirk
    Jun 22 at 7:46
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    $\begingroup$ Is the purpose of the canyon living because the water is in canyons? $\endgroup$
    – hszmv
    Jun 22 at 15:10
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    $\begingroup$ @void_ptr the Grand Canyon, being rather grand, is also rather wide. A narrow canyon is mostly shaded by its walls (and an artificial one away from the equator could run east-west to maximise the shade). Of course you'd need suitable rock to allow such high artificial cliffs $\endgroup$
    – Chris H
    Jun 22 at 15:10
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    $\begingroup$ The orientation of a canyon determines whether more or less light reaches the bottom than would occur for a similar area of a flat plain. East/west orientation allows sunlight into the canyon longer than if it had a north/south orientation. In the case of the Grand Canyon, the altitude of the upper rim, combined with normal wind direction is the primary reason it is cooler. $\endgroup$
    – jwdonahue
    Jun 23 at 0:28

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No.

I'll assume here that the planet is like the Earth, and its star is like the Sun.

Beam spread

The Sun has an angular width of about 0.5334 degrees, or 0.009 radians. That means that the light reflected off a flat mirror will also spread by about 0.009 radians. Given that a mirror in low orbit is at least a hundred km up, the reflected spot on the ground will be blurred to at least 0.9 km wide, plus however wide the mirror is. That would result in a wide valley, rather than a canyon.

This might be overcome partially with curved mirrors. However, see this physics stackexchange post. The consensus is that even with a focusing curved mirror, the spot will still be about a km wide.

Limited time over the target site

In such a low orbit, the mirror will orbit the planet every couple of hours. It will have a speed of over 10 km/s. If the hot spot on the ground is 0.9 km wide, then it will be exposed to heat for 0.09 seconds every hour or two.

This assumes, by the way, that the target site is on the equator so that the mirror keeps passing over it with every orbit. Otherwise, with a non-equatorial site and a non-equatorial orbit, you'll get one or two shots every day, maybe - forget about it!

There's a limit to how hot the light focused on the ground can be. See this xkcd post. At most, you can use lenses and mirrors to focus sunlight to about 5000 K, the temperature of sunlight. This would require practically the whole sky filled with thousands of square km of mirrors. So you momentarily expose the spot on the ground to 5000 K heat for a tenth of a second, and then give it an hour to cool down.

That's not going to work. The rock's not going to have enough time to melt before it cools down again.

If we imagine the mirror or mirrors are spinning with exactly the right timing (a big engineering problem probably involving flywheels and counterweights), then perhaps it could start aiming at the target spot when it's 100 km away from it, and rotate to keep aiming at the target spot for 200 km of its orbit. This means you have 20 seconds on target, once every hour or two. Maybe that would be enough to start melting the rock, but I'm still very skeptical.

One thing that would work would just be to have many, many huge mirrors in orbit, encircling the planet, so many mirrors that the target site is always getting hit with sufficient heat. This would just be an absurd expense.

Disposing of the lava

If, against all odds and at a truly unbelievable expense, you somehow do start to melt the rock, the lava doesn't go away - it just sits there. So you're limited to carving 0.9km wide channels in the sides of mountains, so that the lava can run downhill into nearby natural valleys. The mountains have to be on the equator, by the way, as mentioned in the previous section.

Cheaper and better options

Dynamite. Excavators. Heck, even picks and shovels and muscle power would be far more feasible than orbital mirrors.

If you really want something in orbit, then perhaps you could use a really big solar power satellite in geostationary orbit with a laser. This solves both the beam spread problem (lasers can be much better collimated than reflected sunlight), and the time-over-target-site problem (because of the better collimation, the laser can be effective from geostationary orbit, which is much farther up). You'll still be limited to melting holes in mountains, though the mountains don't have to be on the equator since you can aim the laser. The mountains shouldn't be too far north, however, because the laser has to travel through more atmosphere at higher latitudes, which diminishes its effectiveness.

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    $\begingroup$ The question specifically states focusing light with the mirrors, so flat mirrors should by my logic not be considered. $\endgroup$
    – Trioxidane
    Jun 22 at 6:01
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    $\begingroup$ @Trioxidane It cannot be done. You cannot focus an image of the Sun into a spot with mirrors. Any mirror — curved or not — can is the equivalent of an infinite amount of infinitely small flat mirrors. Any infinitely small flat mirror is the equivalent of a pinhole camera, only that it also has the ability to redirect the image. But — as you know — a pinhole camera will result in a larger image, the more distant the target surface is. Hence, even with a curved mirror, the best you can get a very accurate visual representation of the Sun, but it can never be focused into a spot. $\endgroup$
    – MichaelK
    Jun 22 at 7:58
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    $\begingroup$ Flat mirrors redirecting the sunlight to giant convex lenses that are also in orbit? $\endgroup$
    – Ben
    Jun 22 at 12:16
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    $\begingroup$ @Ben It does not matter, you cannot make any optical system that reduces the size of the image on the target plane, without that system being very close to the target. Your only hope is to capture the energy and convert it, and then re-emitting it as something else, as causative writes in the final paragraph. $\endgroup$
    – MichaelK
    Jun 22 at 14:29
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    $\begingroup$ +1 for pointing out that the plan would require draining the molten rock. That was the first problem that came to my mind. $\endgroup$
    – JBH
    Jun 22 at 16:15
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Don't Excavate -- Accumulate

You can't "dig" a hole from space using lasers or light. You'd need to not just melt the land, but vaporize it. Even if you could somehow manage to focus the energy onto the spot of interest, -- and causative makes a pretty convincing argument that you can't -- you'd end up ejecting non-trival portions of your atmosphere into space as you pump ridiculous amounts of energy into it's upper reaches.

Better to build up.

In a desert planet, you would expect lots of sand. Gather it up, and use a Fresnel lens 3d printer to melt it into shape. It should be pretty easy for a space fairing civilization to automate that kind of thing and just let it run with whatever plan you program into it. Build in whatever intricate canyon shapes you want!

Bonus points: now you have towering crystal walls all over your planet, which is pretty sci-fi.

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Mining Byproduct

Because many people have pointed out why it would be stupid and unnecessary to use orbital mirrors, instead of explaining why it wouldn't work, I will give an alternative with the same effect.

You populated the trenches left by mining out ore veins.

Let's say your planet has some weird geological history, putting massive veins of copper, nickel, lithium or some other useful something-or-other along fault lines that plate tectonics formed billions of years ago. It wouldn't be a stretch to assume your colonists or their ancestors mined out these chasms years, maybe centuries ago.

It took about 2 seconds for your strip-mining engineers to figure out that these trenches make fantastic homes. Put a layer of canvas over the edges to block out the sun, dig into the sides and line it with homes.

After a while they decide to upgrade to a dome over the top and BAM! The Neom Line! Lush futuristic megacities in the side of chasms!

This idea is so good I actually want to write a story based around it!

Advantages

The rule of cool already more than justifies it, but there are some actual advantages to doing this.

Space efficiency: Not only are you using surface space more efficiently, which probably isn't a concern considering its a desert planet with scorching dunes, your also condensing the city, thus having to maintain life-support in a smaller area, and increasing the general efficiency of the city by making it denser and cutting travel times.

Ease of construction: building on the fact that the city would be denser compared to building a "traditional" city which sprawls out in all directions, it also makes construction easier compared to the above-ground equivalent, as there is no need for towers or sub-structures, as you can build right into the walls, which act as the foundation.

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Here's a rule-of-cool solution to the problems outlined in causative's answer.

Your canyon-loving colonists are bent on using their space mirrors to carve their serpentine abodes. It is the way of their ancestors. An eon is measured as a thousand generations. The end of one eon and the beginning of the next is marked by the latest fleet of migration ships, complete with their sacred mirrors.

Natural canyons will not do for your colonists. They will only dwell within the canyons carved by a Finger of God. A Finger of God is hard to find: it is a picoquasar, the final stage of some shrapnel from a supermassive black hole merger. These oddities are trebucheted far and fast, and they produce an intense, narrow beam of radiation in the final years of their lives. The source is small enough and the radiation powerful enough that the mirrors can carve suitably narrow canyons.

Throughout the eon, your colonists have listened for the mergers that will grant them their next Finger of God. They find one, harness its power, and carve their next home. Their sacred mirrors are reduced to dust, forming a Great Arc across the sky: a sign of God's approval of their sacrificial mirrors. They begin the next eon, listening for the merger and pointing their children to the Arc. It is said that the Arc is itself a canyon where God may dwell.

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Yes its possible but not in the way you think.

You use the heat of your beam to heat an ice cap producing water which flows away carving your canyon. Maybe your aliens were harvesting water or CO2 or something else frozen in the ice. the water flows away carves your canyon, empties into a large basin and refreezes. They could keep this up for as long as you need. it also gives you a convenient source for water, well ice anyway.

If you want a really huge crack you can just have it from from the planet cooling we have several examples of those, Valles Marineris on Mars being the most popular example. We don't get them on earth because the earth is still too hot and soft for it.

Even better you can combine the two, It started as an ancient cooling crack which is why the meltwater started and kept flowing down such a chokepoint, this will give you the biggest canyon. it can even give you a canyon that is wider at the bottom than the top.

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A side remark in causative's answer inspired me:

Yes, it's possible

Reflecting light has it's problems in terms of focus, but the short on-site-time that that answer mentions isn't a problem: It's the solution.

By quickly super-heating small spots in a generally rocky area we can either get the stone to explode (just small flakes on the very surface) or vaporize (again, just a tiny bit per pass). This gas or flying debris thereby removes itself from the work site [in case of explosive flakes, the debris randomly lands in the vicinity] and disperses in the area. Some of that will end up in the rest of the to-be-dug canal, but some will not, so it just takes more passes.

The short nature of this also means that total energy injection is limited, reducing potentially negative effects on the planet's (or areas) climate

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    $\begingroup$ Super-heating spots to get them to vaporize/explode and expel material by force is what is done in laser drilling. Laser drilling uses peak power densities on the order of 1 MW/cm^2. Unfocused sunlight has power density around 1 kW/m^2. So, to reach laser drilling power density using sunlight, you have to multiply the sunlight by a factor of 10^7. However, the sun's solid angle takes up around 1 part in 10^5 of the sky's solid angle, so you're short by a factor of 100 even if you fill the entire sky with perfect sun reflections. $\endgroup$
    – causative
    Jun 22 at 20:48
  • $\begingroup$ Short bursts of energy in no way reduces the total energy required and therefore the total amount of energy delivered into the atmosphere. Unless you intend to spread that out over millions of years, in which case, wind blown debris is likely to back-fill any progress you might have made. This whole idea defies the requirement that Sci-Fi should at least convince the reader to suspend disbelief long enough to absorb the full content. $\endgroup$
    – jwdonahue
    Jun 23 at 0:20
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    $\begingroup$ @jwdonahue yes it does reduce the total amount of energy required because it minimises losses in the stone itself because the rock doesn't have enough time to transmit the energy away $\endgroup$
    – Hobbamok
    Jun 26 at 8:27
  • $\begingroup$ @causative hm, that does call my proposal into question, but (depending on how hard-science OP's question was meant) a "desert planet" implies a stronger sun, so a factor of 200+ isn't too unrealistic (or at least close enough to realistic for most stories) $\endgroup$
    – Hobbamok
    Jun 26 at 8:30
  • $\begingroup$ @Hobbamok, that doesn't seem logical to me. The time in between pulses actually increases the time available for energy to be dissipated, but that's not necessarily the primary path of energy transfer into the atmosphere, unless you find a frequency window, but those aren't always optimal for energy transfer into the target material, and that also requires selective reflection at the mirrors. $\endgroup$
    – jwdonahue
    Jun 27 at 17:08

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