K^2

I call it insignificant amount of math by GR standards. You know? I've never found one that was concise. I'm doing a lot of hand-waving above which just wouldn't do for a proper paper. The original Alcubierre paper is pretty good, because if you understand GR at all, you can follow along. But everything that followed, less so. Most of the work in the field is, "We loaded these parameters into simulation, and this is what we got," and it's just not particularly readable. Part of it is that GR wasn't my primary field, so even my eyes glaze over some of the math. The computational part actually makes more sense to me, but that always goes after very specific cases. Like, how do you reduce total energy needed to create a bubble, etc. And even with the background, the lightbulb moment for me was when I was trying to work out if a linear gyro was possible. There are a lot of ways to create apparently motionless objects with momentum, like if you have mutually perpendicular electric and magnetic fields, even if they aren't moving, there is net momentum. So it feels like you ought to be able to make an electromagnetic "jar" to hold momentum. But then you keep running into complication after complication that all seem solvable... It reminds me a lot of how if you don't apply conservation principles, it just feels like you ought to be able to build a perpetual motion device with magnets. But just like with magnets, if you actually step back, consider conserved quantities and how they apply to the problem, it's possible to show the fundamental incompatibility between what you are trying to achieve and these conservation principles. It's not all a total dead end, however. Some interesting questions remain. Like, can you create an empty warp bubble with exactly zero mass? Because even if you can't transport matter inside it, if you can just make a stable warp bubble that travels at FTL speeds, you can use it to send information. Nothing in classical GR or mean field quantum mechanics suggests it to be strictly impossible, but then if it is possible, then so is time travel, technically, which would make things... interesting. The other avenue is wormholes. There are a lot of new unknowns there, like whether necessary topology can even be found naturally or be created, but also some very familiar restrictions. For example, the only known traversable geometries require negative energy. In general, if you see FTL in GR, expect negative energy somewhere in the mix. But unlike warp, there is no known lower bound on negative energy required. Can we use Casimir Effect to stabilize a wormhole? Maybe! I wouldn't be t any money on it, but nobody found a reason why it would be fundamentally impossible yet. One thing is for sure. Whatever we come up with will seem like magic, just like Clarke said, but it's not the same thing as saying that anything that looks like magic will be achievable with sufficient technology. Some things really can exist only in realms of imagination.

Being old enough to remember the original announcement and having spent better part of the past decade working at game studios, I have to point out a few crucial differences. DNF was in development hell for over a decade before given to another studio, Gearbox, who promptly finished it. (Read, pretty much made it from scratch.) KSP2 was basically given to a new studio because it was decided that it's going to be a bigger game than originally envisioned and, presumably, disagreements arising from it. The new studio has then given a new timeline for release. (Yes, with a few false starts along the way, where they tried to salvage original timeline, which was a mistake to even try, IMO.) I would argue that comparison to DNF is a stretch at best to begin with, but if we were to draw parallels, we have to compare KSP2 now to how DNF was going after it got handed off to Gearbox. And while Gearbox eventually still delivered a rather mediocre game, in that regard, I think KSP2 is in much better hands. At least, Intercept leadership appears to genuinely understand what kind of game KSP is and want to make something that would be fun for its fans. As for DNF... Well, if you look at the timeline, it's clear that the A team at Gearbox was working on Borderlands 2. Even at larger studio, it's always a problem with two projects. The best talent always gets diverted to the flagship project with anything else getting built by people with less experience, fewer resources, and frequent distractions to put out fires on the main project. Gearbox clearly channeled its early days of porting games cheap to quickly cobble together DNF, and given the amount of effort that went into it, that didn't come out as bad as it could have. But a masterpiece it was never destined to be. So as much as I understand concerns, there is no real reason to worry about KSP2 at this point. We haven't seen a lot of updates, but ones we have seen show the game that looks to be on track for a 2022 release. Materials are looking sharp. Terrain and atmospherics are taking shape. We have old and new parts for ships and colonies. The big unknowns are the state of physics and multiplayer. But also, I don't expect either to be presentable right now even if they are on track. So the fact that we haven't seen much of either isn't necessarily a warning sign.

Alcubierre Drive is a good example to illustrate why all of these "magical" drives really are a bit too magical. Standard way of deriving the warp metric is to say that space-time is flat inside and outside the bubble, with all curvature contained in bubble walls. Problem is, the moment you place something inside the bubble, the space-time is no longer flat due to gravity of that object. This doesn't really cause any problems inside the bubble, but outside, it results in gravitational waves produced whenever the bubble accelerates. Emitted gravitational waves actually compensate for the momentum of the ship, and in effect, you have a graviton drive, which is positively not what you want for warp. Graviton drive is subject to the same efficiency limits as photon drive in linearized case and gets worse at higher energies due to self-interaction. What does it mean for the warp drive? It means that you might as well have a photon drive rocket, and you'll need infinite energy to reach light speed. So forget about FTL. How do you fix this problem? Well, you need to flatten exterior space-time. That's easy. Well, easy if you have negative energy you need to make a warp bubble in the first place. You just uniformly increase negative energy contribution throughout the bubble, meaning you now have more negative energy than positive energy. In fact, the total mass of ship and the bubble combined needs to be exactly zero to keep exterior space-time flat. A ship in that configuration requires no energy to accelerate, and if you were to match the masses perfectly, would be capable of going superluminal. Of course, there is no known way to match these perfectly, so you'll still be traveling at the light speed at the most, but given that interior time can run arbitrarily slowly, this is still great for interstellar travel. Despite all the problems, warp might still be the answer to how we go to the stars even if we can't beat the light barrier. That said, lets look at this situation from an alternative perspective. Solving all of the above is a lot of math. Original Alcubierre paper did not include any of these nuances, because this is computationally heavy, and yet, these limitations could have been called out immediately with a bit of thought. Here's why. You can look at movement of anything through space - flat or warped - as flow of energy. This way, we don't have to distinguish between light, gravity waves, energies in the warp bubble, or the ship itself. If we are talking about general relativity, we do have to consider the entire stress energy tensor, of which energy is just a projection, but the advantage it gives us is that it contains information about momentum as well. More crucially, it's not just a conserved quantity but a conserved current due to symmetries of Minkowski metric. ∂νTμν = 0 That equation is just a very fancy way of saying that energy and momentum are neither created nor destroyed, and can only flow from one location to another. Moreover, momentum is the flow of energy. Without getting into mathy details, we can apply a generalized version of Divergence Theorem to this. ∰S nνTμν dS = ⨌V ∂νTμνdV = 0 That's a lot to unpack, but vaguely speaking, if you imagine a boundary around a region of space-time, same amount of stress energy flows into it as out of it in total. So now, let us construct a specific case for a ship preparing to depart. So time flows upwards, and one of the spatial directions is across. Picture a hypercylinder in space-time region surrounding the departure event. We can consider ship prior to the departure sitting still in space. As it does so, it moves forward in time, so it "flows" into the cylinder of interest through the bottom face. At this point, the only energy the ship has is its mass energy, so that's the exact amount of stress-energy that enters the cylinder through the bottom face as indicated by the bottom arrow. The exact same ammount must now flow out of the cylinder. If the ship was to remain at rest, all that mass energy would flow out of the top face and the net change would be zero, which is exactly what we expect. However, we are picturing a ship that by some means of propulsion departs this area of space. So the top arrow indicates the flow of stress-energy out through a side wall. This is where things get exciting. We must still have the total mass-energy of the ship depart, so there is energy flow. But the side-walls of this cylinder are purely spatial boundaries. Flow of energy through a spatial boundary is momentum. So the stress-energy that leaves this cylinder is mass-energy plus some quantity of momentum. But no momentum entered the cylinder. The only way to rectify that and have the total be zero is for something else to depart this cylinder with opposite amount of momentum. This is why you cannot have propulsion without exhaust. That exhaust can be matter, light, or even gravity waves. But there has to be something emitted that carries away momentum. The warp drive gets around this by having on board the ship a source of negative energy enough to create the bubble. Because the total energy cannot change, the total mass of a warp-capable ship is precisely zero even before it goes into warp. Because of that, the mass-energy of the bottom arrow is zero, and so the energy and momentum of the top arrow can be zero as well, allowing a warp ship to depart with no exhaust. That, however, leads to other problems. If the net mass of warp-capable ship is zero before the jump, what if something applies a force to it? A slightly more realistic version is a ship whose total mass is just a few grams, allowing it to reach ludicrous speeds on a graviton emission alone once it forms a warp bubble, but such a ship will be strictly sub-light capable. As for FTL or exhaust-free ships, this principle, unfortunately, puts an very heavy damper on the very idea. There are other means of going from point A to point B faster than light, like wormholes, but that comes with its own set of caveats and is another long story. I hope that the above is at least somewhat helpful in filtering out impossible magic ideas in propulsion from ones that are simply incredible. Like antimatter beamed core rocket or a wormhole drive. Both of which are still total science fiction for now, but with at least the physics of how it would work being completely clear.

I don't know much about ice phases, but it shouldn't be too different from other phase transitions, and based on what I recall of physical chemistry, unless you have absolutely pure water, you'll end up with a sort of a slush layer. In terms of physical properties, I don't imagine it will be too different from silt and organic slime that forms at the bottom of some ponds. Lower bellow, it will compact into something a bit more solid, but more like packed snow than solid sheet of ice until you get to a depth where this formation is more or less permanent. All in all, not too different, physically, from a bottom of a deep lake or even sea bed. From perspective of a game like KSP, I don't think this warrants any special treatment compared to a rocky body with water on it. You just treat this layer as the "terrain".

It's a bad incentive for both developers and publishers. I'm saying this as someone who makes games. I want to make good games, but if pre-orders drive sales, then marketing is going to make it very difficult for me to spend my time making a good game and not a pretty advertisement for one. If you care about games, wait until they are actually available to play before putting money in them.

It's not too difficult to add a few discrete locations with elevated water level. But these would just be set pieces. In order to have significant impact on look and feel of planets, you really would need a way to generate river systems, and that's an entirely separate class of a problem. Convincing river systems are hard to generate, and while I've seen some tech demos that can produce decent results with some artist input, I've never seen anything that would let you cover entire planet - even a toy-sized one, like Kerbin - in realistic waterways. There is just so much connection between paths water takes, erosion, and overall terrain that you have to have it be considered as part of your world generation. But set pieces would be nice too. Maybe a lake in a crater of a large volcano? That'd be easy enough.

That's going to be so ridiculously inefficient... I'm wondering if it makes sense to drag suits inside in the first place. Can't be that difficult to build an airlock that mates directly to the hatch on the back of the suit, can it? Seems like it'd be a much better option to just have the suits always stay on the outside.

I would almost prefer something like KOS that you can get scripts for from Workshop and have that handle tasks you'd normally do with MechJeb.

You would think somebody would have come up with better tools for organizing projects, but truth is, there are weeks when I spend more time in Excel than Visual Studio.

I would rearrange that slightly. They are responsible for keeping the vision clear. That's not to say that they don't influence the vision, but it's not their primary function. Production makes sure the goals are stated clearly and tasks are keeping the project on track towards these goals. But yeah, very underappreciated team members, especially, by outsiders. You don't really see the work they do. You just see consequences when they aren't there to do that work, and these consequences are never good. And you start appreciating this more and more as your responsibilities grow. As a junior developer, you might not be aware that producers exist. At mid level, you still don't know what they do and why they keep bugging you about Jiras, but you still don't get a whole lot of interaction with them. By the time you end up leading a team, though, they are basically your patron saints. Without good production, large projects can still happen, but it's probably better for all involved if they didn't.

Well, this is the place where I actually have relevant experience. Subatomic particles are kind of the same way - we draw them as tiny little spheres, but it's all fields, so collisions are never really collisions - it's interactions. And because they're all just whizzing about at relativistic speeds, you don't care about specific details of a particular interaction. What you start talking about are cross-sections. It's the section area within which a particular interaction, such as capture, will happen with given probability. And yes, cross-section can depend on relative energies. So you start looking at it statistically. Given the average energy within a cluster and average mass, what is the probability per unit time that two black holes will come close enough to each other that gravitational wave this generates will steal enough kinetic energy to cause them to merge. And no matter what your cluster parameters may be, it's a finite number. So eventually, any cluster will merge - what we care about is how that "eventually" compares to age of the universe. But we're still talking billions of years here, potentially, so the odds don't have to be that high. And the crucial part is that cross-section is increasing as square of the mass, because whatever the shape of that curve is going to be based on your threshold probability and energy, I know that it will scale with Schwarzschild radius. So if on average, a stellar mass black hole in your cluster will encounter another black hole in a billion years, then in two billion years, the entire cluster will be a single black hole. So again, what this comes down to is, a) Is this the only mechanism, or can you really grow a cluster to the point where you can't treat stellar mass black holes as individual objects, and have to treat the whole thing as one GR mess, b) Which mechanism is dominant, and c) Is either of these relevant on the scale of life time of the universe for a typical galaxy. To answer these you need to actually build models and crunch numbers. Hopefully, somebody has done that already, and it's just something you can find out from somebody working in the field.

You can only draw a combined event horizon for a swarm if the entire swarm is contained within that volume. So, like we can compute Schwarzschild radius for Earth, but since Earth isn't contained within that radius, Earth doesn't have an event horizon anywhere. Similarly, for a cluster of black holes that has enough objects to exhibit high symmetry, you only get a combined event horizon if all of the mass is within the combined Schwarzschild radius. This becomes more and more likely as the swarm grows, but I would still expect density near the center to be high enough for pair-wise merges to start way before you achieve that critical mass for the whole swarm to become a black hole all at once. Then again, dynamics of a black holes in a near-critical swarm might be rather wild. It could very well be an aggregate sort of merger rather than pair-wise, starting at the core and growing out. Seems unlikely to me, but this is also why I'm saying you should run this past cosmologist, because this is definitely beyond my background.

This is something you might want to reach out to a proper cosmologist or astrophysicist about. But I have two quick thoughts. First of all, yes, merger of a cluster of stellar-mass black holes into a supermassive black hole is a runaway process. As you pointed out, Schwarzschild radius is proportional to the mass. That means the gravitational cross-section of a black hole goes as square of its mass. And because the probability of collision is product of cross-sections, two 2M black holes are twice as likely to have a collision in a unit of time as four 1M black holes. There is a percentage of energy that's lost to gravity waves during merger, but it's not too high. So if it takes a billion years for your cluster to go from an average of 1 solar mass to 10 solar masses, it will only take 100My to go to an average of 100 solar masses, then 10My to go to 1,000 solar masses... And near the end, it's actually going to get even faster. The final black hole is likely to be comparable to size of the initial cluster, possibly a lot bigger. So you'll start running out of space, severely increasing the rate of merges. What I can't tell you is what expected densities are for this runaway process to happen in time comparable to ages of galaxies. I suspect that critical density is very, very high, as stellar mass black holes are tiny. One thing that can speed it up drastically is if you start out with a swarm of stars with just a few black holes. Cross section between the star and stellar mass black hole is way higher than between two stellar mass black holes. But of course, now the black holes have to get way heavier before this is a runaway process again. Either way, all of these conditions sound like they'd be far more abundant in early universe. So one possibility for why we're not seeing this is because it just doesn't happen anymore. That's a very ad-hoc explanation, though. Second, the signal. For the longest duration of this process, I don't expect anything special. You'll have a very occasional collision between two black holes, and we've already looked at these. And part of the problem is that while we have very clear expectations for what intermediate mass black hole merging with any other kind of black hole will look like, the signal isn't going to be very strong. This might be part of why we're not seeing a lot of that. If intermediate mass black holes are a brief note in a history of young galaxies, there might be nothing close enough for us to detect. On the other hand, that final ring of black holes with thousands of solar masses merging into supermassive black hole should be distinctive, as you'll see a huge number of very heavy objects coming together almost at once. Trouble is, there might still not be any candidates close enough even at that strength, and also, I'm not sure we'll be able to recognize it. This is the sort of thing that will make any GR sim cry binary tears, and the only way we have right now to analyze signals is simulate event we think it might be, and compare signals. But yeah, definitely run this by a cosmologist if you want concrete answers.

From some screenshots, it actually looks like they are experimenting with Horizon Zero Dawn approach to procedural vegetation. It doesn't actually make the terrain more interesting, but it makes it more interesting looking, which is a start. Of course, for planets without any kind of vegetation, all it helps you with is placement of rocks and craters, but that's better than nothing. The problem with NMS approach is that you can make 90% of your terrain look pretty cool, but the remaining 10% will be hot garbage. And the more varied you try to make majority of your generated terrain to be, the more outlandish the outliers. There are some more modern approaches to procedural terrain generation that use neural nets, but it's very green tech. I don't know if I'd recommend it for production. Then again, if there's a game out there that it'd be a fit for it's KSP. You also have advantage that you don't need true procedural planets in the sense that they'll be generated for the first time before a player sees them. You can do a fly-over and make sure nothing particularly egregious got generated, and even fix some of the problems by hand. And that should address most of the larger features, but you can still end up with a few locations that will look like the game glitched out, so it's a risk.

Oh, no, it's absolutely worth it to release on consoles. That shouldn't even be a question. And it's worth doing simultaneous initial release across platforms. What might not make sense is releasing fixes and updates for all platforms at once. It's far more likely that PC will get more frequent, smaller updates, and once these are stable, a larger patch for consoles will be released with all the fixes and new features. And it has nothing to do with differences between platforms or how many people are playing on consoles. It's just that I can publish a dozen patches in a day to Steam, while pushing through a single patch through console cert can take weeks. Especially, if any problems do come up in cert. And there can be some messed up ways to fail cert. "Game freezes if controller is disconnected while A is held in the audio options menu." Have fun catching all of that in QA if you need to roll out a quick fix! Large studios can sometimes throw more engineers and more QA at it and have patches synchronized across platforms. Smaller studios have to use PC as a test platform if they want to stay within budget. It's just how things are.

I don't know if you're mis-remembering something, but it's trivial to show that this isn't true. Take a brick and drop it with zero orbital velocity from some apoapsis height r. The energy is -μ/r, the area of ellipse is zero. In fact, energy is always -μ/2a. So it depends on the major axis only. Doesn't change your point, but it seemed worth pointing out. But yeah. I've mentioned the fact that eccentricity can drift and that can cause collision with the surface. It's not really de-orbiting, but that just makes the crater bigger, so maybe we shouldn't be splitting hairs on this one. And while it seems rather unlikely for any given orbit, it can technically happen. Perhaps, I should even say will eventually happen, but it should take an exceptionally long time unless you're intentionally trying to chose an orbit which will quickly drift to collision.

Well, that's the Kzinti Lesson for you. Whenever we end up building orbital installations to beam power down to Earth, they'll be publicized as needed for energy generation. And we might very well be in the situation where it's the only way for us to get enough power on the planet without ruining what's left of the environment. But of course, anything that can replace a power plant and concentrate its energy to a relatively tight beam is a weapon. The world will just have to deal. Fortunately, as Pds314 helped to establish, it's not as simple as throwing some mirrors into orbit, so we have some time before this becomes a burning issue. Yeah, but with that, you won't even be able to pretend it's anything but a weapon. A bomb pumped laser has only one purpose. You might be able to convince people that it's for asteroid defense. And indeed, powerful nuclear-pumped lasers might be our best defense, but it's going to be a tough sell to have it under control of any military.

Bussard Ramjet. It's garbage for speeding up, but might actually work for braking.

That's actually a good point. A thin/light enough structure can be supported against Sun's gravity by light pressure alone. It's on the order of 1g/m² and, of course, since both gravity and light pressure scale as inverse square, this works regardless of how close to the Sun you are. So you don't need to be orbiting the Sun at several hundred kilometers per second to stay put.

Just so we're clear on this, you're suggesting we put mirrors in the Sun? Because I'm in. I have no idea how to even begin solving the problem of station-keeping inside the corona, but this is just too good. It needs to happen.

Bah. You're right. One way or another, somewhere along the chain, you'll need a Really Big Mirror™. Ok. **** it. We use the sunlight to pump an actual laser. Directly. We take a big mirror, we focus the light on lasing medium, and then we beam the energy at Earth. Yes, we'll lose, like, 99% of incoming power due to low efficiency of the laser, but now we can put this laser on orbit of the Moon with a 10km mirror and still have a multi-megawatt beam hitting the planet. Mwahahahahahahaha. I've decided to cut myself off from old James Bond movies. They're clearly having a bad effect.

In geometrical optics, the rule is that all rays passing through a lens at the same angle will meet at the same point on the focal plain. Also, all rays that pass through center of the lens will not be deflected. So what you do is construct a ray parallel to ray of interest that passes through center, and you see where it strikes the focal plane. The ray of interest will go through the same point. Here's diagram for this particular case. Red dashed line is that parallel ray through center of the lens. It doesn't correspond to any real ray in the image, and we just use it to see where our ray, in red, should go through the focal plane. And, of course, the ray ends up at the bottom of the arrow in the image on the right.

Did I say 2 mirrors? I clearly meant, like at least 4. Yes, you're right, though. Etendue needs to be conserved, which means relative to each mirror the images need to have the same angular size. I... uh, completely forgot about that. So once I tried to diagram this out with 2 flat lenses, I realized that I'd need secondary half-way between Earth and primary for this to work out... And it'd naturally have to be a few kilometers across at that point. But you can still make the final image much smaller in angle compared to the primary even if you don't move the secondary that far out. Consider the following simple setup for illustration. Here, there are two lenses with focal plains marked with dotted lines. The original image is on the far left. Final image is on the far right and is half the size despite being same distance from the primary. The reason this works is because we make the intermediate image a lot smaller, and then the secondary can be a bit closer and still give us a net win. If we can make the image of the primary a lot smaller, we can keep bringing in the secondary until we have it close enough and still produce a suitably small image at desired distance. And, of course, etendue is preserved for each pair of images with respect to relevant lens. Now, the limitation is that we want a large primary, so we can only bring in the focal distance so far. So we can only make the image made by primary so small. And that's why we need extra mirrors. For example, lets say we keep the 110m focal distance on primary. So we have a 1m image of the Sun 110m from the mirror. Etendue preserved. Now we take a secondary mirror that's only a couple of meters in diameter and place it about 10m past the image. This one will have a much shorter focal distance, producing an image just 1m away which is now 10cm across. Again, relative to the secondary mirror, etendue is conserved. Tertiary mirror goes another meter past the image. This one only needs to be about 20cm across and will focus the image of the Sun just 10cm away to a size of just 1cm across. Yes, megawatts of power in a 1cm spot. What can possibly go wrong? At this point, we're already pushing limits of practical optics, so lets be happy with 1cm image and set up the 4th mirror. This one is located 5km away on a separate satellite that keeps station with the first one. It hosts a mirror 50m across, which is, yes, 1% of the distance, because, as you pointed out, optics! But now this mirror can reflect the sunlight from a 1cm image 5km away to a 1m image on Earth that is 500km away. Science! And all it took is two satellites, one with a 100m primary mirror and a bunch of very carefully configured additional mirrors, and a second satellite with a 50m mirror that's keeping station with respect to the first one to within millimeters from 5km away, maintaining perfect orientation at all times. I think, this might juuuust be possible to build with modern technology and considerable effort. But the odds of this staying hidden went from impossible to bwahahahahahahahaha. And, of course, thank you for correcting my mistake.

So like I implied before, in order for the energy of the satellite to change, you need a potential that varies in time. And even then it's not so simple. So for example, as Earth goes around the Sun, the tidal bulge rotates, so that's technically a time dependence, but I can trivially go into a rotating coordinate system where Sun stays still and the satellite will pick up an additional centrifugal and Coriolis forces, which will certainly affect the trajectory, but they can still not change the total energy of the craft. Coriolis forces never do work and centrifugal force is time-independent. So for a single planet orbiting a sun, energy of satellite in planet's orbit can never change due to any gravitational interaction. And that's even if planet is very asymmetrical one and tidal forces are significant. It can lead to some wild orbits, but they will maintain constant energy, and therefore, stay around roughly constant semi-major axis. Now, we do also have the Moon and a tidal bulge and forces due to it. Because the moon goes around the Earth a lot quicker than the two go around the Sun, the two frequencies are different, and now we can say that the potential will have time dependence in any coordinate system. That's technically a foot in the door, but all that says is that energy can vary. It's far cry from showing that energy is going to be consistently increasing or decreasing for any choice of orbit. Usually, if you have a periodic perturbation like that, average energy will stay the same, and you'll just have an additional source of precession. But maybe you can come up with some wild resonance, which is why I've asked for a reference. It'd be interesting to see. But I do doubt that anything like this is worth considering for any practical case.

With a single mirror, yes. But since *sigh* the origin of conspiracy theory is beamed power, the "mirror" would actually be a system of mirrors for this very reason. Yes, primary collector can only create an image about 1% the size of the focal distance due to angular size of the Sun from 1AU. However, if instead of 550km, the focal distance of the mirror is just 110m, then you'll have the virtual image of the Sun near the focal plane that's just 1m across. Now you can put another reflector there to maintain an almost perfect 1m beam from there to the ground. With a two-mirror setup, the limit is actually the ratio of wavelength to secondary mirror diameter. At half a micron for visible light, that's a 1:2x106 ratio, so if we're trying to keep it at 1m, you'll just get some blurring on the edges from 500km. And a primary mirror just 10m in diameter will be sufficient to raise surface temperature well above 1350K, which is enough to ignite almost anything given some time to warm up. Of course, that'd still be far from instant ignition. We're still talking well under 100kW and not terribly well concentrated. To make this interesting, and actually of interest as means of power production, you'd want a primary mirror at least 100m² in diameter. Now we'd be talking about megawatt ranges of power and a beam that can ignite forests almost instantly if it's misaligned. But then we're also talking about a 100m mirror in LEO, which isn't a thing you're going to be able to hide. Yes, I suspect it won't get spotted instantly, since it's reflecting all of the sunlight at the secondary mirror, so you might actually not get enough reflected sunlight from the rest of the structure to see it, but something that big is actually going to show up on automated asteroid surveys because it would occasionally block a star, and we're actually looking for that sort of thing now. Which is interesting, because it means that a conspiracy about a secret power satellite starting fires would be more convincing 20-30 years ago, when we didn't have automated surveys, than it is now.