K^2

If you are telling me that a 10% change in pressure differential is going to make a significant difference to the design of a structure that's meant to take more significant stresses from everything ranging from normal loading, to shears and twists, to vibrations of every kind, then I will take you word for it. There can certainly be nuances that I cannot foresee, but it is rather unexpected. So I hope you'll forgive me for jumping to conclusions. And I'm definitely not prepared to discuss what is and isn't economically viable. I know that's sort of what OP was going for, but if I'm talking about viability of a certain approach, you can pretty much assume that I'm ignoring any economical factors. So, like, if I make assumption about crew being trained to deal with depressurization, I assume they have military-like training and can deal with it in under ten seconds. In practice, it might not be possible for airlines to keep crews that are this well trained due to economical realities. If we need to fly supersonic airliners, I can't imagine any physical reason why we couldn't work around all of the problems. Feel free to correct me, but I'd be completely shocked to learn otherwise. But I can easily believe that all of these fixes would cost too much for this to be worth it for passenger transport.

At 10km you are looking at a little over 25% of sea level pressure. At 15km, it's going to be a little under 15%. That does not make a principal difference for aircraft structure. Time of useful consciousness is reduced, of course, but it's not a problem for trained crew. It is a problem for passengers, but again, it's something that can be addressed with the right procedures. While useful consciousness is going to be less than 10 seconds, actual consciousness time is going to be longer, and revival with oxygen will be effective longer still. So as long as you have crew moving around assisting people, you shouldn't have serious problems. Finally, while this is bellow partial pressure of oxygen at ground level, pure oxygen is still breathable at 15km, and the systems that feed oxygen at a bit of a pressure bring it to an almost comfortable breathing level. (Though, at an expense of effort to exhale.) 15km is pretty much at the limit of how high an aircraft can go and still save the majority of passengers in event of depressurization, but it's still within such a limit. That said, we will have to venture beyond these limits some time. There are a lot of failures in modern aircraft that you cannot have a backup plan for. And when we finally graduate to hypersonic, and then, hopefully, suborbital and orbital flights, loss of pressure will have to be such a thing. We'll just have to make sure that loss of pressure does not happen in flight.

That is absolutely wrong. I think you might be confusing stability with equilibrium. I've given you an example where three masses arranged in equilateral triangle are unstable, which can be shown with the most basic perturbation analysis of the effective potential. Three bodies in a line are never stable, as far as I know. They do have an equilibrium if certain conditions are met, and three bodies in an equilateral triangle arrangement are always in equilibrium. Finally, equilibrium is the only thing that Newton looked at. So check your notes, but if I had to bet, I'd say you just mixed these two up. I'm more and more puzzled that I can't find any papers on resonance stability of L3 specifically. It's not a trivial matter, but it's not exactly a problem of the century, either. If I can't find anything, I might have to write it.

Supersonic flight makes more sense at higher flight levels than subsonic flights. So I don't think that's going to be a big problem. If all your subsonic traffic is around 10km, and your supercruisers are above 15km, you're in the clear. And by the time they need to descend, they'd be in radar-covered area.

Three in a line definitely is not stable. These are equilibria, certainly, but are you sure you recall correctly about stability? Three bodies arranged in equilateral triangle are not stable in general. Somewhat stable arrangements obviously exist, but it isn't true in general. For example, if all 3 bodies are of equal mass, the arrangement is unstable. (Take a look at article on Klemperer Rosette.)

I can't find anything on L3 specifically right now. Here are some slides for a talk on L4/L5 resonances. The approach would be exactly the same. You'd start with a rotating frame, and try to figure out which resonances are going to be stabilizing and which are going to be de-stabilizing. But in a nutshell, consider a very simple picture. Two objects of equal mass at each other's L3. Introduce a third object which is in 1:2 resonance with one of these. It is, obviously, in the 1:2 with the other body as well. This means that any drift of one of the two bodies results in interaction with the resonating body, which both restores the original perturbation and adjusts the second body to match it. Now, all you have to do is make sure that stabilizing effect of the 1:2 is greater than de-stabilizing of 1:1. Now, it's entirely possible that I jumped the gun on 8:13 being capable of stabilizing an object in Earth's L3. It might depend on a huge number of factors. But it'd be interesting to investigate, at least.

(In)stability of Lagrangian points is not speculation. It's well-studied fact. Possibility of proto-planetary body forming at such points is also a well-studied fact. That's what we are talking about. Whether such an object actually existed is besides the point. The reason the hypothesis exists is because it is physically viable. Again, all we care about in this discussion. L3 can be made stable by resonances with other objects. L4/L5 cannot. The 8:13 near-resonance of Earth-Venus motion could have been offset into a true resonance with a planetary body at L3. Now, feel free to remove your foot from your mouth.

Young Sol system was a much different place. When a lot of the junk is orbiting in all sorts of weird trajectories, perturbations average out a lot better than when you have fully formed planets which have thoroughly cleared their orbital neighborhoods. Furthermore, the best way for an object to stay as perfectly at L4/L5 as possible is to have it form there. Junk would be falling in from various quasi-stable orbits to form a planetary body, which would allow it to stay put at the L4/L5 much longer than a fully formed rigid body would. Basically, this particular flavor of large impact hypothesis gives you the best possible scenario for an object to stay in Earth's L4/L5, and it still fell out of there pretty much as soon as it finished forming. There is just zero chance of an object from early system formation to still be there. Like I said, capture isn't all together impossible, but it'd have to be a very recent one. And? We aren't talking about whether that actually happened or not. We have no sufficient evidence to confirm even the large impact, even though it is most consistent with observations, let alone say where the body came from. But that's entirely tangential here. We are discussing if a body could exist at these locations. The hypothesis of large impact caused by an L4/L5 object is studied well enough so that we know what sort of dynamics to expect from such a body. Whether it existed or not, this is how a body in L4/L5 would behave. That's all we need to know for this discussion. P.S. If you really need a good hiding place for a planetary body, I'd go with L3. Now, an object there, one that's small enough not to cause significant gravitational disturbance, can stay there undetected by anyone who doesn't have a telescope in interplanetary space. So for a science fiction work, one which assumes a gov't conspiracy, that'd make for a plausible location. It's hard to picture something with .8G not to cause enough disturbance to be indirectly detectable, though.

Lagrangian points derivation assumes point-object. A large object can modify the solution. But that's not the real problem. The real problem is that L4/L5 aren't really stable. An object can stay there quite a long time, but it will be shaken loose eventually. One of the hypotheses for the large impact that formed the Moon is a body that came from Earth's L4 or L5. It's just not stable enough for something to still be there. Though, a recent capture is not impossible. As for the object remaining undetected, that's very unlikely.

No, actually, because gravitational attraction drops with expansion, it's predicted that we won't have an equilibrium again. I'm saying again, because measurements suggest that there was a phase of deceleration following the initial rapid expansion. Between that and current phase of accelerated expansion, we must have passed an equilibrium point. So the universe is heading for a cold death, by the looks of it. Edit: I don't know all the details, but there seem to be 3 factors. Radiation pressure of the big bang, which dropped off quickly as the universe cooled, gravitational attraction that tries to pull everything together, and the dark energy pressure which seems to win this tug-of-war once the universe is large enough.

Can't help but note the irony in you forgetting to translate the statement about the new agency given an English name to help cooperation with foreign agencies. By the way, has anyone already made the joke about the "reverse Polish thruster?"

The problem isn't just that there isn't enough gravity. It's that there is an actual large scale repulsive effect. As I've pointed out, it's more of a pressure than anti-gravity. Leaky branes could help explain dark matter. Not as an intersection, however, but by having multiple branes running almost parallel to each other, all causing distortions in the bulk. This would effectively increase the mass of something like a galaxy or larger, because locations of galaxies in neighboring branes would correlate strongly, but not affect gravity on the local scale, because locations of stars would be pretty random. There are some problems with it as well. First, the elephant in the room. If the above is true, there should be locations in our space which behave as if there is a star there, but without there actually being one. To generate as much "dark matter" effect as we observe, the leak has to be strong enough to keep entire planetary systems by a star from another brane. Now, that'd be pretty rare, and we might simply not have detected something like this, but the universe would have to teeming with "phantom" objects ranging from gas clouds, to asteroids, to stars and black holes. They should outnumber normal matter. But we see no evidence of this. There are more subtle, but deeper issues as well. For example, curvature of the brane itself would generate its own gravity. But it'd have restrictions due to the effective manifold being embedded. Gravity goes from problem of curvature of a non-embedded manifold to one that's embedded in another curved manifold. Curvature in the bulk would then have to work according to General Relativity, due to symmetries, while curvature in the brane would follow more complicated equations. This would result in significant corrections to General Relativity, and again, we don't see this. With some gravitational effects measured to 12 orders of magnitude in precision, we ought to have noticed something. Finally, there is the question of dark energy. As I've pointed out, it corresponds to pressure in energy-stress. The interesting thing about that is that it does not depend on larger scale makeup of the verse. It's like stress in the real structure. Doesn't matter what's causing it. Stress is a real measurable thing. And so it is with the dark energy. Even if the actual cause of the inflation is the brane being inflated like a soap bubble by who knows what, the dark energy would be an actual energy in the brane. And we ought to be able to detect it and measure it. For the moment, I'd say that we should be looking at it as a problem in standard 3+1 dimensional field theory. Whatever else is going on, either the dark matter and dark energy should have corresponding measurable energy in space accessible to it, and we should find it and study it, or we are missing a big piece of the puzzle, like another field, and until we fix that, trying to guess the bigger picture is blind guessing. Once we do find the actual sources of these effects, then we can start talking about their nature. And if we'll need extra dimensions then, then we'll use them.

Ah, your question is even simpler than I thought. But yeah, the fun stuff happens when you don't fly at full thrust. Turns out, if you want to travel as far as you can on a tank of fuel, you should keep a certain horizontal velocity. So suppose, your horizontal velocity is responsible for drag Fd = kmv2. (Reason it's k*m is because of how KSP handles drag.) And, of course, you have to support the weight of the ship, Fw = mg. Because the two forces are perpendicular, the total thrust necessary is given by the following. T = sqrt(Fw2+Fd2) = m*sqrt(g2 + k2v4) Now, if you wish to travel some distance d, it will take you some time t = d/v. Meanwhile, you are going to burn a quantity of fuel T*t/(g*ISP). In other words, the quantity you wish to minimize is proportional to T/v. I'm also going to cheat here and take out the mass. (There are conditions when this can be done properly, which you are almost certain to never break.) And that gives me the following. S = T/(mv) = sqrt(g2/v2 + k2v2) And the first order necessary condition for optimization is dS/dv = 0. Skipping over some calculus and algebra... -2g2/v3 + 2k2v = 0 v = sqrt(g/k) = vterminal Which everyone who've been playing KSP long enough should have seen coming. Just like in the case of optimal vertical ascent, your best use of fuel for horizontal flight is to travel at terminal velocity. The rest is very straight forward. If you are traveling horizontally at terminal velocity, drag is equal to weight. That means your rocket needs to be at 45o, and TWR should be sqrt(2) which is about 1.4. Naturally, all of this only applies to planets with atmosphere. In vacuum, the faster you can accelerate the better. So just push throttle to the wall, and angle will be determined by TWR as you've previously calculated.

It's just a choice of parameters, though, isn't it? I very much doubt that something would go horribly wrong with Grasshoper control algorithm if somebody adjusted parameters for gravity and atmosphere. I suppose, some stopping conditions could be hard-coded magic numbers, but it's kind of a bad practice, and I sincerely hope that SpaceX would know better.

Without air resistance, you are best off accelerating as much as possible. But with air resistance, there is actually an optimal angle at which the rocket should hover in order to consume minimum amount of fuel per distance traveled. It's a bit complicated for real rocket in real atmosphere, but for KSP, it's a very simple optimization problem. I don't recall the exact answer and don't have a moment to derive it just now, but I'll drop back later and show you how to get optimal angle a bit later, if nobody beats me to it.

That's incorrect to begin with. Field dynamics is just as objective as classical mechanics that you are used to.

Yeah. The main problem is that anything that enters the system via Moon gravity assist would be greatly influenced by the moon thereafter, so it will likely be flung out of the system. The only exception I can think of is if a binary asteroid/comet enters the system, with one of the pair getting captured. That can happen with a much gentler assist from the Moon-Earth system, which can allow the captured asteroid to stay far enough out to remain stable for a long time. Earth's Hill Sphere can accommodate a body in 1:2 resonance with Moon-Earth system. That can allow a captured asteroid to go from the initial capture orbit to a stable near-circular orbit in the system. The odds against that are astronomical, of course, but it's not impossible.

Gas giant can be problematic. All four Galilean moons are tidally locked to Jupiter. And this is going to be the situation for any large moon that has formed near a gas giant. That means you can't rely on moon's rotation for day-night cycle. Instead, it has to be the moon's orbit around the planet that provides the day-night cycle. A cycle significantly longer than Earth's is going to cause very extreme temperature variations, so it has to be on the order of couple of days. This would put Io in the golden zone for habitable moon if Jupiter was in Sun's habitable zone and Io was a bit larger. But Io experiences all sorts of problems due to its proximity to Jupiter. An Earth-like planet in such a low orbit would be losing too much of its atmosphere and having too much geological activity for any complex life to be plausible. The other possibility is having the moon orbit far enough from the parent planet to prevent tidal locking. Large moons aren't supposed to form so far out, so it'd have to be a capture. But a capture from the wrong part of the system would mean that the moon missed out on the young Earth stage of development crucial for generating sufficient quantities of organic molecules needed for life to start. So it needs to be a capture from habitable zone. But we have a gas giant in a habitable zone of this star, so not much else. Now we are looking at a capture from another star system, a planet that got knocked out of its cozy habitable zone orbit, remained frozen in the void, and became alive as a captured moon of a gas giant in a habitable zone of another star. I'm sure in all of cosmos such things happen. But I wouldn't count on finding one of these. On the other hand, if we take parent planet to be a super-Earth, this whole thing becomes more plausible. An impact event in early formation can result in an Earth-sized moon that's far enough from the super-Earth to prevent tidal locking. And it would allow normal geological evolution of the planet, allowing for subsequent biological evolution if the conditions are right. So yeah, I'd go with a moon of a super-Earth if I was looking for a habitable moon.

In a nutshell, he thinks that a closed box with a fan in it is going to move. Which is really rather sad. Also, annoying. Can the mods at least take away his ability to start new threads?

It's related, but one should keep in mind that this was quite expected, and dark energy has nothing to do with dark matter, other than both being so far undetected. (Hence, "dark".) The observation of the structure is nice, but it doesn't help us understand dark matter or dark energy.

TheDarkStar is right, though, in that it still requires an interaction. "Watching" which slit a particle goes through involves interaction with that particle. Observation isn't a passive thing. Though, things do get way more complicated when you start considering experiments like Quantum Eraser, but that's a bit beyond the scope of this discussion.

A real quantum thruster is effectively a photon drive. We have a discussion thread on it a bit bellow. There is simply no way to get the power generation capability required for this into a cubesat.

I was going to suggest deploying a drogue. It might sound silly, but if you do the math, it can actually get you more than 10Pa of pressure as you are flying by a star at these speeds, which is a good amount of deceleration. Unfortunately, the probe is going to buzz by the region with any significant solar wind density so fast that the net effect is negligible. Now, for a slightly larger probe, this is still an option. If you use a magnetic scoop instead of a drogue, you can get that incoming hydrogen to something like 1GK, which is more than enough for fusion. So you can organize a reverse bussard ramjet, which can provide significant braking even in interstellar space. But this isn't something that you can put on a 4kg 3U cubesat.

Your information is outdated by many decades. Accelerator experiments confirm that anti-particles and anti-matter have exactly the same energy as normal particles and matter. So while we don't have experimental measurements of gravitational forces due to anti-matter, that's really not necessary. It is well established that the "charge" of the gravitational force is the energy-stress tensor, which is equivalent for matter and anti-matter. So as far as gravity goes, matter and anti-matter are absolutely the same. They don't. The only things affected by observation are measurements. Which is quite intuitive. You can't have a measurement without an observer of some kind' date=' even if it's just measuring equipment that's going to play a role of observer. What's interesting is that choice of observer makes a difference on observation. But that's no different than choice of coordinate system making a difference in observations in Relativity. The actual physics does not change. QM works the same way. Unfortunately, Copenhagen Interpretation is absolutely terrible at treating a system with multiple observers, which lead to a lot of people claiming that QM actually has some sort of "magic" properties, where observer influences the universe. That is not the case. Many Worlds Interpreation is much better at this. It allows you to treat a system with multiple observers same as you would treat a system from multiple reference frames in relativity. This is why I frequently point people to MWI whenever they get confused about QM. It's the same physics, but under MWI, it's way more intuitive. Sorry, this would take too long to explain, so I hope you'll just take my word for it. It simply doesn't work like this. While stress-energy is a kind of conserved charge, there are no matter states corresponding to negative amounts of it. It's a broken symmetry, if you will. Anything with negative energy must very rapidly decay. Another way to think about it, it would be like having pockets of vacuum in a room filled with air. Yeah, you can come up with something like that, but these pockets will instantly collapse. There is just no way to maintain large quantities of negative energy without doing something really tricky. It's something that'd be very difficult to do artificially, let alone be something that occurs naturally. Dark energy, in contrast, isn't negative energy. It's more like pressure. Normal matter energy has no pressure. If you have something like very energetic gas, it will have pressure. Both in normal sense, and in energy-stress sense. But for ordinary matter, regardless of what you do with it, the pulling strength of gravity is going to be greater than pushing of stress-energy-pressure. Dark energy, however, has to be something with a lot of pressure compared to how much energy it has. So it pushes instead of pulling. I suppose, from layman's perspective, it's the same thing. If it pushes things apart, it must be anti-gravity with negative mass. But from perspective of theory, it's actually very different. We expect it to have positive mass, but causing space-time around it to expand anyways. Which is really, really weird, and we all want to study the hell out of it, but we have no idea where to get any.

You can't burn continuously. Continuous burn would actually cause you to gently spiral down, requiring a much longer delta-V. Of course, if you are only time-limited and not fuel-limited, then that doesn't matter. But if fuel is a concern, you can only burn at apoapsis, once per revolution. That's going to take a very, very long time.