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That's because you never even attempted to study science. You want things simple. Real things aren't simple. If you see a perfect agreement and harmony that are easy to understand in something, you know it's made up.

Scientist A will only experience a few years during his trip. (A little less than 2 years at 0.999c) During these years, he will see planet he's flying towards age 80 years. 40 to account for distance and 40 more for duration of the trip. And yes, it will take scientist B 80 years to see scientist A arrive at destination planet, making the two observations consistent. See Wikipedia's article on Twin Paradox for some notes on how to think through such an experiment.

What you should be searching for is Light-Front Coordinates. That is the mathematics for limit v→c. It's not going to be terribly helpful for this discussion, though. The only practical ways of traveling at light speed involve event horizons, warp bubbles, wormholes, or some other distortions of space-time preventing a hard singularity that would arise otherwise if you tried to drag anything with a mass shell at these speeds.

Do you understand, at least roughly, how a solid rocket engine works? Look it up on Wikipedia if you have some doubts. MSMH rocket would work exactly the same way, with heat causing Hydrogen at the interface to transition, increasing pressure and temperature in the chamber as a side effect. This is somewhat unusual, as materials usually take energy away while evaporating/subliming, but metallic hydrogen has such ludicrously high enthalpy, that it would not only offset energy required to turn Hydrogen into gas, but also leave enough energy overhead to significantly surpass any chemical rocket in every metric of performance.

Yes on the density. Both properties imply high conductivity and makes it a fantastic candidate for superconductivity. (Not that it's news.) Optical properties, in a word, shiny. Again, not surprising for a metal. And yeah, for metallic hydrogen to be usable as a fuel, it has to be metastable. MSMH would be an ultimate chemical fuel by all accounts, but there is currently no evidence of metastability.

What you saw was 2-dimensional crystal growth. Seeds floating on the surface have a bit of attraction. If nothing disturbs their movement, they will clump together forming a lattice. If you get them to move, however, they will prefer the state of increased entropy and start moving independently of each other. That's effectively a phase transition, equivalent of going from solid to gas for substances. I'm guessing, liquid was either boiling or simply moving quickly enough (stirring, convection) to cause the seeds to move about. As movement in liquid died down, it was equivalent of cooling down for the seeds, and they started to clump together. The reason the process started from the center is that microwaves tend to heat ceramics better than fluids, despite wavelength having been selected to achieve just the opposite. So in a bowl, liquid warms up from outside and moves up and towards the center. So any clusters of seeds would float towards the center, and that's also where the lattice temperature will be the lowest. Crystals tend to grow symmetrically as it is, but in this situation it's almost a guarantee.

I am not really an expert on fluid dynamics, but that low pressure area looks believable and seems like bad news for the efficiency of the rocket. Although, it might subside dramatically as rocket builds up speed relative to air flow around it, in which case it wouldn't be a big deal. There are several things you might want to look into. 1) Are the input temperature and velocity reasonable? An engine concept isn't much use if there is no fuel that can possibly generate it, or if it's incompatible with much better fuel options. 2) Is temperature at boundaries sane? As in, can any materials actually withstand it? 3) Once your flow hits the expanding portion of the nozzle, speed of the flow should always be right around the speed of sound. If that isn't the case, consider adjusting geometry. 4) Given that all of the above is tuned, what's the efficiency of this rocket? How does it change with changes in ambient pressure and and air speed? The numbers you're looking for are TWR and ISP, just like you would in the game. TWR is a big hard to estimate without doing a crap load of additional material science footwork, but ISP you should be able to get. Just run a boundary around the whole rocket, closer to the outer boundary, but not quite touching it, and look at momentum in vs momentum out through that boundary. Net will give you net thrust, and knowing that and mass flow of your fuel you can get the ISP. P.S. See that vortex on the 3D view? That's the result of the low-pressure and that's what's going to generate a ton of drag. When considering efficiency, make sure the boundary you draw includes the entire vortex system. Move outer boundary further out if you have to to accommodate that. Otherwise, your estimates will be unreasonably optimistic. But like I said, this might not be a problem at higher air speeds or lower pressure, and at low speeds and pressure, you might be getting enough air-augmented effect going to set it off. P.P.S See how flow starts to expand, then contracts back in and hugs the fuselage? That tells me that the expansion isn't quite right. This happens to nozzles designed for vacuum when operated at sea level, for example. And it eats a LOT of efficiency of a rocket. If you look at Space Shuttle nozzle, you'll see how its expansion kind of slows down near the end. that's exactly to avoid this sort of a problem. Aerospikes do, typically, manage to avoid this problem. So I tend to think it's something you can tune out of the design by playing with the size of the opening gap.

We've had proper description of gravity for one hundred years now. It's called General Relativity. And it's a theory that withstood not only the test of time and countless experiments, but has for the past fifty years been understood to be a special case of Gauge Theory. I don't know where you are getting your ideas from, but it's not from scientists of any kind. The only reason we are looking for alternative explanations for gravity is because General Relativity doesn't quantize well. Some people think that alternative explanation could come with mathematical tools that will let us bypass this problem. But it's more of the limitation of Quantum Mechanics than of General Relativity. Unless you are trying to work out quantum physics at the event horizon of a black hole, our current understanding of gravity is quite complete. Even for things like neutron stars, where you have to actually use Quantum Field Theory in curved space-time dictated by General Relativity, the two theories work quite nicely together and make accurate predictions. So I'd argue we know what gravity is. It's a gauge interaction due to the underlying local symmetries of the four-dimensional manifold we happen to be a part of. We can still ask questions about the symmetries involved and about consequences of it all, but none of it changes the answer to what is gravity. This we already know.

3D printing is a very broad category. Most people think of something like thermoplastic extrusion-based printing. It's cheap, widely available, but has very significant limitations. You can't print something that isn't connected to everything else. But there are many, many other methods of additive manufacturing that fall under the 3D printing umbrella. Direct Metal Laser Sintering, for example, can produce parts with precision of a few microns and with no requirement for any sort of connection. You just have to clear gaps of loose metal powder when you're done. In addition, it can work with titanium alloys. People have used these techniques to print everything from high quality firearms, to turbines, to actual rocket engines. So in the broadest sense, the answer is certainly yes. You can absolutely print parts with gears, bearings, and all manner of other moving parts. But you aren't going to do that with a printer you pick up on Amazon for a few hundred bucks. It takes equipment that costs in the hundreds of thousands of dollar range, usually custom-built for your particular needs.

Inelastic collision works exactly the same. It's just that your E1 < E0. Figuring out the exact loss will depend a lot on material properties, but typically, an approximation where a given fraction is lost for a given material is sufficient. From there, you set up a system of equations where momentum is conserved and energy is constrained by the above and solve it exactly the same as in the elastic case. Non-spherical bodies are slightly more complex, because you have to take normals at impact point into account, and that can generate angular momentum transfer in addition to impulse transfer. Which means you have to take moment of inertia tensor into account. As a result, the system of equations grows quite a bit larger to account for six degrees of freedom for each body. But again, you'd go on to solve the problem in exactly the same form. Total momentum and total angular momentum are conserved, and energy is either conserved or you lose some fraction to heat. Set up system of equations, solve it, get your results. Caveat is that point of impact computation and your system of equations are likely to end up being non-linear, which means you'll need a computer to solve it. Which isn't unexpected.

You don't need to take into account forces if you are dealing with energy, so long as all forces involved are conservative. (Gravity and centrifugal force are.)

There is absolutely zero reason not to use double on modern CPUs, unless you are dealing with massive arrays of numbers, where you'll be hurting for cache performance otherwise. Absolutely always use double precision for intermediate results. It costs you nothing in performance, and can help you avoid nasty, unforeseen rounding errors. This includes trig operations and square roots, since modern compilers are good at replacing these with SIMD intrinsics, meaning you can compute these in double precision just as fast as single. The few rare exceptions on somewhat older CPUs where this can cost you an extra tick are not worth optimizing for at cost of precision. This goes for C# as well, since JIT will convert all these trig operations to SIMD.

If you want to know how much energy it'd take to lift something from surface to GEO straight up, while always staying above the same point on the surface, just use conservation of energy. Total energy at each point is mv²/2 - MGm/r. At surface, v is sidereal velocity and r is Earth's radius. At GEO, v is orbital velocity and r is semi-major axis. M and G are Earth's mass and Gravitational constant respectively. You can look up all of these numbers in Wikipedia, take the difference of energy at GEO and at surface, and this will be the energy you need to supply. As p1t1o points out, in real world, things get a little more complicated because of Coriolis force, but you can ignore that for an estimate. The neat thing about energy conservation approach is that it completely accounts for all forces, including centrifugal, without you having to even think about it.

As LN400 hints, your problem starts with true anomaly computation. Cos(+x) = Cos(-x), and Acos function always returns the positive result. So your true anomaly will always fall in the [0, pi] range. This isn't a mistake, either. Based on position alone, it's impossible to tell which way the object is orbiting. Which means it's impossible to tell the difference between positive and negative anomaly. You need one more piece of information that will tell you direction of motion.

MWI and Copenhagen are interpretations. You can pick either one you like. If you feel Copenhagen offends fewer of your sensibilities, you can take that one. I like MWI because it eliminates illusion of randomness in QM, and that bothers me more than infinite universes. The important part is that you cannot conduct an experiment to distinguish between Copenhagen and MWI by definition. When I say it's matter of preference, it really is. Neither is provable. And the only way to disprove Copenhagen or MWI is to disprove the entirety of QM. More importantly, a corollary of above is taht any sound conclusion under one interpretation applies to the other interpretation. As far as measurable quantities are concerned, at least. Which can be a wonderful shortcut. You can prove the No-communication Theorem using just Copenhagen. And it takes a bit of work. Or you can pose the problem in MWI and wonder how people got confused in the first place. On the other hand, some problems are way easier with Copenhagen. Explaining Quantum Zeno under MWI is a total pain. It requires introducing a Hamiltonian responsible for the measurement and showing that under that Hamiltonian the eigen states are stationary. Good homework problem for Ph.D. students, bad times for anyone else. But under Copenhagen, it's absolutely obvious. So take your pick for a favorite, and I strongly recommend understanding both for practical purposes. Pilot Wave is different. It actually requires a different theory, which can be distinguished from QM. Of course, every experiment so far has fallen onto the side of QM, which lead PW proponents to keep adding features to try and bring it to parity. Which, granted, doesn't automatically disprove the entire approach, but it makes it very dubious at best. As for space-time characteristics, this would have been a good argument back in Michelson Morely experiment, if you tried to argue that we might not need Special Relativity, but we moved on quite a bit past that. Relativity effects are no longer considered a curious feature needing an explanation. They are a direct consequence of the underlying symmetries, proof for which comes from absolutely every corner. Special Relativity, General Relativity, conservation of energy and momentum itself comes from the same principles. Saying, "We might simply not understand how it works," while isn't technically wrong, is not very productive. Until we find an actual smoking gun in the theory, like if EM drive turns out to actually operate at above photon-drive efficiency, I say we assume these things are fundamentally correct. In which case, Pilot Wave is still broken. No, as measurement problem is part of interpretation, not theory. In aforementioned MWI, there is no measurement problem, but it's the same quantum field theory.

Less sublimation, more a violent explosion. Even without oxidizer, metallic hydrogen stores a huge amount of energy which gets released when converted back to gaseous form. And since this first explosion is going to be sufficient to rupture pretty much any enclosure one might have for it, it's going to mix with oxygen in atmosphere and produce a nice fireball to round off the effect. Nonetheless, even though this would certainly dramatically reduce the list of viable applications, regardless of how volatile it is, if there is some form of metastability, we are guaranteed to find uses for it. It's just that cool of a material. Mtastability is the crux, though. We have known that it can be turned metallic for a long time. We know that it will have a lot of interesting properties, including high temperature superconductivity. But all of this is useless information, outside of explaining Jupiter's magnetic field, unless metastability is confirmed. And theoretical evidence for it is not particularly strong.

Gravity turn optimization is a really hard problem. Analytically, I have not seen it solved even with the old, simplified aerodynamics. To contrast this, for a vertical ascent, I was able to solve optimal TWR even under conditions of ISP and gravity varying with altitude. Once you throw in a second dimension, however, optimization becomes really hard. Numerically, it's not quite as bad, but still a tough problem. I had pretty good success with genetic algorithm. But the best way to go about it is parameterization of ascent profile and running a good optimization algorithm on the parameters. I have not gone to the trouble myself, but I've seen people here run the numbers for specific craft, coming up with very reasonable results. There are also some good approximations. For example, during early ascent, you pretty much rely on constant fuel flow. Under these conditions, fuel spent is a function of time only, and rocket's speed is function of density only. So you can use optics to figure out the correct trajectory, using ratio of terminal velocity at each altitude to sea level's as your optical density. This, however, relies on you knowing the optimal angle at which you want to exit the region where this approximation is fair (up to about 10km). Which means you have to solve the rest of the problem the hard way anyhow.

Ok, so first of all, any rocket engine you build is a potential explosive. If you can't make sure you will be safe under assumption that it can explode at absolutely any moment, including while being made, simply sitting on your desk, or while you are trying to ignite it, then don't do it. Second, the safety of an engine is primarily due to materials and size. One gram of nitrocellulose in a closed hand can sever a finger. And unlike some other options for rocket engines, it can explode even without an enclosure. I would avoid it. With enclosure, things become even more dangerous. After explosion, it becomes shrapnel. Never use metal. Cardboard is least bad, but can still do damage. If you live in US, the reason you can't find potassium nitrate is because it's on the ATF list as an explosives ingredient. While you can still obtain it, any rocket motor you make with it will be an explosive device according to US federal law. Sugar motors are technically legal to make, but it's illegal to transport them without a license, so even just taking it from your home to a place you will launch it could be a felony under federal law. Many other countries have similar restrictions, so check before you make something like this. For safety and avoiding legal complications, best option is to do what NASA does and go with APCP. It is less volatile, has better performance, and as far as I know, won't put you onto any gov't watch-list. On the other hand, it's still a rocket motor, so when these things do explode, they explode well. And while not in as much of a legal limbo, ammonium perchlorate is still not trivial to obtain. Which is probably for the best. Hopefully, all of the above is sufficient to talk you out of it. If not, maybe it will at least help you to keep your fingers and eyes and keep you out of jail.

Pilot-wave theory is an archaic attempt to bring Quantum Mechanics in line with human intuition. The notion that nature should be intuitive is idiotic, of course, which is why there is absolutely no sense in any of this. Modern Field Theory, of which Quantum Mechanics is a branch, is fully deterministic and local. There is no faster-than-light action or any random effects in it. Basically, none of the perceived problems that led to attempts to develop a pilot-wave theory in the first place. Moreover, modern Field Theory has withstood one test after another, while pilot-wave fanatics keep needing to come up with one patch after another to prevent the whole thing from coming apart. Field Theory describes all fundamental forces, yes, including gravity, via gauge symmetries, thereby, bridging the gap between Quantum and Relativity. Pilot-wave models can barely avoid violating Special Relativity. Nobody has a clue how to make them compatible with gravity. It is possible, in principle, to keep adding features to a pilot-wave description of the world to make it match any Field Theory. Just like it is possible to keep adding epicycles to orbits of celestial bodies to describe any star system. But at some point, any sane person would have to admit that epicycles just don't work, and gravity is a much better explanation. Unfortunately, proponents of pilot-wave lack that sanity. They are much happier with a needlessly complicated theory, one which needs to be patched up after each new discovery, just so long as it doesn't offend their intuition of how the world should work. To be fair, it should be noted that there is some scientific and mathematical interest in pilot-wave models as cases of duality. In that sense, it is on the same shelf as holographic interpretation or string theory. There are interesting things you can do with it, and some useful knowledge can be gained from juxtaposing it with Field Theory. In short, not all people who spend time on pilot-wave are crackpots. But no serious scientist looks at it as a viable alternative to Standard Model. P.S. Yes, Many Worlds is probably the closest we'll get to an intuitive interpretation. But one important distinction is that Many Worlds and Copenhagen are both interpretations of the same underlying theory. They are not distinguishable by experiment. So you'll never have to make tweaks to one or the other because you got new experimental data. The underlying theory could be in trouble, but not the interpretations. So you really are free to just pick the one you like. Pilot-wave started out as an interpretation, but it only passes that bar in a one-particle case with fixed frame of reference. Once you introduce variable reference frames and multi-particle interaction, pilot-wave actually becomes experimentally distinguishable from Quantum Mechanics, making it a distinct theory. Of course, it's a very bad theory, since it needs patch-work for just about every serious test of Quantum Mechanics.

Energy isn't the only game in town. You also have to kill angular momentum. This is why Hohmann isn't always your best option for transfer. You want to be as low as possible to bleed energy, but you want to be high while bleeding angular momentum. The maneuver that maximizes angular momentum loss without giving you even more energy to bleed at periapsis is a retrograde burn. In general, almost all of your burns should be prograde or retrograde. There are very few exceptions. Notably, inclination change, intercept adjustments when you just have to be at a certain place at certain time, and the last bit of landing on an airless body if you are going for optimal efficiency. Edit: Scratch that. What I wrote above is true for 1-body approach from infinity. You brake retrograde early, dropping perigee. If you are in KSP physics, highly hyperbolic, and already entered SOI, this changes things. First, you made a nav error with such approach, but there is no use crying over it. Energy is your main enemy now. You need to do a minimal burn that redirects you towards a lower periapsis at first opportunity. In general, this won't be exactly radial, unless you already reached your initial periapsis. But given size of SOI and high entry, it's going to be mostly radial. Basically, the earlier you make this adjustment, the more retrograde and more efficient the burn. But if you wait until the last moment, you'll have to burn radial and waste fuel. Still not as bad as burning retro at the last moment, though.

@p1t1o The only thing that matters are torques. In steady hover, the torque generated by main rotor always passes through the axis of its rotation. So the tail rotor needs to produce torque exactly opposite to that, meaning still along the line of the axis of rotation. To achieve that perfectly, rotor would need to sit directly behind CoM. Whether that's close or far to the plane of main rotor is absolutely irrelevant. Of course, if tail rotor doesn't sit directly behind CoM, you'll also be generating a slight amount of rolling torque, which you'll have to compensate for with the stick. And of course, depending on how much rudder you give it, you'll have to adjust compensation. But that's nothing new for heli piloting. Pretty much any input you give will require you to compensate with something else, then compensate for that compensation, and so on. Unlike a fixed wing, where we can at least pretend like inputs are independent (it's not true, but it's more subtle), with rotors, everything influences everything else in very obvious ways. @Green Baron Yeah, but there are many different ways a heli pilot can screw up. My claim is that most frequent mistakes leading to accident are these two. It's a claim based entirely on stories I've heard, and not any kind of statistics, however.

The reason why ground-effect doesn't add to stability the way you think is because of gyroscopic effect. Lets start with hover at high altitude. Suppose, you pitched slightly forward. There is no immediate change to lift, but you start accelerating forward. That results in advancing blade having a slightly higher lift due to higher relative wind velocity. If advancing blade gets more lift, gyroscopic effect causes the helicopter to start pitching backwards. So once you have a bit of altitude, hover is actually self-stabilizing. If the flight stick is slightly displaced from center, this will result in a constant air speed in that direction. This is very easy to get used to, so hover at altitude tends to be straight forward. Now lets look at the same situation in ground effect. Again, we start with a small tilt forward. Before helicopter even started picking up speed, the forward blade already has more lift. And due to gyroscopic effect, this will cause a tilt to a side. Which side, depends on the rotor rotation direction. As you are tilting to the side, you are also picking up forward speed. That will result in maximum lift shifting a bit towards advancing side, and this will still correct the forward tilt, but by this point, you are tilted to the side, picking up lift on that side, and are starting to accelerate in that direction. Now you are tilting to the back, and the cycle repeats. This is inherently unstable. Because the self-righting mechanism from high hover is still there, the level attitude point is still nominally stable, but it is not dynamically stable, and that's what you really care about. Instead of stabilizing, the helicopter starts to gyrate, building up more and more deflection from center. Worst part is, the inexperienced pilot will try to correct for the immediate tilt, which is going to be corrected by increased lift on the advancing blade anyways, instead of correcting for the ground-effect. So there is a 90° phase lag between what's happening to helicopter and pilot's corrections, making it very difficult to keep helicopter put and could actually make the situation worse. This is why an inexperienced pilot should never try to hover in the first place except for learning how to do it under instruction. If you have to fly a rotor in a simulation or in case of emergency, do takeoffs vertically up, then build up forward speed. Once moving, helicopter isn't that different from fixed wing. For landings, come in with forward speed, as if you were landing an airplane. You can come down with much greater slope, though. If you flare to a stop, you'll have much better chances of putting the machine down gently than if you tried to come in vertically and land from hover. You'll also be that much less likely to encounter the other great enemy of rotor, settling with power. I would wager that settling with power and hovering errors account for majority of helicopter accidents. As to the reason why tail rotor is placed high, yeah, I think the chief reason is tail strikes, as shynung suggests. Although, helicopters have fairly high CoM, since the engine is typically up top, and so I doubt any significant torque comes from tail rotor that isn't in line with the main rotor's torque.

That's quite normal, since it's starting to stall at 30° already. Most airfoils stall at even lower AoA, but narrow lifting bodies tend to have high critical AoA. In the configurations in red and green, you can clearly see the onset. On the blue one, the actual critical AoA is a bit further out, but L/D ratio is well on its way down, so you aren't likely to try and fly like that anyhow. If you need to plug this into a simpler model, this airfoil is amazingly close to thin airfoil theory. For a thin airfoil, drag coefficient is quadratic in AoA, and lift coefficient is linear. And I see a very neat set of parabolas and almost perfect straight lines there. Since the vertical axis isn't labeled on these graphs, it's hard to extract effective wing area, though. Do you happen to have a table with actual numbers represented by these graphs?

The actual problem with that statement is referring to the Mach number in vacuum. It depends on atmospheric pressure. But there are certainly stable orbits around Earth with orbital speed equal to Mach 7 at sea level under standard conditions.

We are still talking about something which has odds of being wrong a little better than one in a thousand from this experiment alone. Other experiments, while having lower sigmas on their own, confirm this one. Which brings up the total into 4-5 sigma range for the theory. Sure, it's still not certainty, but the headline of the article is in the same category as "Evolution hasn't been proven."