K^2

I'm honestly not trying to step on how cool paramagnetic levitation is. And it only gets cooler once you start diving into math and physics of paramagnetism. (And also, because of all the liquid helium.) All I'm saying is that at 1G you can "levitate" a human on a bed of nails. The mark to beat is 15-20Gs. That said, even 1G, if it's uniform enough, can be great for all the times your engines aren't running. Mag fields have a wonderful property that they don't diverge, so a relatively light Helmholtz coil can provide fairly uniform B field throughout a rather large ship. I don't think mass requirements will scale well for small exploration vessels, but if we have liners like what BFR is meant to lift, the additional mass might actually be sensible. Granted, on a larger ship, it's significantly easier to set up something like tethered centrifuge as well, but having a solid-state system without hundreds of meters of cables involved seems beneficial. And keeping superconductor magnets cool in space is significantly easier than on Earth. I'll throw some numbers at it. See what I get for tonnage of the coil rings to get artificial gravity on BFR's Starship.

For a mag field, it's a hard limit. Not something you're going to be able to compensate for. It's like trying to levitate a cake with a fire hose. It should technically be possible, but we all know what happens in practice, because you'll never be able to create a flow that perfectly cancels all the imperfections in the surface creating a pressure differential. The way a magnetic field penetrates materials that interact with it in any way really is more like a flow than anything. That's definitely doable. There are limits on how much you can push even fully submerged - even if you manage to fill all the voids, at some point, density difference between bones and flesh will be sufficient to separate the two - but you'd be able to go way higher than anything a modern fighter pilot can handle. Without somebody carrying out definitive tests it's hard to say for sure, but I'd be surprised if you can't go well into triple digits in units of G. Even without breathable fluid, human body can handle several times higher g-forces submerged in water than simply in a g-suit and a proper chair. And these, on their own, provide a factor of 3 or so from unequipped person. Abyss - yeah, but with caveat that despite some successful tests on animals, and limited pressure chamber tests on the same, the tech was never really proven. Russia has recently restarted the research in that direction, but what I've seen hasn't really done anything the old Soviet research hasn't. In fact, it seems to be catching up still. That said, still probably the most believable part of the Abyss.

Even at MRI strengths, human body distorts the magnetic fields, and you have to correct for it when reconstructing the slices from corresponding Fourier spectra if you want high quality imaging. If you were compensating high acceleration with a magnetic field, the gradients from that distortion would be the thing that kills you. You have to apply force evenly throughout the body and in direct proportion to density in order to get anything but marginal improvement in maximum acceleration. And the only force that can do this is gravity. The good news is we know how to generate gravity artificially and on demand. An electric field orthogonal to a magnetic field produces energy flux in direction orthogonal to both and of strength proportional to the product of two field strengths. (see Poynting Vector) Modulating either of the two fields, consequently, produces modulation on the energy flux. And that can be used to generate an effect that is the gravitational equivalent of electromagnetic induction. In other words, you can briefly generate a gravitational field that doesn't terminate on any mass. It's true artificial gravity, however brief. The bad news is that the most optimistic estimate I could come up with for the field strength could compete with gravitational field of a grain of sand. There's a factor of 1/c4 that shows up in the relevant equations, and no matter how much magnetic and electric field you can throw at it, and how quickly you can can kill the electric field to produce the effect, you just aren't picking up enough decimal places to compete against the c4. Now, if we could get our hands on some of that negative-mass dark matter/energy fluid from the other thread, I could probably come up with a scheme that gives you effect of an at least limited inertia dampener. But that's a separate story entirely.

For real engine, ISP will, in fact, vary with throttle. And the max ISP is not necessarily at max throttle, either. I could probably list nearly a dozen factors that ISP generally depends on, and amount of fuel you inject into the chamber will impact, directly or indirectly, a third to a half of these. I'm not sure if the impact of throttle position on ISP will be higher with or without an atmosphere. The fact that the bell for atmospheric operations is shorter might actually help reduce the impact, at least, in some throttle ranges. This will probably depend a lot on the engine design.

The aliens let the first one slide, but now we're definitely getting a fine for littering. An object on hyperbolic trajectory is in an orbit, but I'm not sure if I'd call it orbiting, because then we'd have to say that everything orbits everything else, making it a kind of a useless definition. I wouldn't even be able to claim that Earth orbits the Sun at that point, because there is nothing inherently special about the Sun as far as Earth's track through cosmos goes. So to me, saying "A orbits B" implies that the two objects are gravitationally bound, which is no longer the case for an object above escape velocity. At that point, it's more of a scattering. The trouble is that semantically the words "orbit/orbiting" can imply both the trajectory and periodic motion. I'd usually go to Latin root as a tie-breaker, but it's the same issue there. 'Orbis' is something round, and 'orbita' is a track made by a round object, such as track left by a cart. And while I'm pretty sure that the noun 'orbit' is derived from the later, and that's consistent with standard scientific usage, when we talk about 'orbiting', things get fuzzier. Bottom line, I don't know if I'd correct someone when they say that Voyagers aren't orbiting the Sun. Although, if we look at it that way, they haven't stopped orbiting when they left Heliopause, and rather back when they did their final fly-by boost to get the necessary velocity to leave the system. So if they aren't orbiting now, they haven't been for decades.

The effect on the ship is the same. Something continues to apply force to it as its punching through the limit. Depending on some details of the physics of vacuum, it's not strictly impossible, since we do see this work in very limited sense in fluids. See Cherenkov Radiation. But there is no indication that true vacuum allows for it, and any means of force mediation would have to survive infinite stress. So whether you're trying to build a rocket that does it, or use sails to capture something that's already moving FTL (all kinds of problematic in the first place, by the way,) it's absolutely not clear how to have your mountings survive the process. E.g., if your sail is made up of normal matter, yet somehow interacts with tachyons, the net effect ought to be your sale getting evaporated away. All FTL ideas require us to stretch the known a little bit to admit the what-ifs, but you're definitely stretching it a lot more when you propose that there are other dimensions or that there are particles/materials that can survive brute-force approach (if the vacuum even supports it). So we're still looking at ways of working within General Relativity as the most plausible ones. And that's warp and wormholes.

There are some repetitions there. Hyperspace and Intertwined are essentially the same idea of having a separate space that provides a shortcut. Details of the shortcut hardly make a difference, really. Then you have wormholes and back holes. These, likewise, are variations on the same principle. And while we're at it, Warp Drive is closely related. The limitations on all 3 are related to some conjectures about CTCs. Finally, tachyon sailing would be a type of brute-force, since you're still trying to punch the light barrier. That said, the only thing we have any sort of math on is Wormholes and Warp. So they look most plausible right now. P.S. Yes, causality goes out of the window with any of these.

Gravitons are massless, and have no charge other than due to stress-energy. A particle with negative mass will have to have a charge other than gravitational. So we know it's going to interact with other particles in some form or another. Which means that it ought to be produced in particle accelerators, and since it's not massless and it does interact, we ought to be detecting it. We aren't. So something fishy is going on there. Oh, it's not perpetual motion. You can't get any energy out of it. What it is is a linear gyro. A device that can store a lot of momentum without going anywhere. It will also saturate, like any proper gyro, so there are limits to how far you can push it. But if it buys you a single orbit around a planetary body, you can use it to transition to any other orbit by just paying mechanical energy cost of it. Alternatively, stuff some momentum on it, and send your ship gently spinning on longitudinal axis. You now have gravity on your ship.

I'm not saying that you're wrong, because you're not, but it's a little bit like saying that because there are negative electric charges, we have Teslas. Also true, and it's hard to complain about that fact, but we've been making great many uses of electricity long before we got to capability to build practical electric cars, and we've found an enormous number of uses for it in the process. Electricity is everywhere, and is at the core of nearly all of our technology. Negative masses have applications in General Relativity, yes. Among them are warp drives, stable wormholes, and time travel. Nothing to sneeze at, but comes with enormous challenges even if you have negative mass on hand. In the mean time, consider a 1kg box. It uses electromagnets to levitate a -1kg anti-mass inside of it. You give the external box a light push. What happens? If we learn this little trick, we'll have absolute freedom to explore this star system. Which ought to last us until we do figure out that warp drive thing. In terms of the paper, the idea isn't exactly new. Although, I have not seen quite this thorough of analysis before. The problem is rather that we expect to see indications that this sort of matter exists in the lab. It's obvious why significant quantities of this matter wouldn't be found around. (Though smaller quantities might still orbit as part of star halos.) But we ought to see indications of something like this in particle physics experiments. And we don't. It's very difficult for me to even imagine a possibility of a lighter than vacuum particle (and that's all a 'negative' mass really has to be) that we would not have observed. Moreover, if such a thing existed, it's hard to imagine why vacuum itself wouldn't decay to that state.

Duration isn't the only factor. The fact that we were, in fact, running crews from all over the world with all kinds of background and training is very valuable in the first place. But also what we were seeing from recovery times after various durations of stay. If we send a crew to Mars, they'll have to get up and work on arrival after 7 months in a tin can. In lower gravity, granted, but it's still going to be a huge hit. Simply going for the record on duration of orbital stay isn't the thing that gets you through it. And not everyone we'll want to send to Mars will have the kind of physical health that makes them capable of breaking any such records. Mir had its own objectives. And I'd say, data gathered there is probably sufficient for the kind of manned Mars mission USSR would have considered when Mir was conceived. And this data was valuable all around. ISS added the kind of knowledge we wanted to have that's more applicable towards the sort of joint international or commercial Mars missions we're likely to actually see. Something a little bit less do-or-die, with more varied crew, and which requires greater safety margins all around. A lot of it we probably could have inferred from Mir data, but it's one thing to have a good guess on the effects, and another to know them with great certainty. There's a reason both USSR and USA sent animals into (sub)orbital flights before going for manned missions, despite nearly everything we gathered from these was easily predictable. We needed ISS. We needed it to put certainty on a lot of good guesses. But we've also squandered a lot of opportunities due to endless budget cuts and the death of the Space Shuttle. We could have and should have gotten a lot more out of that station. Unfortunately, it's not something I expect to improve greatly, so what we got out of it will just have to be enough for now.

Yeah, I don't see anything that would account for 0.05 radian difference. The steps I use to break down the arc are 0.2, and using golden section pretty much prevents it from getting stuck on 1/4 of that for some numerical reason. It's also not a precision issue, since that's well within even single precision, let alone double. The max2d is set to 10-6 as well, so again, right out. If you want to try diagnosing it further, try computing positions using your algorithm and the JS code I provided using the same identical orbital elements and a few values for true anomaly between 0 and 2pi. If you get a difference, you can start tracking it back to see which numbers are coming up different in between.

If you ever plan to send humans further than the Moon, figuring out what a year of microgravity in close confines does to 3-6 people working as a team is very important in itself. Mir was a good starting point, but nowhere near sufficient to plan Mars mission from. ISS did a lot better, in big part due to things learned from Mir project. And there are more things we can be testing on ISS in this regard if money gets dropped for essential upgrades. Centrifuge habitat would be among these. And while mission to Mars might not bring any direct benefits in day-to-day life that couldn't have been achieved by investing this money elsewhere, Establishing remote outposts is critical for our long term survival. I would argue that if you're not planning to leave Earth, then all of our achievements are for naught, making this kind of research the most important thing we should be doing.

Well, I'm not one, so it makes it a lot easier for me to like a hypothesis that has very little to do with reality. At no point did I claim to like it because it has any merit. I completely agree with your points. Purely for arguments sake, I could argue that hominids are adapted to water better than most non-aquatic animals (holding breath, more even fat distribution), but neither are they sufficient by themselves, nor are they unique to aquatic animals. I could use the same arguments to say that sea turtles are well-adapted to high velocity flight for a non-flying animal. And I have to admit, sea turtles flying formation at 300 knots, relying on body-lift of their sleek, aerodynamic shells, is another idea I like very much. Just don't ask me about means of propulsion or power generation for that feat. But as I've said from beginning, aquatic ape is entirely ad-hoc. Its proponents will keep and try and force the pieces fit, and as more evidence is presented, more and more alterations will have to be made to try and salvage it. Which is a the very mark of a bad hypothesis and good indication that it's entirely false. I don't have to be an anthropologist to recognize a bad ad-hoc hypothesis when I see it, even if I don't understand all the details, and entirely not up to date on the latest batch of evidence against it. I just happen to find the situation humorous, because I don't have to deal with people that take it seriously.

Of course. Being agile swimmers, our ancestors had experienced significantly more dangers on land. So they had to adapt to crossing vast distances between watersheds very efficiently. It only makes sense for aquatic animals to be goid runners. Seriously, though, as a curious human with a mind full of "what if"s, I really like aquatic ape h. It fits so very neatly. As someone trained in a field of science, I have to admit that it's the most ad hoc thing ever, for much the same reason, with no evidence that can't be dismissed as incidental. So yeah, I wasn't serious either.

That's probably the best solution right there. If you have business getting military on the arctic ice, odds are, you are either a NATO or ODKB power, and can probably request data on sub movement from one of the above.

Possible, yes. Practical, probably not. You'll be losing a lot of acoustic intensity from ice-water interface, any bubbles of air trapped bellow or in the ice, and any cracks or imperfections in ice itself. It's unlikely that you'll be sitting on top of a perfectly smooth, solid sheet of ice. Physics says if you cover large enough surface of the ice with microphones you'll be able to compensate, but unless you're trying to pick up the sub sitting directly beneath you and making distinct enough noise, the area you need to cover might become impractically large. The other problem is localizing the source. Water and ice have very different speeds of sound in them, so if you think natural ice can be hard to see through, it's way worse with sound. Longer wavelength will certainly help, so you won't have to worry about small imperfections and bubbles, but you'll still get crazy lensing due to any surface geometry at the bottom. To continue the light analogy, looking for a sub through ice is going to be like trying to see somebody on the other side of a stained glass window. Enough light's certainly going through, and if they stand right next to the glass, you can see them clearly enough, but for anything further away, you'll have trouble distinguishing what you're looking for from all the noise. And subs are generally built in pretty well to blend in with the noise. Again, if you have sufficient surface covered in acoustic pickups, and you've taken the time to map the imperfections, which you can do from the surface by listening to reflected sounds, you ought to be able to compensate both for refraction and for intensity loss and reconstruct the same kind of signal you'd get from a passive sonar submerged in water. At that point, however, drilling a hole in ice and actually submerging a passive sonar, or even just getting a sub of your own into location, is going to be drastically simpler.

Hence the aquatic ape hypothesis. (I'm going to run away really, really fast now.)

Emphasis/stress on last syllable, actually. I'd transcribe it as Korol'ov. 'R' is thrilled. I think Spanish uses the similar thrilled r's, but I'm not positive. The 'L' is soft (hence apostrophe). It's the same kind of 'L' that you'd usually find before the 'ee' sound in a lot of languages, hence the 'y' showing up in transcriptions and when some people try to pronounce it. But the actual vowel letter on the last syllable is 'ё'. It's pronounced as 'yo' by itself, but following a consonant, the 'y' portion is dropped and it softens the consonant instead. So it's an 'o' sound, despite the common transcription putting in 'e' instead. The later is due to the similarity of the symbol. Indeed, in Russian we'd often skip the dots over 'e'. (The fact that ё is terribly positioned on Russian keyboard layout only made the trend worse in the last decades.) There should not be a 'y' or 'ee' sound anywhere in pronunciation of that name. Depending on dialect, the first two 'o' sounds could be closer to 'a' instead, but that's details. Pronouncing all three syllables with an 'o' sound is certainly correct. Edit: My explanation might be a bit lacking, and the soft 'L' might be hard either way. If you pronounce 'Korolov' with stress on the last syllable, you'll already be closer than most non-Russian speakers.

These are the rows of the rotation matrix used to transform from 2D to 3D. So if you have initial vector v = {x, y, 0}, we can write down the transformed vector in 3D as v' = v R, where R is the rotation matrix and v' is the vector after transformation. We can then alternatively write it out as v' = x X + y Y. Here, X and Y are first two rows of R and exactly what transformX and transformY compute. We don't need transformZ because z = 0 before transformation. Alternatively, you can think of them as directions of the X axis and Y axis of the original, 2D coordinate system, if we apply transformation to them. Since the equation for ellipse I've used has periapsis on positive X axis, transformX can also be viewed as vector in direction of periapsis, and transformY gives a vector orthogonal to it, but also in the orbital plain.

Yes, but you probably don't want to. Since oxygen is 16 times heavier than hydrogen, at the same energy per molecule, you'll have four times less impulse, so a quarter of ISP. However, there are some smaller differences between oxygen and hydrogen, such as thermal conductivity, differences in critical velocity of the flow, and even the ratio between energies of various excited states that will play into it. So I don't expect the difference to be exactly a factor of four, but rather somewhere in that region. That said, it's not going to be much better than a quarter. You really do want the lightest propellant you can get with NTR, and the only gas that's even close to hydrogen's mass is helium, being "only" twice as heavy.

@Syntax Well, it depends on how hard-core you want to get into it. If you really want to understand coordinate transformations, you have to approach it from perspective of Linear Algebra (or Differential Geometry, if you're planning to dive DEEP, but if you stick to Euclidean spaces, that's overkill.) I don't know how good your background is, and how much time you want to spend on it. Ideally, you want to either take a course, or at least read a textbook on Linear Algebra, but that's a serious time investment. As far as directly relevant materials, I did a quick search, and Texas A&M has decent slides up from a course a few years back. The three most relevant chapters, leading up to the actual coordinate transformations, are as follow: http://www.math.tamu.edu/~yvorobet/MATH304-2011C/Lect2-03web.pdf http://www.math.tamu.edu/~yvorobet/MATH304-504/Lect2-06web.pdf http://www.math.tamu.edu/~yvorobet/MATH304-2011C/Lect2-10web.pdf If you can follow these slides from start to end, you basically know as much about coordinate transformations as anyone, (again, so long as we stick to neat, linear transformations, such as rotations in Euclidean space). Naturally, you can dig up slides for earlier lectures to fill in gaps if you need to. The good thing about a course in Linear Algebra is that it requires very little foreknowledge. It's not like being dropped into, say, a Topology or Partial Differential Equations course without pre-reqs. So long as you understand systems of linear equations and matrices, you're basically set to go through it. And while it's not strictly necessary just to get the mechanical skill of doing coordinate transformations, if you want it to MAKE SENSE, this is the best way to get there. For a much simpler overview, you can look at some practical tutorials for video games. And it might be way easier to get a hang of it in 2D, since you can draw neat little pictures for yourself. Again, just following a quick search, this one looks like it covers the basics: https://www.alanzucconi.com/2016/02/10/tranfsormation-matrix/ This sort of thing won't give you the deep insight into why it works, and prepare you for more general cases, but if learning Linear Algebra is beyond your time availability, looking for tutorials like this one might be a good start. @mikegarrison It should be double, but even single precision would be fine, as that's good to one part per million. Big numbers is waaaaay overkill. That said, Math.js is a fine library.

Yeah, there was also a local maximum that I did not expect. Like I mentioned before, max2d is a VERY simple algorithm. So I broke the orbits into more chunks, and now it seems to be good. I've updated the code with the fix to transformX/transformY, made it consider more segments of the orbit to avoid local maximum, and added plotting of the results. The updated code took place of the original further up. One more thing I've changed is that I replaced distance with distance2, which returns square of the distance. Square root is a convex function, there's really no reason to crank it out every step of evaluation just to find the maximum. Square of the distance will always be highest in the same configuration where the distance is highest. So instead, I take the square root at the very end. Oh, and I pre-filled the form with the numbers above. It just made testing so much quicker. Don't know why I didn't do that from the start.

None of them are particularly good, and nearly all of the half-decent ones include deep learning. Rasterized image invariably has quantization noise, which makes it impossible to recover the original strokes even if they are simple splines. Never mind something like a simulated (or real!) brush stroke. The algorithm has to basically make assumptions about what's the "important" information in the image, and what can be sacrificed to produce vectorization. There are DL NNs out there trained specifically to do that, but usually for a very specific category of art styles. If you throw something a bit more free-form at them, results tend to be terrible. Unless the artist produces vectorized art from the get-go, and saves/exports it as such every step along the way, trying to compress the image via vectorization is not a worthwhile thing to even try. Other kinds of compression are worth discussing, @Spaceception. In the modern world, it really comes down to two options. JPEG or PNG. JPEG is lossy - meaning some loss of quality can and likely will happen. It will compress images with a lot of gradients very well, but there will be some loss of quality around sharp edges. There are quality settings that will significantly impact compression and quality. But generally, even at highest settings, compression is pretty good. The visible loss of quality will depend on the type of image. PNG is lossless. It will compress images with a lot of repeating patterns or uniform colors way better than JPEG could, and it is entirely lossless, so the compressed image will look exactly the same as original. PNG comes with compression settings, but they will not make a stellar difference. You should always go with highest setting on these, however, as there is no real downside (for modern machines) either. For traditional art scanned in, it's very hard to say which compression format is going to work out better in terms of size vs quality. But there is no harm in trying both, playing with image size and quality settings, and seeing what you can get out of 5MB worth. Personally, I like IrfanView for image cropping, resizing, and compression. Especially, since it has batch settings letting you process dozens of images in a go. It's free, but it has a touch of a learning curve. If you only have a few images, though, and you're strictly downsizing the image, you can probably get away with MS Paint, though, as people have recommended.

@Syntax Good catch on periapsis. There are several ways that combination of three angles can describe a 3D rotation, and the one I used is not the standard one. So while orbital plane is correct, location of periapsis on it is not. The fix will be updated TransformX and TransformY functions that interpret orbital parameters in the standard way. I'll edit the post with the code with a fix and post any further updates. Edit: Actually... Try changing (w - O) to just (w) in first two lines of both the transformX and transformY functions. That might actually fix the whole thing, but I'm going to have to spend a little bit more time with it to be absolutely sure that's correct. Late edit: Last two days have been trapped at work until late. Tonight's looking much better. Hopefully will get around to all of that.

@Syntax I'm still going to take a closer look at the code, but I just made a quick plot, and it looks believable, at least. Jool position: [-34184.36954230997, 61424.45691029616, -1474.0485511224515] Jool true anomaly: 2.078729696847789 Dres position: [17768.806076568617, -42588.466156726034, -883.9372007234914] Dres true anomaly: 3.537671968402128 Note that true anomaly is angle from periapsis, not from datum. So for Dres, you need to add 90o.