K^2

You can't have the He*-He molecules. Like I've mentioned before, any covalent bond with He* state is going to destroy the state. Instead, what you'll have is a bunch of He* atoms that are slightly larger than Lithium and about as reactive, and a bunch of He atoms that don't want to react with anything. And the only way to get a stable solid out of it is to use the VdW forces between them to make an FCC lattice. Pretty much the same as you'd get from a normal rocket of similar thrust. The only added danger is that it will be a strong UV source, so looking at a launch directly, without protective goggles, might be harmful to your eyes. Critical distance on that will depend on the rocket.

And it'd stay there because?

That's something I've never even thought about, but yeah, Earth and Moon actually have sufficient separation and brightness to appear as two distinct objects even to a naked eye as viewed from Mars. Can you imagine what sort of stories and legends this would have sparked in primitive star-gazing cultures? Two "stars" that move through the skies, but always stay very close together.

Many Worlds relies on superposition principle, making it impossible to travel between worlds. To put it simply, from perspective of any world, all physics is equivalent to that one and only one world existing. Of course, if the underlying field theory isn't actually linear, and superposition is just an approximation, things could be different, but then, strictly speaking Many Worlds doesn't hold either. We'd need a different many-histories theory to explain all of it. As for allowing for travel, you'd effectively be back to dealing with geometry of space-time, so you might as well cut out the middle man and talk about warp drives and wormholes to begin with.

1) We do know how much energy a red giant burns. Or any other star we can observe. 2) Doesn't matter how much energy you put into it. To travel at light speed, you need an infinite amount.

No, the energy of the rocket does increase at a faster rate than chemical energy is depleted. The energy required to give a rocket a certain delta-V increases as velocity does. But chemical energy released from expended fuel is exactly the same. Furthermore, the reason why it works this way has been addressed in this thread several times. It's worth reading the whole thing before adding in another reply, especially, an incorrect one.

It's possible, of course, but it's not what we live in.

No, it's not. Our space is inherently 3+1. Or 1+3. So there are either 3 dimensions and 1 time, or 3 times and 1 spacial. That you can pick either way you like. But there are 3 of one and 1 of the other. This has to do with fundamental structure of our space. It's something we're stuck with, because that's how time and space actually work. Which you need to understand before making stuff up.

The parachutes have to be symmetric, as pointed out. There are several things going on. Air spills over. There is a vortex state running around the edge. And finally, the whole thing can have a lift component. All of these are going to play a role. And that last one is probably the only way for parachutes to end up as far separated as they are in the picture. But that does require initial separation, which is most likely provided by the vortex state.

Or I can take a bunch of 2D objects and stack them together. So 3rd dimension is also time. This isn't what defines time. Time is defined by signature of the metric. We happen to live in a 3+1 space, which gives us 3 spacial dimensions and one time dimension. And exact direction of time is not specified. That's frame dependent. But any way you look at it, it's 3+1. But you can have spaces with other signatures. AdS formalism is defined on a constant "radius" shell in 4+2 space. That's four spacial dimensions and two times. (Restricted problem is then equivalent to a curved 4+1 space.) So again, I ask you to actually read a bit on how dimensions work and what makes time - time, before you start making stuff up and especially telling people who know much better than you that they are wrong.

No. Nope. Better comparison would probably be Lithium, but still, no way. Look, the only way this He* atom is possible is because you have one electron removed from its ground state and placed into excited state that it can't easily drop down from. This is no longer the case in a metallic state. A valence electron in a metal does not belong to an atom. It belongs to the lattice. It no longer counts for the orbital shell. It is one of the electrons that fills the conduction band instead. And there, you also have energy levels. And you also have two electrons per energy level. And with all electrons having the same spin, every other level ends up vacant. So now imagine all the electrons in the lattice, half as many lower energy level to drop down to, and all the possible interactions. Not only is this going to take way more energy than just exciting all of the He atoms, but it's something that's going to collapse instantly. Whatever else may be going on, He* metal is not an option. That, I'm not as certain about. Could be. But in either case, it's much easier to maintain the He* at lower temperatures, so even if it has a high melting point, we should be considering cryo options only. Hard UV to soft X-Ray is absorbed by air extremely well. And at that energy, you can start looking at light as particles. So you are looking at mean free path as the typical absorption scale. And the effect will be ionization, which will result in Ozone production. Does that answer it?

Could we, please, start looking at the big picture? This mission isn't designed to land or enter orbit, so we must disregard challenges and benefits of landing there? Then why the hell are we even sending anything there in the first place? The only reason for such a mission is to study the moon so that we know if we should send a landers and/or orbiters there, and if so, how we should go about it. That's the whole frigin' point. Because, why else? Because we think it will make for some awesome desktop wallpapers? We have a number of potential targets for unmanned exploration in this Solar system. Titan and Europa are definitely high on priority. If we are deciding which one we are sending a probe to, we should be thinking about what it means in terms of future exploration. Whichever one we chose, it will make preparations for any subsequent missions that much easier, besides all the information we get from this mission directly. And there is no doubt that we can get more information from Titan than Europa when we do start sending orbiters and landers. Not only that, but even a single fly-by mission, without any follow up, would be more valuable with Titan as the target. We might be able to learn something about Europa's oceans, if they do in fact exist, with an orbital probe. A fly-by is going to give us very little info on that. A fly-by mission of Titan can give us additional info on its weather, geological processes, and atmospheric composition. Each of these, by itself, is way more valuable than what we can get from Europa. Finally, say we really do forget about everything else, like you suggest, and just focus on the easiest target for a fly-by mission. It's still Titan. Europa is much lower in gravitational well, meaning that any probe you launch will be passing by at higher velocities, requiring higher precision, and giving much less time to do any data gathering. Or getting these awesome desktop wallpaper shots. Because if you aren't planning to land there any time soon, that's all its going to be good for anyways. As for getting to Saturn or Jupiter from Earth, it's pretty much the same thing. Which means Titan is easier to get to, any data we get from it is more valuable, it will be easier to organize consequent landing/orbiter missions to, and the data we get from these will also be more valuable. There is not a single sound scientific reason to go to Europa before going to Titan. None. It's all politics and spin, as usual.

That's precisely why mission to Titan would be infinitely more valuable. Europa can only support Earth-like life. Which means we can't exclude possibility of common origin of life on Europa and Earth even if we find it. Titan, in contrast, shows strong evidence of processes consistent with metabolism on global scale. Now, it can easily be a natural geological process, but even if so, it's a process that can be used by a life form in an environment completely different from Terrestrial. Either way, we learn way more about possible life in other star systems from Titan than we can learn from anything we find on Europa. (And we are very likely to find squat there.) Titan is dramatically easier to land on than Europa. Not only does it have lower orbital speed, making it much easier to get to, but it has an atmosphere allowing no-power landing. Europa has virtually no atmosphere, meaning you'll have to do a powered landing. Titan allows you to deploy rovers, aqueous probes, and balloons, and you can do all 3 with the rocket you'd need to put just a lander on Europa. There is just no comparison. As for the decadal survey, I can only conclude that it's influenced by politics more then science. Because claiming that we can learn more from dropping something on the surface on Europa than Titan is absurd. Perhaps, with the right equipment, we can find something worthwhile on Europa. That would require remote drilling equipment, all sorts of surveying equipment, a constellation of communication and survey satellites, and so on. In other words, we need to put more stuff on Europa than we've put on Mars and Moon combined in order for it to be worth the effort. On titan, one probe with the right equipment dropped in the right place can be enough, because everything of interest there is going to be right on the surface. So again, no objective scientific survey would ever conclude that Europa is a higher priority than Titan.

Seriously, why Europa? Titan is a much more interesting target.

Again, not how it works. Please, learn a little bit about models we already have in place before making stuff up.

Right. If you are seriously considering ice-mining, you have to be looking at objects beyond the Sol's frost line, which is located about 2.7AU. That excludes moons of Mars, but does include a large portion of the Asteroid Belt. There are plenty of objects there, including some rather large ones, that are bigger than Phobos, at least as easy to get to, and are likely to contain large quantities of water ice. (e.g. 65 Cybele)

No. Not at all.

Ascent and descent aren't quite time-reversals due to mass of the ship changing the wrong way. Since thrust is constant, you can actually end up with different optimal profiles for airless landing and ascent. Edit: I've been able to do a bit more with analytical side of things. First, for vertical ascent, given variations in gravity and drag coefficient with altitude g(y) and k(y) respectively, yielding thrust T[y,t] = g(y(t)) + k(y(t)) y'(t)² + y''(t) The solution y'(t) = Sqrt(c(y(t))/k(y(t))) is locally optimal whenever c'(y) = g'(y). In other words, vertical ascent is optimal at terminal velocity even with arbitrary variation in gravity and air density with altitude. I know everyone suspected as much, but it's nice to have a rigorous proof of it. The other thing is that in constant density and gravity ascent, if you have to apply some horizontal thrust to maintain course, say Tx, the optimal ascent velocity goes from Sqrt(g/k) to Sqrt(Sqrt(g²+Tx²)/k). In other words, it behaves as if instead of gravity g, the craft experiences gravity Sqrt(g² + Tx²), which does make a lot of sense. Unfortunately, I have not been able to prove this for general g(y) and k(y), because algebra is a total mess, but it should at very least be close for small g'(y) and k'(y). Finally, if we now take 2D motion, and consider drag along y, we have k vy Sqrt(vx² + vy²). This can be expanded nicely under two possible conditions. Whenever vy > vx, this becomes k vy² + k vx²/2. While expansion for vy < vx yields, k vx vy + k vy³/(2 vx). What this lets me do is split the horizontal and vertical motion and then use some iterative methods to find mutually-optimal vx and vy throughout the ascent. There is still a whole list of nuances with that, but it should at least put me on the right track.

You are just telling me why a naked singularity couldn't exist naturally, anyways. That's absolutely irrelevant. Could you make a black hole with enough angular momentum? Easily. Electron's L/m is already over this limit. Just feed it a polarized stream of electrons, and you'll have a black hole with too much angular momentum. And this was just a demonstration of why there are obvious problems. If we assume Kerr metric to continue into interior of the black hole, there are way more problems with that. There are CTCs in the interior regions even without naked singularity. So if you've fallen into a sufficiently large rotating black hole to not be shredded by the tidal forces, there is a trajectory you can fly to go back and meet yourself from before you flew that trajectory. Then fly it again, and meet the two of previous you. And then keep doing this so that you can throw a big party for yourselves. And then, maybe you can find the you from the other universe, because interior of the Kerr metric has two exteriors, only one of which is our space. It's crazy stuff. But like I said, the most important fact is that Kerr metric in the interior is known not to be stable. It's not the interior solution for the rotating black hole. So what's a Kerr black hole above the horizon, is not a Kerr black hole bellow the horizon. Which puts the whole question of a ring singularity rather up in the air. What is a point object if not a purely mathematical concept? And if that is what elementary particles are, how can purely mathematical concept exist in reality?

For some reason, I thought it only applies to the spectrum. Making digitized spectrum indistinguishable. But if this is the actual definition, then yeah, jagged lines definitely qualify. Thank you for correction.

In terms of safety, yeah, I think I'd go with liquid-core NTR as well. But assuming we can make both, NTR is an absolute disaster if it explodes, while He-A is just an ordinary chemical explosion. So I doubt liquid-core NTR would ever be approved unless we can make it way, way safer. He-A could still be useful for cargo even if it's high risk. At that ISP, it only needs to be better than a coin flip to be competitive. By the way, fact that this has to be kept at just a few K, rather than LN2 temperatures as I was thinking initially, means that we can probably drop the stabilizing mag-field to just a couple of Tesla. Now that you can do with permanent magnets. They'd still be pretty heavy, but you can get a large enough bore to offset this with extra thrust. I still can't see it being practical, seeing how expensive He has become, and how much extra expense all of this is going to be, but it might just be plausible.

You are confusing things. Uncertainty in position and finite size are two different things. Elementary particles, such as electrons, for example, are point particles, but they are delocalized. What this means is that you can take two non-overlapping regions of space, and ask what are the odds that each region contains at least a portion of the particle in question. Delocalization says that we might find this probability to be non-zero for both regions. But if we ask what are the odds that we found particle in both of these regions, this comes out to be precisely zero. Black hole's singularity can be delocalized and still be a true singularity. There is no contradiction there. It still leads to all sorts of interesting features. But whether or not it is so, we do not know. We do not have a field theory that works on such short scales. That isn't quite so simple, either. There are some problems with Kerr solution in the interior regions*. I'm not an expert on this, so what I know could be outdated, but as far as I know, we still don't know the exact ground state solution for the Kerr singularity. Ring is a solution, but not necessarily the only solution, and not necessarily what a rotating black hole collapses to. It might even be the case that there is a critical amount of angular momentum that a black hole must have in order for ring singularity to exist. * A good example of problem with Kerr metric is that if we take a black hole with enough angular momentum, a naked singularity emerges. In simple terms, a Kerr black hole with enough angular momentum does not have an event horizon, and if such a thing existed, it would allow for time travel. Of course, that by itself isn't a deal-breaker, but it is a major warning sign. And indeed, such a solution is known to be unstable.

Like I said, that's not necessarily bad. You can turn a detonation wave into a rocket. You just have to have a matrix that brings down the heat transfer and detonation wave speed. In principle, a det wave is a perfect way to accelerate yourself. The problem is that a conventional detonation wave reaches you with all of the momentum at once, which your structure usually can't take. If you find a way to mitigate that, then detonation gets rid of a ton of problems with conventional SRB. You don't need a nozzle or a bell. You aren't risking detonation due to a crack or other problem because, well, it's already detonating, and the shell doesn't have to hold the pressure, so it can be way lighter. Of course, all of this in early experimental phase. But mostly, because the losses you get from the matrix often make it easier to just have a conventional SRB. Here, you have lots of excess energy, so you keep ISP high, and it'd be entirely worth the research effort to bring it all up to operational quality.

Not necessarily. As it consumes stuff, a lot of energy is radiated, which also carries away considerable amount of momentum. In case of accretion disk, the radiation is more or less symmetric. But when it swallows a single large object, radiation can be asymmetric, resulting in net momentum change. I don't know how significant this is, but I would discount it without some study.

No, not possible. If you say that an object has event horizon (point from which light cannot escape) then everything bellow horizon can only be in one of two states. It's either falling directly inward, or it's already at the center. No amount of pressure can result in an object of finite size sitting bellow event horizon.