K^2

And it's on the money. 4He->5He requires a fast neutron capture, something around 10MeV. That's almost 15% of the speed of light for a neutron. On the plus side, there doesn't seem to be much of a barrier, so if you managed to prevent 5He from decaying in a fraction of a zeptosecond, you could probably use it as an extremely high storage battery.

Backwards is only iffy from perspective of practicality. In terms of what it means to paradoxes, it's pretty straight forward. General relativity is nice and self-consistent if we allow exotic matter. With exotic matter we can most certainly allow for time travel. (Though, I do recall some solutions without it, I still need to look it up.) In either case, if GR allows for time travel into the past, even if it cannot be practically achieved whether it is due to very high energy requirements, unavailability of exotic matter, or any other hick-up, the very fact that GR allows for it in principle must mean that any theory that works with GR must allow for paradox resolution. And in fact, within the framework of quantum field theory in curved space-time, where you can have closed time-loops, any and all time traveling paradoxes are resolved. The simplest explanations are from Many Worlds Interpretation, but it works in any interpretation you like. There is one big exception, which is paradoxes which involve construction of the time machine. And unfortunately, these require space-time curvature itself to be a function of quantum fields, and that, in turn, requires quantum gravity to describe properly. So that part is iffy. But since the time machine can be constructed entirely outside of realms of quantum gravity, at least in theory, quantum gravity itself must allow for self-consistent time travel. And therefore, it must look after paradoxes involving time machine in some fashion. I suspect that the results will be identical as the quantum field theory resolution, but that's already speculative. The short version is that we already know enough to say that any self-consistent theory must look after time travel, even if time travel is not actually possible in practical terms.

That is a pretty gross lack of understanding of physics. Inertia doesn't resist motion; only changes in motion. And the only acceleration that should result in is centripetal. There is absolutely nothing to effect change in angular velocity.

I suggest you look up what Cold Fusion actually means. I have no idea where you are getting that reduction of entropy deal from, but it's completely wrong.

Somebody needs to look into this. If there are three, and they are at 90° angles to each other, I'd get really suspicious.

There's nothing wrong with calling it delta-L. It's clear enough in context. And yes, so long as the net change in angular momentum is zero, the reaction wheels can account for any difference during the maneuver as many times as necessary. In that sense, sure, you have an "unlimited" resource compared to what you'd be doing with RCS thrusters. I understand what you mean now. But calling it unlimited delta-L is a bit confusing, as the net delta-L is zero. Still, if you need limited amount of maneuvering, the clearly finite resource of RCS thrusters might still end up adding less weight to your craft than the reaction wheels.

We do have net gain cold fusion. It's called muon catalyzed fusion. The only trouble is that there is no good way to produce muons with sufficient efficiency. It's still nothing we can practically use, but the lesson here is that there are definitely things that can be done to reduce the barrier. We have not explored all options yet. I still wouldn't expect cold fusion any time soon, but I wouldn't completely bury the idea either.

Delta-L means change in angular momentum. And it's not by any measure unlimited.

Yeah, I got the actual refraction in visible band backwards. Sorry about that. It does reverse further into IR, though for reasons I've specified. Looks like there is another absorption band in UV, however, which is what throws things off.This is pretty typical. Astrophysics isn't my field. But basically, if you have stray neutrons flying about, you'll have plenty of captures resulting in beta decays. So I would imagine any sufficiently energetic event to produce neutrino bursts. I just have no idea where the boundary of "sufficiently energetic" lie.

Neutrinos definitely don't travel faster than light. We have experimental confirmation of that. Unfortunately, we don't have any experiment that definitely shows that they are slower. If we did, it would prove without any doubt that neutrinos are massive. We do not have such proof, but there is plethora of indirect evidence suggesting that they are not entirely massless. And that would, indeed, require them to move slightly slower. As for why they arrive sooner, I always thought that was pretty clear. The spike in fusion certainly starts in the core of the star. Neutrinos escape the core without any hindrance, but all other radiation is re-absorbed into the star. Energy takes quite a while to propagate outwards, even as it builds up to the supernova scale. By the time the outer shells can be blown off by the supernova explosion, fusion has been going on for quite a while at an extreme rate producing the neutrinos that can be detected. Isn't it nice that we have means of detecting something like that a bit in advance, though? Not that a day buys you a lot of time to prepare for something like this if it happens in your immediate neighborhood. You got that backwards. In water and glass, red light travels slower. That's why it refracts more at the interface. But this has to do with both materials absorbing in IR. The closer you are to absorption, the slower the waves propagate. So this is far from general rule. There are materials and ranges where shorter wavelengths propagate slower. As for gamma radiation, nothing really absorbs it all that much, so the speed of propagation in medium is going to be very close to speed of light. If there was anything that could slow it down significantly, we'd have gamma ray optics and gamma ray lasers by now.

No. Light at any frequency propagates at exactly the same speed. The speed of light. In fact, any massless wave will propagate at that speed.

You can re-orient yourself with gyroscopes, yes. But you can't correct for gaining net angular momentum, and there are any number of sources for that. Undocking, collisions (planned, or otherwise), atmospheric effects, solar effects, ablation of material on the ship, any leaks... You can't just assume that you aren't going to pick up any considerable angular momentum during the mission.

Not only does it have to deal with time dilation due to satellite's velocity, but also gravitational time dilation due to Earth's gravity. If you ever need to convince someone that General Relativity works, GPS is the most evident proof. By the way, because here on Earth we experience only the gravitational time dilation, there exists an orbit on which time flows at the same rate as it does on the surface.

You are technically half a time step off with drag in Verlet, but in practice, it's not a big deal unless you have huge swings in velocity. And no, I'm not on Github. I don't usually go for genetic algorithms. It just somehow feels right for this one.

So instead of time stamps, satellite broadcasts some predetermined f(t)? Does the later have an easy-to-compute inverse, then? I would imagine that this is only an advantage when the clean signal can be interpreted without having to wait for multiple time stamps. Otherwise, error-correction encoding would make more sense. Or am I misunderstanding that completely?

Ha, ha. Yeah, I know the feeling. Well, I've been wanting to try something along the lines of a genetic algorithm and see if I can "evolve" a near-optimal solution. The "genome" would consist of adjustments to attitude and throttle position. It should work, but time... As for the RK method, you shouldn't need to go for RK4. Just do a Velocity Verlet. It's equivalent to a mid-point RK2, much easier to implement, and should be sufficiently precise for the given problem.

I tried to get a numerical solution with gravity turn. I wasn't able to find anything resembling an optimum. If you have good ideas on that, I'd be interested.

Technically, yes. I was a bit lazy about doing this strictly analytically, and I'm not sure how hard it'd be to actually do. If you take h to infinity, even thought time required for ascent is finite, fuel requirement diverges because acceleration goes to infinity as h does. So you probably need to set up cutoff height, optimize for v0, and only then take the limit. Alternatively, one can be satisfied with the fact that numerically v0 = vt works. That's the attitude I chose. Call me lazy if you must.

Actually, you could measure tidal forces to figure out quite a few things about your orbit assuming you know the relevant parameters for the planet you are orbiting. But yes, you can't just measure gravity directly, and that means much, much finer measurements to get any useful data.

I'm not too familiar with how things are done these days, but I know that on early flights, all of the computations for orbit transfers were done on the ground. The flight control would have tracking data, they'd use it to figure out the orbit the ship is in, find the necessary burn times and orientations and send these to the pilot. So if you want to think of it in KSP terms, the flight control center would have equivalent of the map view in KSP and would be able to set up transfer nodes. The pilot would receive instructions equivalent to what the little blue marker on the nav ball tells you. That is, set heading for whatever it needs to be, wait for specific time, then burn for that many seconds. So in that respect, KSP is pretty similar to what actually happens, except the player has access to both sides of the mission planning and execution.

They be heavy. So it's all about which one's going to require less additional mass on board. Bringing more RCS monoprop or installing huge gyro wheels. For a Lunar lander, gyros would make zero sense. For the CM such a thing would probably be more viable, but CM didn't need that many precise orientation changes, so RCS was probably still an easier option. And as somebody already mentioned, reaction wheels (or CMGs) aren't a replacement for RCS. It's not like KSP where reaction wheels can absorb any quantity of angular momentum. They can store some, but it's limited. One way or another, you have to have RCS thrusters on board. But on longer missions or for better precision, CMGs might reduce the amount of RCS monoprop you need significantly enough to be of use. For scientific equipment there are additional considerations, of course.

Oh. Uniform? No arms or anything? Then it's uniform in time, as well, and that makes it a 2D problem. That's totally solvable. Still a hell of a mess, of course, since velocity field will depend on metric and vice versa, and that means the equations will have to be solved very precisely. But since the grid is only 2D, there are no hardware limitations. Just complexity of the code. This would be a lot of fun to implement. I can already see how it can be spread over a computing cluster nicely. If you seriously want to try it and don't mind taking the brunt of the analytic work, I can work out all the numerics. There's probably a paper in it if nobody has done this with high enough fidelity before.

Is this even doable numerically? There are no obvious symmetries to exploit, so this would be a full 4D sim. And I don't know if there might be a better way to do this, but the only thing that comes to mind is lattice, and 4D lattice computations are tricky. Even in QFT a considerable amount of trickery goes into it, and that stuff's all 100% linear.

That will either not work at all or be too much of a pain. Has to do with the fact that each spaceship consists of many many meshes each one with its own transform matrices. 3D Ripper won't know which models go together, so it won't be able to rip it all into a single 3D file. You might be able to rip individual components and put them together by hand, but I suspect there is an easier way to get the models from a Unity game.

When you say "Newtonian," do you mean pure Newtonian, or something along the lines of linearized gravity? Because I can entirely believe gravitomagnetic effects to be quite significant on the scale of galaxies. But if they are actually saying that the problem is highly non-linear, that would be rather unexpected. I really would like to see some computations supporting that.