K^2

Free neutrons do decay pretty fast, but you would need them to be ejected at a pretty low energy. At any rate, seems impractical. You would need a huge chunk of nuclear fuel for pretty negligible thrust. Now, if you could work out how to get it to eject neutrons in one direction, you would have an awesome rocket, but I see no way of forcing this.

As usual, main danger is in ionizing radiation. The gamma radiation from Sol is actually pretty low. It's mostly high energy particles. In VA belt specifically, it's going to be charged particles, as these are influenced by Earth's magnetic field, and are much more concentrated in radiation belts. It looks like Alcubierre metric specifically requires negative energy density regardless of speed. So even a sublight Alcubierre will require exotic matter. But way less of it. It's proportional to square of the velocity, so a 0.1c drive would take 10,000 times less negative energy than 10c drive. But that's a specific kind of warp drive. I could not find any confirmation for warp drives in general. There is a strong argument in General Relativity that suggests that any FTL travel requires negative energy density. It's more a conjecture than a proof, but we seem to keep confirming it with special cases, so it's probably true. But can a sublight warp drive operate with positive definite energy densities? There seems to be nothing to contradict such an idea, and yet, I cannot find any literature that would suggest a specific configuration. And yes, it'd be super useful. You still need to have delta-V to make the transfer, but instead of taking half a year to get to Mars, you could get there in hours without wasting any more fuel. Who wouldn't want that? Not to mention traveling further out in the Sol system. It's no interstellar drive, but it'd be a huge help in getting around the star system.

Superinsulators have pretty low critical voltage. Actual capacitance of your "supercapacitor" will not be at all super.

Little advantage of higher order RK here. Should work with 2nd. Have you tried linearizing your diff eq? Ideally you want to see it turn into critically damped harmonic oscillator. But anything close should be stable.

Have not had a chance to take a proper look at it, but from previous experience with aerodynamics sims, my first guess goes along with PackledHostages. Taking into account rotational velocity usually takes care of damping. Just compute relative wind vector for each fin, then use thin air foil theory as approximation. Oscillations building up into tumbling could be due to integration errors. You should use at least 2nd order method for problems approximating harmonic oscillator.

I would strongly urge running it as closed cycle reactor + ETR/Scram, rather than open cycle NERVA style. Any dust passing through NERVA heat exchanger can become secondary source of radiation. Bad mojo. But having electric exchanger eliminates such possibility. Otherwise, only danger is if the thing crashes. Even then, there are reactor designs that would minimize risk of contamination. Bigger question is cost efficiency. Such SSTO would be huge, but have small payload. Fuel costs might be low, but operational and maintenance costs will probably be way higher than conventional rocket.

Do Rutherford scattering in the case where alpha particle is stationary, and it is hit with gold foil traveling at near c with M >> m. You will find that there are just two possible outcomes. Alpha either passes straight through, or is sent directly backwards. All other outcomes, where alpha is scattered to the side, are forbidden by conservation laws. Id est, no other scattering conserves both momentum and energy. Relativity. Now, for a subluminal warp, we might be interested in what happens in the frame where bubble is stationary. But for superluminal warp, it is not even a proper question. And in either case, for the chosen frame, 1+1 assumption is valid.

Which is fine. But it is a boring problem otherwise. Good exercise, I suppose, but nothing conceptually difficult about it. If you are having problem maintaining attitude, consider writing a plugin. That is a proper engineering solution.

I *think* I can verify local optimum. That is not the same thing. There could still be better solutions. But arkie's solution simply assumes the strategy to be a correct one.

You don't show that the strategy is optimal. You need to show that thrust vector must cancel gravity + centrifugal. That's the hard part, since it's calculus of variation.

I might be too used to this from particle physics, so I'm not clear why this is troubling you. Longitudinal momentum is always far more important than transverse. We have non-relativistic particles encountering a hyper-relativistic object. Significance of longitudinal momentum in chosen frame is inflated. Significance of transverse component becomes minuscule. Even when both particles are relativistic, transverse component doesn't play as major of a role. Warp drive encountering space dust is effectively a 1D + time problem. Sure, I would also like to see corrections from a proper 3+1 treatment, but they aren't going to invalidate these results. Merely refine them. Oddly enough, no. I've seen a paper that does all of the necessary calculations, then says, "Well, from these, it's clear what the outside world will look like from the bridge of the ship," and just leaves it there. One of these days, if I get some free time, I might dig up that paper and write a visualization sim. Qualitatively, what you'll see is the sort of distortion that makes things to the side of the ship appear to be somewhat lagging behind. If you go FTL, things behind you are going to start disappearing from view, but you'll still appear to have a 360° view, so things that are behind and a bit to the side will appear to be directly behind. In addition, things in front of you will be getting severely blue-shifted. Dim brown dwarves will shine like small suns. And vice versa. Things behind you will be getting very red shifted, to the point where things appearing directly behind you fade out completely. But it's one thing to picture all of this, and another to see. And it shouldn't be all that difficult to simulate. Just a bit time consuming.

Warp ship is moving at, above, or near the speed of light in that analysis. Deviations from symmetry plane are negligible. You might hit a stray oh-my-god particle that's going to come at an odd angle, but almost everything you will encounter during the voyage can be analyzed in T-X plane.

He means putting sat into GEO from GTO.

There shouldn't be. At least, not enough for sustained reaction. But if heat causes the ox to powder, and blowback pushes some of that back, who knows? The more realistic scenario is pressure simply causing the valve failure on the tank, turning it into a missile. Either way, likely or not, I would not want to take chances with this. If you can burry your fuel tank during tests, it's probably a good idea.

I'm sorry, but did you just compare building a bunch of coal-burning boilers with the problem of mining, refining, and using uranium or another nuclear fuel safely? Germany basically had to weld some tanks and buy some coal. That's the extent of this particular infrastructure change. Don't get me wrong, its still massive on scale alone, but converting the other way, from coal to nuclear, is a whole another problem. There's a reason why steam power is early 19th century tech, and nuclear power is second half of the 20th. Return from oil field is within months. Not decades. Completely different time scale. I'm not saying it's not economical. It's just that if you can have your profits later this year, or later this decade, most people go for former.

There are two cases with simple analytical solutions. No gravity, or strictly along gravity. The general case for 2D motion with gravity is extremely complicated. There are analytical treatments, but you can never get a fully analytical general solution. If you understand PDEs, I can walk you through the key steps of derriving 2D motion. Otherwise, I'm afraid the only useful formulae I can give you are these for simple special cases. No gravity: v(t) = v0 / (1 + k v0 t). v(0) = v0. Gravity, object is falling down: v(t) = - vt tanh(g t / vt). v(0) = 0. vt = sqrt(g/k) is terminal velocity. tanh is hyperbolic tangent function. You can find it on most calculators, or just use Google Caclulator. Gravity, object is launched upwards: v(t) = v[sib]t tan(g t / vt - a). You need to solve for a, such that v(0) = v0. This solution works right up until body reaches the apex. Then you need to switch to the above solution for falling back down.

Just another reminder that it will explode. Ideally, you'll eventually figure out how to stop it from happening, and you might even get lucky on the first run, but your assumptions going in should be that it will explode. Make sure your casings aren't metal and in general, try to minimize use of metal/ceramic parts. Replace with plastics wherever possible. I really hope you don't have to worry about blowback with this one, but just in case, Make sure your propane tank is in no danger of injuring anyone if it also blows up. Preferably, dig a hole in the ground for it. You'll need a remote way to close the valve. Then make sure that anyone in the viscinity has good cover an no line of sight. If you need to see what's happening, your best bet is probably a cheap web cam and a laptop. Goggles, gloves, clothing that covers all of you (no synthetics), and something to put out fires. At very least, a wet towel.

You are double counting. The whole point here is to capture excess of CO2.

Yeah. Dedicated biofuel farming is stupid, since we are throwing more fuel into harvest than you'd get out of biofuel from the same land. But if we start utilizing biproducts of farming we already do as biofuel, we can significantly cut amount of fuels we put into farming. And that's a significant chunk of our CO2 emissions, at least in the States. (Note that even if we don't turn cellulose into biofuel, it still contributes to CO2 footprint as it decomposes.)

Ah, yes. The 3 radii is only true for Schwarzschild black hole. A Kerr hole would have a different value. I can believe a 2.5.

We think, Casimir Effect produces the right conditions. It's not negative energy on the absolute scale, but that's sort of irrelevant. It's negative with respect to zero-point, which is the same thing for GR. What we don't know is how to make a lot of it, without putting in enough matter into the same place to completely offset it.

Germany is an edge case. Most pollution is produced by China and US. EU follows with notable gap. Politics is a huge factor, but even with the right policy, we cannot switch everyone over in just a few years. Sounds about right. Now consider that life time of a panel is about 20 years. So that is 3 years before it pays for itself. And this figure is for optimal illumination, which is rarely the case. In a cloudy region and with no sun tracking, you easily roll over a decade. Look, if it was easy, it would have been done already. We are on the right path with solar. But we need an intermediate solution as well.

Too close is actually 3 Schwarzschild radii, which is well above event horizon. For a supermassive black hole, like A*, you can see entire stars moving along strange trajectories, impossible near any other type of a body. Again, gravity is not linear. Kepler Laws break down completely near a black hole.

Gravity of a black hole is not the same. It is the same out where you would be able to orbit before, but not closer to the center. It is fundamentally different, because gravity is not linear. For example, there are no stable orbits close to the black hole. Even well above the event horizon.

Long term, sure. But short term? We don't have operational mines in the state they need to be to produce required quantities of nuclear fuels. No, in the eighties, and even well into the 90's, solar panels flat out took more power to make than they could produce in their life time. Solar panels of 90s were effectively means of exporting pollution to China. Solar panels with net positive output are a very new thing. And yes, it still takes several years for them to produce power that went into manufacturing. Run the numbers yourself if you'd like. In some parts of Europe it can take up to a decade. It's better in sunnier parts of the world, but it's still years. Non-photovoltaic power plants are more efficient, but they are not practical for replacing all, or even majority of our coal plants. They take up a huge amount of land, and they cause environmental problems of their own. Fact that solar farms literally fry birds in flight is just part of the problem. They also work like a giant parking lot, absorbing more heat than whatever environment they replaced, resulting in updrafts. You put enough of these in one area, and you have yourself a whole new means of weather change. The great thing about photovoltaics is that they can replace artificial surfaces we are already using. Roof tops primarily, but even roads in principle. Covering US roads/highways in photovoltaics would produce several times more energy than US is currently using. I'm pretty sure it'd be true of the world in general, but I have not seen the numbers. But even that we don't have infrastructure for. Regardless of what you will want to replace coal burning plants with, it will take decades. Even with technology already being in place and even when it makes financial sense to do so.