K^2

That's not quite correct either. The difference is in momentum. Momentum of a ship under warp drive does not change. Yes, it's moving, but there is no way to "extract" that motion. You can't, for example, have a warp ship physically push against another object, because there is a warp bubble around the ship. If EmDrive was to work, it would be capable of changing net momentum of the ship. Even if we were to assume that something weird going on with relationship between velocity and momentum, as is the case with a warp ship, the EmDrive ship can physically push a brick, increasing its momentum, withiout having anything to take up recoil. And that's a violation of a conservation law. In your jumping off a building example, momentum of the person jumping off changes, but total momentum is conserved. That's equivalent to a normal reaction engine. In fact, Earth acts as a reaction mass.

In relativistic scenarios, conservation of momentum is a consequence of Hamiltonian's invariance under translation, which is one of the assumptions of relativity. In other words, once you said "relativistic scenarios" the conservation of momentum comes as part of the package. People who invented EmDrive either don't understand anything about relativity, or simply banking on investors who don't. Either way, it's nonsense. That still produces a light-like "exhaust". (EM radiation, gravity waves, or the like.) Conservation of momentum is just as much part of the Quantum Field Theory as it is of Relativity.

Not even straight up equatorial. It's all going to depend on the launch window and where the thing is heading. Choosing inclination of the fly-by trajectory is going to be a big part of the optimization routine.

Fixing fly-by to be polar would result in inclination and final heliocentric velocities being related. That can make something like an Earth fly-by a far more delicate maneuver, further reducing your options. I'm not sure how much it would impact an L1/L2 mission. I feel like this should be one of these "one or the other" situations. If we don't think we can hit a target in heliocentric, then polar fly-by would at least mean it's not a wasted effort. But if we want to try and pull Earth fly-by, for example, then it's best not to restrict Lunar fly-by, and look for the optimal solution there.

Orbits around Phobos are going to be very tricky. It's far enough from spherical body to require constant corrections. It'd be possible to make a few turns, using propulsion to adjust trajectory, but for anything interesting, you need to land. Fortunately, gravity is low enough that you can land on an electrostat, requiring minimal lithobraking if any.

I didn't realize ATV program was being terminated. How come? Just politics, or are there any tech/cost problems and/or replacement on the way?

There isn't really a single answer, because it all depends on mission complexity, relative positions of relevant bodies, and on whether you want to enter Mars' orbit, or just do a fly-by. The least expensive Mars fly-by mission with free return to Earth, via Lunar and Earth fly-by can be done with less delta-V than it takes to enter Geosynchronous orbit. (A touch over 3km/s from LEO.) It is, however, an incredibly complex mission that would take years. Basic Hohmann transfer is very simple, but requires you to burn to Earth escape, and then to establish transfer. Map from Redjoker's link gives an outline, but it has a completely wrong number for Earth-Mars transfer. Realistic number there is about 3km/s, depending on position of Mars at intercept. At any rate, that gives you a total of about 6.2km/s for a free-return. So for a fly-by, you'll want anywhere between 3km/s and 6.2km/s depending on mission complexity. If you plan to enter Mars' orbit, you'll first need to match speeds with the Red planet, which will cost you about 2.6km/s and then break for about 30% of escape velocity to actually make orbit. So that's another 1.5km/s. A lot of this can be saved via aero-braking, but you will have to burn it again to make return. The absolute minimum, therefore, is 3.1km/s, with 5.7km/s being more realistic, meaning a capture burn with aerobraking to circularize orbit. So if you are planning a safe, reliable mission to Mars orbit with a return to Earth, you are looking at about 12km/s. With high risk and long duration, you can bring it down to 4.5km/s using multiple fly-bys and aerocaptures.

No, but when you keep insisting that one is wrong without being able to do even the basic computations on the problem, you're doing it wrong. Same as that of any other single electron. Or any other elementary particle. States are defined by transitions, not in absolute. Since there are no transitions to/from one-particle state, there isn't usually anything to talk about. There is, most certainly, a transition to the black hole state. Which is accompanied with a jump discontinuity in the entropy, characteristic of first-order phase transition. Similarly, black hole evaporation has characteristics of phase transition. More importantly, you didn't just insist that black holes don't have a state. You insisted that they are "nothing". Not matter at all. Which is specifically when I brought up elementary particles. Care to try and address that? Or do you just want to continue being obtuse and hostile when someone who spent time studying the subject is simply telling you that you are wrong, and giving you plenty of examples why. And no, I'm not going to try and explain it to you. I do not have time to read a course on black hole collapse to someone who isn't familiar with basic statistical mechanics. I can point you to some textbooks if you want to learn, but expecting me to actually explain it to you is neither reasonable nor appropriate. Typically, that statement is made once you've established some authority on the subject. As it is, I don't really understand the point you're trying to make with it.

That's absolutely wrong. A stelar black hole will tear you to shreads. But hey, why don't you do the math, eh? Since, apparently, you know more about black holes and phase transition than a theoretical physicist. Don't forget that you can't be using Newtonian gravity for it. I'll let you get away with assuming Schwarzschild metric to start from. Have fun.

So is an electron. So are quarks. I guess, they are nothing as well. In fact, black hole singularities don't have to be points. There can be ring singularities, for example. While elementary particles are always just points. Singularity in the black hole has energy, momentum, mass, angular momentum, and an electrical charge. Just among the significant qualities of matter. Furthermore, there is a definite phase transition when neutron star collapses into a black hole. So singularity is certainly matter, black hole is certainly a state of matter, and just because something disagrees with how it should be, doesn't make it "nothing". So please, stop claiming that modern science is on your side on this issue.

No. There is no theoretical or experimental knowledge to suggest that black hole is "made out of nothing". Black hole is a state of matter. Collapsing stellar core undergoes several phase transitions, transition to black hole being one of the final possibilities.

Solid, liquid, gas, et cetera are states of matter. Black hole is another state of matter distinct from all of the above. So technically, the type of matter of which black hole consists is black hole.

I agree. The only question is, if you are going to build a giant centrifuge for gravity, why build on a planet/moon at all? Just build it in orbit, and mag-rail processed materials from surface. Presumably, workers would have to leave centrifugal habitats and work in low-G either way, and shuttling them back and forward is easy/cheap enough if there is no atmo to get in the way.

If you mean "relatively trivial" compared to making black holes for artificial gravity, then sure. But it's not a trivial task compared to what we've managed to build or put into space so far. I know you're aware of it, but a lot of people don't seem to realize how large the centrifuges need to be to guarantee no ill effects from long term habitation.

Got any experience coding in machine language and/or assembly?

It does. In fact, the relationship is exponential, and the relevant exponent is one of the main characteristics of solid fuel. That said, even at ambient pressure, it will be burning at a very high rate. So pressure drop won't exactly extinguish the booster. But it's way better to have a burning booster than an exploded one.

Should work. If it replaces the top plug, it should be able to fail without blowing the whole booster to bits. Of course, this only makes sense assuming that there is nothing above, or even close to the blowout panel. It will torch anything nearby. That will severely limit applications of such booster.

Black hole to generate Earth's gravity on the surface of the Moon would weigh six times as much as the Moon.

Gaseous exhausts are definitely allowed. There are plenty of propulsion systems designed specifically for cubes. And yes, the tethered ideas are higher budget, and most likely exclusive with bio experiment. I have nothing against doing theoretical work for both until we have some sort of an idea on the budget, however.

Supersonic flows are complicated. If a rocket has a blunt nose, there is going to be a normal shock area just ahead of the rocket, which means that flow immediately around the rocket is likely to be subsonic. But most of the sound is probably from the structure, as people suggested.

Manned Lunar orbiter mission would be very expensive compared to just a highly elliptic orbit mission to the edge of the Hill sphere, which can have an arbitrary duration outside of the Earth's mag field. And Lunar fly-by is a fairly short mission. They might have it penned down for now, but unless they decide to do a Lunar lander, I doubt NASA would end up doing Lunar fly-by/orbiter. I suppose, they could do free-return as one of the first short duration missions, but it feels like a waste financially. Unless they decide that publicity would be worth it.

This warrants a clarification. By itself, density doesn't enter into ISP, since you only care about the weight of the fuel/oxy. But pressurized O2 means you have to carry a huge pressurized tank as dead weight. If you add that weight to the weight of your fuel/oxy, you do, indeed, get better effective ISP even with straight up liquid N2O.

The only good, economically justified reason to do a manned fly-by of the Moon, is a free-return rehearsal for a manned landing mission. So I'd strike anyone not seriously planning a landing mission, and by seriously I mean they have resources for it, off the list. That's Russia and any smaller programs off the list, I'm afraid. Including any private companies, for near future. Space-X or similar might get big enough for it in the 20s, but that puts their manned fly-by into very late 20s to mid 30s. Russia has ambition, and they might have a reasonable chance of not killing a crew on a fly-by, but landing mission is out of their league, so it'd be just stupid to send a manned fly-by. And by the looks of latest events, Russia will only end up in a worse economic situation in the following decade. So no way. That leaves US and China. ESA is a potential contender, but they'd be getting into the game late if they decide to go with it. Between US and China, I just don't think US will get off their collective asses until a good kick is delivered by China. And manned fly-by is probably what it would take. So my money would be on China.

Kermunist gave a really good explanation. But what it honestly boils down to is that it'd be easier to just try and get "lift" out of Earth's magnetic field, and the field just isn't strong enough to support a structure capable of making use of it. It's like trying to build an airplane on the Moon - there is some ionized gas there to provide lift. Just nowhere near enough to lift anything heavy enough to have the sufficient wing area.

The axis of rotation would point towards the Sun. (Not necessarily directly at it, but in general direction, at least.) So illumination would simply have the 1h:30 day/night cycle (ISS orbit) due to being in Earth's shadow for half of the turn. Tethered version would be nice to try, but that's considerably higher funding. It would require better attitude control on both the primary and counterweight. The base mission would simply have 0.5U of "cargo" space, and the entire cube will rotate. That's sufficient for 0.1G. Tethered version would allow 1G+, of course, which has advantages. For a funding++, I could even see tethered system of several trays at different G levels, with two 0.5U on the ends for control. But that'd require a 2U-3U unit that would unfold. Tricky stuff. In the basic unit, however, we can set up several tiers of hydroponic nets. Looking at root growth of germinating seeds at different G levels would be a really cool short-term experiment. Something we can definitely do, and it would have some value. I'll see what research has been done on the subject. Plus, if the camera or even CPU bites the dust in a week, we'd already have useful data. Ideally, however, it needs to be something that would be interesting to observe for a few months, if hardware survives that long. On your tethered drive idea, I've looked at the sizes of aluminum foil rolls available. It should be possible to get a narrow, continuous strip that's almost quarter of a mile long without having to get it custom made. It wouldn't be very strong, but barring any foo bars with attitude control, it doesn't need to be. I'm going to re-run the numbers with this in mind. This might be viable after all. It still feels like a riskier mission, but any sort of a propulsion idea appeals to me personally. Yes. We've discussed some custom machined parts in this thread. There are definitely options there that would give us better flexibility and lower price tag.