K^2

Find that Ti-83. It's a good machine. A bit over-priced if you buy it new, but in terms of capabilities, nothing outdated about it. You can flash it with fresh firmware if needed.

I'm having hard time picturing an O2 main sequence star. That's already way off. But if there was one, it'd have to have magnitude of -10, at least. (That's the closest I can get to an O V star from the charts.) Making it about a million times more luminous than the Sun. So lets take 5x1034W as a ballpark estimate. At 52,500K, that would require the star to be about 96 million km in diameter, which is already way larger than distance to the brown dwarf. Basically, the whole system is total fiction. You can't orbit 0.278 AU from an O2 star.

Technically, false. Buran orbiter was fully reusable and did fly one unmanned mission.

Actually, you don't need Quantum Gravity here. The scales we are dealing with here are many orders of magnitude above Plank scales. So there are no inherent QG effects. Next, we look at whether we have to consider QM of the black hole itself. Since its mass, again, is many orders of magnitude above that of the electron, we can treat it as a fixed object at the center. Any uncertainty in its position is going to be much smaller than event horizon size. So we're clear there as well. The only place where gravity and QM interact in this picture is behavior of electron near event horizon. And we know how to deal with this. Because we assume BH to be a static object, we can simply do QED in Scwarzschild geometry. Basically, any place you see a partial derivative in QED Lagrangian, you replace it with covariant derivative. And anywhere you see a dot product, you'll need to insert the appropriate metric tensor. From there on, you just do normal Quantum Field Theory. I'm oversimplifying a bit, but this is the general way in which you'd compute interaction between tiny black hole and an electron. In a nutshell, that's also how Hawking Radiation is derived, except that you consider the vacuum of relevant QFT there. I don't know how complicated of a problem this is going to be as I haven't tried to work it out. I suspect, proper treatment is very difficult, but there might be nifty shortcuts for a good estimate that I can't think of without writing this all out. At any rate, you'd be able to estimate the probability of such an "atom" eating its own electron without getting into Quantum Gravity. And like I said earlier, this is only relevant if we want to know the life time of such "atom". The electron's distribution, on average, is far enough from the center to be considered as a classical QM problem, giving you solution identical to Hydrogen atom. So we basically know all the energy levels right off the bat. Just to clarify a bit on what christok said. Hydrogen atom is exactly the case where the probability is non-zero. In fact, radial component of probability amplitude has a maximum at zero. (I don't recall if it actually diverges, but that doesn't really matter in this discussion.) So at any given time, there is probability that electron is actually inside the proton. But because electron doesn't interact strongly, it just passes through like it's not even there. The only interaction is electromagnetic, and that's the very thing that gives you an orbital in the first place.

It shouldn't. It can, but it shouldn't. Almost any cell you can draw too much current from, causing it to fail the way any other semiconductor device would from overheating. However, if you regulate the output current or disconnect the cell all together, this won't happen. So we can talk about failure modes of a disconnected cell. Even if the cell isn't connected, as long as there is light flux, there will be internal currents. If you look at an equivalent diagram, you'll see that it contains a resistor and a diode connecting the two sides of a photovoltaic cell. In principle, if current through these "elements" gets too high, the cell can also burn out without being connected to anything. However, a typical cell will saturate before this happens. So if this is a concern, you can design a cell not to fail in such a way. Of course, that's a conventional PN junction photovoltaic cell. I don't know what they have in mind for a gamma cell. If it's just a scintillator with a conventional cell, all the same logic applies. If it's something more sophisticated, I don't know.

Almost surprisingly so. In general, physics of a black hole is very different from that of a charged particle. However, to get equivalent of a Hydrogen atom by using a tiny black hole instead of a proton for nucleus, you need a black hole that has mass of approximately 3.79x1012kg. Such a black hole would have a Schwarzschild radius of roughly 5.6x10-15 meters. In contrast, Bohr radius for Hydrogen atom, which is where you are most likely to find an electron, is 5.29x10-11 meters. That is almost 10,000 times larger. In other words, the region of space where black hole has all of its funky physics is very small compared to the size of the atom. So the electron would behave exactly the same way as it would in Hydrogen. The ground state orbital does have non-zero probability to be found at the center, however. So I'd guess that the electron would eventually get pulled in, but I don't know how long it will take. (It'd be a lot of work to estimate this even from classical QM, and I suspect this is a QED problem.)

Obereth effect is a 2-body phenomenon, so n-body effects have to be accounted for separetely. Basically, ship's total energy is conserved in barycentric coordinates. (Position with respect to center of mass of the 2-body system.) Because of that, Obereth effect is reduced to an energy optimization problem, and you get most energy per unit of fuel consumed when you are at the periapsis. Generally, if you consider a problem of escaping planet into interstellar space, it's more complicated. But if your starting orbit is close enough to the planet so that you can ignore the Sun, the way KSP handles it, then you can break it up into two parts, and Obereth effect will apply to each separately. You'll have most energy if you perform the burn at periapsis around the planet, while the planet is at its own periapsis. This would be relevant for something like return from Moho.

Lift does not reduce delta-V requirement. Ever. In fact, it's guaranteed to increase delta-V requirement. You can engineer a space-plane where the increased delta-V cost is minimal, and TWR requirements are reduced, which can let you get to orbit with a smaller, lighter engine. That can give you net savings in fuel, but because of a lighter orbiter. Not because of smaller delta-V.

If it boggles your mind, it should. If you want to understand why, then you need to understand that separation between any two events is constant in any coordinate system. That's no different from Galilean picture of the world, where distance between two objects is the same regardless of how fast you move past them. Except that in Relativity, separation includes time. So square of a separation s² = x² + y² + z² - c²t². Check for yourself that photon moving at the speed c connects two events with zero-separation. That means that from any coordinate system light appears to travel at the speed of light. On the other hand, if you consider distances and time separation separately, you'll notice that these change. That's length contraction and time dilation of relativity. So entire Relativity is about the fact that space and time have to be considered together, as space-time. Once you do, all of it makes perfect sense.

Your motherboard already has BIOS installed, or it wouldn't boot at all. Updating BIOS might get you a few extra optimization features, but it wont make any significant difference to boot time. If you want your computer to boot really fast, your best option is buying a solid state drive (SSD), setting it up as your master disk, and installing your operating system on it.

Walking though the neighborhood after sundown with a telescope to get to a place with good view of the sky can also look all sorts of wrong. I'm pretty sure that's an immutable hazard of amateur astronomy.

The fact that laws of physics are invariant under rotation leads to conservation of angular momentum. (Noether's Theorem.) And conservation of angular momentum pretty much guarantees that everything is going to be spinning. Technically, the guy who answered "gravity" isn't completely wrong, either. Gravity is a consequence of a more general, Poincare symmetry obeyed locally. So it is all a part of the same thing. But in terms of classical physics, any central potential would have worked, and it is all about angular momentum. They do. If you put an electron in orbit around a tiny black hole, you have to worry about all the same things.

I'm brushing most of it aside in the conversation, but I'm definitely not overlooking it. There are some serious challenges there. There is, however, one very important thing to note. The (sc)ram jet stage would run on Jet-A. It needs to be efficient enough to get the job done, but if it's not very fuel efficient in absolute terms, that's not a big loss. A scram jet, however advanced, is nowhere near complexity of regular, run of the mill bipropellant liquid rocket. We've been building the later for a bit longer, so we have a lot of research to fall on, but once you figure out a good design, a scram jet is way cheaper to build and maintain. This will make a huge difference in cost to launch even with a reusable craft. So if we have to put a bit more kerosene in it to make it work, it's worth it. Here is my thinking on that, partially inspired by the Blackbird engines. Lets start with the easy part. I would use aerospike concept for nozzle. At low speeds, you don't need divergent part of the nozzle, so this will work fine. And at high speeds, aerospike should do exactly what you need in terms of the outgoing flow. On to the hard part. I think the best way to handle the fact that low speed ram jet will need a diverging combustion chamber is to do it the way SR-71 solves similar problem. Place the ram jet combustion chamber inside a toroidal scramjet. In ram jet mode, the bypass is locked off, taking air through the diverging chamber. Once sufficient speeds for scramjet operation are reached, the central chamber is locked and bypass is opened. Bypass will narrow as it goes around the chamber, and give you the right flow for scramjet operation. This does involve moving parts, some expensive materials, and will require inspection and replacement. It's still way simpler than a turbojet, though. So it should be fine. This leaves a few problems. First, the ram jet's combustion chamber has to be designed for specific speed, and will not be efficient otherwise. I say, forget that. At low speeds, we can take a hit of being not terribly efficient. Design the chamber to provide sufficient thrust after boosters are done, and otherwise, to give best overall efficiency, and call it the best we can do. Trying to actually vary geometry of the combustion chamber is not going to be worth it, unless somebody comes up with some pure genius idea similar to aerospike for that. I've got nothing though, so I just hope this is good enough. Same problem with scramjet, technically, and we need great range on that. The scram bypass will be activated around Mach 3-4, and we need it to last to Mach 12 or so. Fortunately, the biggest problem in getting a speed-variable scram jet is the nozzle. As I've said, I'm betting on aerospike to solve that problem. Geometry of the combustion zone is also important, however. It might not be worth the trouble, but shifting the region where fuel is injected might work to improve that. Overall, it's a place where a performance hit will have to be taken. If nothing else can be done, design for best performance at high speeds and thrust at low speeds. Overall, though, we have already improved on bipropellant fuel dramatically by using a scramjet, so if we have to take some performance hits, that's just life. With that in mind, lets go to intakes. Again, I'd turn to existing solutions here. The overall shape of the intake would have to be just the best we can do across the board, but we can have a moving spike without making things too complex. It worked for SR-71 and it works for Skylon. Hopefully, that's enough for this (sc)ram jet as well. The rest is lots of trial and error. Fortunately, cylindrical symmetry of this type of engine would allow for very precise computer modeling, so you wouldn't have to build expensive prototypes until you have a good general idea of what works and what does not. The final build will have some moving parts, and is going to have to be manufactured with very high standards of precision, but it's still going to be way easier to build lots of these than anything else we could use to take a ship to orbit. As I've indicated earlier in the thread. My interest would be in taking a small orbiter, with capacity under 10T, to LEO with the best cost-per-kg we can manage. Discounting methods that involve megastructures, like launch loop and tethers, I really think this is the best option. It would require a lot of research and testing, but it should be very affordable once the technology is in use.

Sort of. GR is non-linear, so your very first sentence is not strictly true. It all very much depends on the matter arrangement. But if we are talking about a sphere of matter whose density you start increasing, yes, it will happen exactly as you say. Event horizon will form once the radius of the sphere is less than Scwarzschild radius for the mass of that sphere. Note that density does not need to be uniform. It only has to be spherically symmetrical. There is, however, a catch. Matter will typically begin collapsing long before that, which will form a shock wave. In a star, that shock wave becomes a super nova event. But even with a smaller object, it will shed some of its mass before forming a black hole. I don't know if there is a size limit there. Perhaps, for a small enough black hole, all of the mass would collapse inward. But like I said, we've only properly studied two ways a black hole can form, which is core collapse, or hadron collisions. There is no known way to achieve required densities by any other mechanism. Just enough to push past the radiation pressure. I can do an estimate, for a proton beam, if you like. A neutron beam would require much lower velocity, because it has lower EM cross-section, but it's harder to organize as well. I think a proton beam is going to be more efficient despite the cross-section. It won't be anywhere close to mc², though, at any rate.

Using planes for first stage doesn't work as great as you'd think. But if you have the first stage do a vertical climb, and then glide to landing, that might work. Ramjet can be significantly lighter than a turbojet, which would give it sufficient TWR to pull that off. So yeah, this might be the best possible setup. First stage is solid-boosted (sc)ram jet, followed by a small LH2/LOX rocket plane that actually makes orbit. Scrams can get up to Mach 12, at least, and will eat up a big chunk of gravity and drag losses. That means second stage only has to pull about 4km/s of dV, which is very reasonable with cryogenic LH2/LOX. Everything but the boosters is fully reusable. Boosters can be partially reusable, like Shuttle's SRBs. Or if it proves economically sensible, perhaps the boosters can be reuseable liquid fuel rockets that work similar to SpaceX's grasshopper concept. Takeoff would be entirely vertical, like a conventional rocket, and the two stages would land like planes. So this leaves two main questions. Should the second stage be a pure LH2/LOX? Or should it bring a more stable fuel for orbital operations, a la Shuttle Orbiter. Should the boosters be solid rockets non/partially reusable? Or fully reusable liquid rockets? I would lean towards using a MMH/UDMH/Hydrazine to be burned with nitrogen tetroxide for orbital operations, which can also be used as monoprop for maneuvering thrusters. So, basically, same as Orbiter. And I think SRBs would make things easier, and in the long run, it's probably a cheaper option anyways. But I can be easily persuaded otherwise. I think I'll do some estimates on how big each of the stages is going to be, and maybe get some idea of costs.

I might be completely off on this, but cities might work like a really large karst spring in terms of updraft. If you've seen one of these, the water is really choppy near the boundaries, but pretty smooth in the center, because while there is significant flow, it's very uniform. The way I'm picturing this with upper atmosphere is that outside the city, temperatures are varied, but overall, fairly constant. So small variations in local temperature will result in many small, fractured convection cells, which gives you a very choppy atmosphere above. In the city, you still get that, but this variation in temperature is nothing compared to the huge difference between city temperature and suburban temperature. So individual contributions from parking lots and buildings might be getting lost in the massive updraft generated by the whole city. This might result in pretty consistent atmosphere above. After all, it's not the wind velocity that causes distortion, but variations in density. And I can at least see how a city might reduce these.

That would work, if we could create matter with these sort of densities. But we don't. Right now, we still know only two ways a black hole can form. Core collapse or collision of elementary particles. Former results in a black hole that's too heavy, and later in one that's too light. There is no known mechanism that could produce a black hole of required size.

It will give you plenty of warning, too. The energy output is going to be steadily increasing as the black hole loses mass. By the time it goes, it will have lost most of its energy, but while it took a year to give up all of that, the last 1% is going to be released in the final seconds. And of that, a sizable chunk is going to be released practically at the last instance.

You can feed matter in a way that doesn't result in a disk. But yeah, you'd be getting radiation from in-falling matter as well. That's still 100% efficient, though.

Being a particle physicist, I do, actually, yes. And that's precisely why I'm talking about a keV range accelerator, and not a GeV range one.

It's unstable, though. So you can't just leave the stream of matter on and let it regulate itself. If it shrinks a little, its output increases, so it will start shrinking faster. And vice versa, if you put just a bit too much in, it will get heavier, and start growing faster. So you have to have a regulator on matter stream that adjusts it as necessary. But yes, if you just stop feeding it all together, it will start shrinking, and eventually go out with a bang.

We aren't talking about building stations here. We are talking about routinely moving crew and small cargo. 10T is very good for that.

The beam only needs to be a few keV, and if you feed protons to it, which is easiest thing to do, you'll be getting a GeV of energy back. That's at least five orders of magnitude greater return than investment. Even if your particle accelerator is only 1% efficient, that's still 1000:1 efficiency.

Information you can get from junk DNA of a single species is very limited, and unfortunately, there are some major bottlenecks between modern birds and what most people think of as dinosaurs. It's much easier to get to the common ancestor. So, for instance, I think we'd have a very good shot at scraping up a fairly complete picture of what Archaeopteryx DNA looked like. The biggest limitation is in our ability to tell a functional protein from a broken one. As we improve our ability to fold proteins, we'll be able to start processing all this information to sort through junk DNA. Dinosaurs are still going to be very complicated, though. I'd have to make some estimates to say anything specific, but if I had to guess, I'd say we don't have enough sources to look back from to gather a good enough sample. We'd need other source, and perhaps an ability to fill in the gaps based on what we think is missing. P.S. Any scientific question that starts with, "Should we," is answered with "Yes." There is absolutely no research that shouldn't be done. Some of it needs to be done with great care. In this case, most dinosaur species wouldn't survive well enough to present any kind of a threat. So the Jurassic Park (I'm talking series overall) sort of disaster isn't going to happen. There is a danger of re-introducing an ancient virus which would be hiding in genetics of one of these beasts. It'd be really rotten luck, and even then, it should only have a chance of affecting avians, but it's something to take precautions for anyways.

Burning OMS early gives you more OMS fuel once in target orbit. So it actually increases safety margin. The better question is why they don't always use OMS assist.