K^2

Mazon Del, is the thrust in Vacuum-Vacuum case reduced to photon drive? Because this is a hell of an elephant in the room if the thruster only works when filled with gas, or PTFE, which will produce F2 gas under test conditions, which is an even better propellant than air for an ion drive.

Khatharr, it is not possible to slow yourself down against a lone star using warp. Any amount of permutations will conserve energy and momentum. This is why you have to use restricted n-body dynamics, and brake with fly-bys. That is why you need Jupiter, and why you cannot have a simple formula for all of this.

Attitude or altitude? Because attitude changes due to weather are absolutely minimal in cruise. They are far more critical on approach. On the other hand, flight levels are based on pressure altitude, and "40k feet" likely really means FL400. The actual altitude of FL400 will, indeed, depend quite a bit on weather. Interestingly enough, if air was of uniform composition at all altitudes and locations, this wouldn't make a difference on radiation levels. Your shielding literally depends on the "amount of air" above you. So does the pressure. So if there were no other weather effects, or humidity, or pollution, the amount of radiation at FL400 would always be the same, even as pressure varies.

I can see the tabloid headlines already. "Forum Regular Uncovers Airline Conspiracy." But yeah, about what one would expect. The increase from Phoenix to Seattle can be brought on by many things, including such trivial things as humidity levels and pressure. Or you might not have held constant flight level despite claims to contrary. I wouldn't make conclusions about magnetic field without comparing data from multiple flights. For instance, you'd expect ground radiation levels to reflect such a difference.

Interstellar Mod's Warp doesn't work correctly. I am putting together some material to write up a sort of Warp Physics 101 post, which will include details on which warp trajectories are possible, and how it affects momentum of the ship. Some of it is fairly intuitive, and some of it is not. In a nutshell, you can have a warp ship do almost anything you could imagine, but there are only a handful of trajectories that aren't going to waste impossibly huge amounts of energy. I don't know if there is an optimal solution here. At least, not trivial one-size-fits-all one. But yes, you can use fly-by with warp. You can utilize it slightly more efficiently with warp, because some fly-by trajectories you simply can't enter without warping or using reaction drives. You can also almost always guarantee yourself the next encounter, even when traveling at an escape velocity, so you can chain together fly-bys that you wouldn't otherwise be able to in any reasonable amount of time. But your first fly-by might as well be by Jupiter. It has sufficient escape velocity to bleed off all of your interstellar speed and become bound to Sol, and it is closer to inner planets than any other gas giant. But you will still be traveling too fast to enter Earth system in one hop. You'll need to do a fly-by of one of the inner planets before doing that. And that's where details are going to start to come in. Relative positions of inner planets will matter. So there isn't really going to be one right answer. P.S. By the way, if there is more stuff you want addressed in Warp 101, this will probably be a good place to ask.

Good call. But this applies to ablative shields as well. Of course, so do some of my reasons. I wonder if it's really the difference between ablative making more sense for small capsules and soak making more sense for large ships?

On the Shuttle, main reason is that they are replaceable. I have no idea if any of the tiles were actually reused from one flight to the next, but even if not, it's still far easier to take the shield off and put it back on if it is made up of tiles. For non-reusable craft, similar considerations are still valid. Servicing and testing the tiles prior to flight is going to be easier than working with a solid shield. And if you discover a crack or another flaw, you only need to replace a tile, not the whole thing. So it's going to be a choice between simplicity of solid shield vs versatility of tiles. I would imagine Solid shield to win out for smaller capsules and tiles for larger ones. But I'm not familiar with enough pure soak designs out there to really test this hypothesis against the real world.

Not even close. Kinetic energy at Fermi levels in a metal are huge. For example, Aluminum's Fermi Energy is 11.6 eV. Electron's mass is 511keV. So the fastest electrons are buzzing at over 2,000 km/s. This is a pretty extreme example, as aluminum a great conductor for a reason, but for all of the metals, typical velocities of electrons at absolute zero are far above the escape velocity.

Yes, it is only the mechanism of mutation back to paralytic and virulent form that is not clear from any of this.

This is not correct. Classical thermodynamics already prevents going to absolute zero. And the difference that QM makes is in what state it corresponds to. As mentioned above, 0K is minimal internal energy. Absolute ground state. Classically, it would mean zero kinetic energy. No motion. But in QM, Pauli Exclusion means that only a few particles can take such low energy state. This results in considerable kinetic energy still present in ground state. But temperature is still 0K, because it has more to do with energy distribution than amount. Calling any of it a jitter is very imprecise. There is no randomness to it. 0K is a very well defined state. It simply has non-zero internal kinetic energy for any system containing fermions.

I am not a biologist either, so this is just an educated guess. Poliovirus is a very simple virus consisting of a single RNA strand and a protein shell. Proteins on virus' surface bind to a receptor on host cell's wall, allowing RNA into cytoplasm. There, RNA is transcribed to produce proteins required to build copies of the virus. Oral Polio Vaccine (OPV) is produced via heat-induced mutations. It is meant to be a non-virulent form of poliovirus. My best guess is that OPV virus can still get into cells, where it is partially transcribed despite mutations. Depending on RNA replication scheme, it is possible that segments of the RNA are swapped out. Given that each dose will contain millions of deactivated viruses, and each cell will make tens of thousands of copies, it is possible that some recombination of mutated strands can make a virulent version of poliovirus RNA. Again, this is a guess, but all I can think of. It is worth noting that injected form of the vaccine is supposed to be free of this risk. Edit: Iskierka, I was surprised to learn this, bu OPV really can revert to virulent form. It has to do with RNA not being fully denatured, as with most vaccines. But I could not find details, hence filling in blanks with guesses.

I have reservations about that mod. Author claims he is using symplectic integrators, but there is no such thing for n-body gravity. Perhaps, he is simply mis-using the term, and just means higher order RK method. I will take a closer look at it.

And if I tell you that entropy increases because of this paradox? That it is the driving force of thermodynamics? You are seriously outclassed here. You keep talking about reason, but refusing to apply it, hiding into your ignorance instead. You have neither the knowledge of the subject, nor willing to apply basic logic to things. You think you know something, and insist that any argument showing you wrong does not apply to reality. And you think you stand for reason? You are standing against it and all it brings.

The above applies to math describing our space. If you do not think math can be used to describe reality, your formula is useless. If you think your math applies to reality, then you have to apply paradoxes. You are just being stubborn now.

And if I tell you that the sum can be double? Banach-Tarsky Paradox Same way, a circle can be unrolled into something with the wrong area. Don't feel too bad though. Even as high up as Calculus 2, kids are basically told to ignore this. This is the sort of math you start learning if you major in pure mathematics or closely related field.

If I cut a solid sphere in two, what is the volume of resulting objects?

Real electric power is not measured in charge. Charge at known voltage gives you total energy stored. So charge per second only becomes power once you establish voltage. That said, HST is about 2.8kW.

No, it is not. It is called measure theory, and it is clearly above your education level. This is a clever proof, but incomplete. You really have to spend a few years on calculus and analysis to fully appreciate why, and encounter countless (indeed, uncountable) examples where your "common sense" fails miserably.

For KSP specifically, you do not need n-body physics. A search for optimal transfer there is purely a solution to a non-linear optimization with constraints. That said, my recommendation on starting resources would be nearly unchanged. For solving the same problem with real gravity, you need both.

Crash dumps via e-mail go way back. But yeah, it's way better these days. A piece of software can have an exception handler within its own code that registers what's about to become a fatal crash, does a stack walk, generates an error report, and if time/connection allow, sends a full memory dump of the process back to the mothership.

What's your background in physics, math, and numerical methods like? In a nutshell, an n-body simulation is just a numerical solution to a differential equation. If you have no experience with that, I would start there. Any good introductory text on numerical methods will cover basic methods and various problems one encounters. Gravity is a very special case, and you'll probably want a text that specializes in that, but you'll probably find the entry curve too steep if you don't get yourself comfortable with standard methods. And, of course, if you aren't familiar with differential equations at all, then you'll need to take another step back and get at least basic familiarity. It also helps a lot when learning numerical methods to be able to try them out, which means programming. If you simply want to learn and write some proofs of concept, you can program in just about anything. But if you hope to solve real n-body problems, you'll probably need to learn C. Almost any other option comes with too many restrictions that prevent getting the computational performance you need. So if you haven't started learning to program, and you have a serious interest in computational physics, I strongly recommend starting with C. Finally, some basic physics helps. But unlike gravitational perturbations or restricted 3-body, which require very serious understanding of mechanics, n-body gravity just requires you to know Newton's Laws of motion and Newton's Universal Gravity. Basically, nothing you couldn't pick up even from KSP. As for specific texts, for introduction to Numerical Methods, Introduction to Numerical Analysis by Stoer and Bulirsch is not bad, and is not too hard to get through on your own. If you know what a differential equation is, but don't know how to solve it numerically, it will get you started. Also, if you are going to be writing numerical code in C, Numerical Recipies in C is going to be your good friend. Note, it will not teach you good programming practices. Just efficient ways of organizing your computational code. Or just use code from the book directly to do some standard computational steps. P.S. If you are already comfortable with programming in C and/or C++, but are looking for squeezing more computational power for your projects (and you'll need it for n-body), consider learning CUDA. Udacity has a fantastic course for that called Introduction to Prarallel Programming with CUDA. So if you are going to be learning numerical methods and writing your own code to tackle n-body problems, you can develop all of that in CUDA as you work through it.

Oh, yes, certainly. I'm not saying that one couldn't significantly OC a chip and get stable performance. Only that there are a lot of people out there who do it haphazardly. And, well, anyone who just starts out is probably going to make mistakes and add to the pile of "impossible" crash reports.

Of course. But OC-ed machines crash exponentially more frequently than the non-OC-ed ones, whether parts were good or bad to begin with. And typically, on computationally expensive tasks. So when I see a crash dump from a game with an "impossible" state, I can pretty much disregard it. Unfortunately, digging through the dump to confirm that it's a bad state is time-consuming.

Ah, I see. Between this link (thank you) and some reading up that I've done, my knowledge was, indeed, considerably outdated. The same exact practice, using two parallel memory units, was in place with older machines to get 64 bits of data per clock from two SIMM units, which were capable of sending just 32 bits per clock. This was later addressed with DIMM, which is modern memory architecture, by having each DIMM unit perform two memory reads per clock. Double Data Rate. When DDR came about in late 2000s, it removed the need for having two parallel sticks of RAM. That was the state of my knowledge. Modern Dual Channel access, however, pulls the same paired RAM scheme on DIMMs, which allows getting 128 bits per clock, effectively, making it quadruple data rate. Hence my confusion. Again, thanks for pointing me in the right direction. Always appreciated.

Maybe my trivia on this is a bit outdated, but I wasn't aware of motherboards being capable of utilizing more channels on dual DIMM setup vs single DIMM. It was my understanding that hardware could either address a single DIMM in dual address mode, or two separate sticks in single mode. Has that changed?