K^2

He means the image of the object's it sees won't be more than a few pixels. As for seeing a planet next to a star, this telescope's main mirror is 6.5 meters across. In 1 micron band, this will let the telescope resolve 1 AU from about 100ly. The figure quoted by the site, 0.1" at 2 microns is only slightly bellow this theoretical limit. So yes, in principle, the telescope is large enough and sensitive enough to resolve planets orbiting some relatively nearby stars. Whether it actually performs as expected, we will find out.

Of course. But this sort of logic only applies if there are many universes. If it is so, then however unlikely life is, if there are enough universes out there, it will happen in some of them, and we are guaranteed to be in one of these. But if there is just one, then it bearing life only by chance is still very unlikely. You can't rely on statistics to fix that. As far as things being just right for life, consider the blocks of atomic matter. Despite up quarks being slightly heavier than the down quarks, and despite the fact that separating two charges takes energy, it turns out that the neutron is just slightly heavier than a hydrogen atom. A lone neutron left to itself will decay into a proton and an electron. This is why the most common element in the universe is hydrogen. Now, imagine that, as common sense would dictate, hydrogen was heavier. Every atom of hydrogen in this universe would decay to neutrons. There would be no clouds of hydrogen plasma to make stars. Just clouds of neutron matter. No such thing as chemistry in all of existence. Not even the most remote opportunity for life. Fortunately, isospin asymmetry played in our favor and allowed this multitude of elements to exist. But this requires quite a few parameters being just right. Do they have to be this way? Who knows. But it's hardly so by chance. Either there were many "attempts," or there is a much deeper reason for all of this.

This is slightly misleading. They produce equal number of both, since charge is a conserved quantity, and KL is a neutral particle. However, it is slightly more likely to first decay into a À- + e+ than À+ + e-. This is a major puzzle, and it might hint at the preference for one kind of matter over the other, but not the reason for why it's not the same of both. The pion (˱) is still going to eventually decay into e± and you end up with equal number of particles and anti-particles produced.

97% of statistics are made up on the spot. The percentage you quote has no chance of being accurate other than by mere chance, and even then, highly dependent on how you choose to gauge the fraction. The most important thing you should understand about science is that while it answers many practical questions, like how we would go about building a bridge, it doesn't actually answer any fundamental questions, like why any of that is true. Or even whether it's actually true, for that matter. Pretty much all of the physics we've known turned out to be wrong, and what little that hasn't looks very suspicious. But science isn't about finding truth. It's about finding practical models. By that measure, there is no guarantee that it's even possible to know how things actually work. So what fraction of the unknowable do we actually know? Is there even a way to answer such a question?

This is a good place to start: Baryogenesis. Edit: They only discuss the spontaneous symmetry breaking as an option. (Universe starting with zero baryon number.) But there are some hypotheses that are based on baryon number starting out non-zero. Simplest having to do with geometry of the space-time and suggesting that anti-matter is "before" the big-bang. All of this goes way beyond Standard Model, however.

You are confusing multiverse and Many Worlds. Many Worlds does, indeed, have something to do with our interaction with the observable universe and the Schrodinger Cat. Though, it's a bit more complicated than that. You don't really "create" new worlds at quantum events, but for simplicity, looking at it as time-line splitting up isn't all together wrong. Also, M-Theory is something completely different. Neither. Think of it more like intensities. A beam of light can be 50% red, 25% green, and 25% blue. It's really all just the same beam of light, but you can decompose it into components of different intensities. The reason it gets interpreted as probabilities has more to do with stat mech than pure quantum physics.

The question isn't why it's just matter and not anti-matter. The question is why there isn't the same amount of both. In every experiment we have ever been able to conduct, we produce equal amounts of matter and anti-matter. Not a single known reaction produces more of one or the other. Not a one. Yet, here we are, in the universe filled with one and not the other. Of course, we chose to call the one that's in abundance matter and the other anti-matter. Which is which isn't really a big problem. But where did all this matter come from? Seems to be from big-bang. But then where is all the anti-matter that should have been created along the way? There are several different hypotheses on the matter, and I won't get into details. Either way, however, it points to limitations of our knowledge, and figuring out the answer will be a major breakthrough in fundamental physics.

Actually, the way gimballing works in KSP, you always want center of thrust behind/bellow center of mass. The gimballing algorithm assumes this to be the case, so if you put CoT ahead of CoM, the controls for thrust vectoring are reversed. Of course, if you turn off the gimball and only use surfaces for control, this doesn't matter.

No, it doesn't work that way. The way the forces split depends only on temperature and density of matter. How the matter expanded and cooled doesn't make a difference. Besides, the constants of which the multiverse hypothesis talks are a bit more fundamental than that. These are, among other things, the very parameters that determine when certain forces will become relevant. There is absolutely zero evidence for this hypothesis, however. It's a convenient one, because it is an ad-hoc explanation for any set of conditions in the surrounding universe that seem to be just right for the existence of human kind, but it is difficult to falsify for that very reason, and as such, will probably remain untested.

Leapfrog/Verlet only marginally improve stability of the orbital simulation, unfortunately. If you want to improve precision significantly, you have to go for higher order implicit RK integration, and that's a royal mess. And even then, you are going to have energy drifts. As far as I know, a general conservative method for n-body 1/r potential is not known. Of course, for a 2-body problem, you can always just fall back on analytic solutions.

What are the exact formulae you evaluate on each step. This isn't just numerical mess, you definitely aren't computing relevant quantities correctly.

Ellipse like that corresponds to a body in central harmonic potential. I suspect it's due to the way you are dealing with force as a vector, but you'll have to paste a portion of your code to say with certainty where the problem is.

I'd start with review of introductory mechanics, then. Udacity has a course that might work for that. First four lessons cover the things you need to know before you get into orbital mechanics. You can also see if your local library has a textbook on introductory mechanics and see if you can follow that. After that, you should be able to follow most of the Wikipedia's article on orbital mechanics. It doesn't replace a proper course, but it should at least answer some questions, and maybe give you a better idea of what else you need to understand. Typically, more serious topics on orbital mechanics are covered in the course on Classical Mechanics, but that tends to involve far more serious math because you typically step away from Newtonian Mechanics and start dealing with Lagrangian Mechanics. You don't, strictly speaking, need to know any of that if you don't want to deal with N-body problems, though. So you might be able to find a textbook on orbital mechanics that's done entirely from perspective of Newtonian Mechanics. I just don't really know what to recommend for that.

That... Wasn't public knowledge? Wow. I used to live about 30-40km from that place. The Star City was on the drive to Moscow, and one of Moscow's defense ring objects was located almost in the city. (Officially, any incident there was reported as taking place in our city, including when a stockpile of AA missiles went boom.) We were basically told in kindergarten that Gagarin's plane went down because another plane flew too close to it. I had no idea this wasn't the official version until now.

Oh, I know that any modern fighter will have all input filtered through a controller. When you want your aircraft physically unstable but stable with respect to pilot input, there is just no way around that. But the requirements there are still quite different from what you listed for Aerobus. Pitch control -> Load factor translation is very natural for large passenger or cargo plane, where you basically want to maintain something like 1G in the cabin during every maneuver. It's not what you want for precision flying, though. Having fine control of attitude is far more important than fine control over the load factor, especially if you are operating near critical AoA while flying formation. And yeah, for a fighter sim, I wouldn't even worry about it. I'd have stick alter reference and PID to that. There's a reason why pilots call these things lawn darts. For the purposes of this discussion, think conventional aircraft with a cable or hydraulic controls and physical trim tabs on control surfaces. It might sound like I'm being particularly picky, but this is the interesting problem. I know how to write a controller for a fighter jet or a commercial airliner. These are solved problems. This one does not seem to have a standard solution. That's what makes it worth solving.

Even with these things disabled, that thing behaves nothing like a normal aircraft. I understand perfectly why you'd want this on passenger plane. Makes for smoother, safer ride. But you aren't going to want this sort of thing on a fighter jet or a stunt plane. I really don't want this to turn into training wheels you'd disable when you get a hang of flying. I want it to be absolutely unnoticed by a skilled pilot while helping a novice. A smart enough system looking after the trim setting ought to do just that.

That's kind of the point. I don't want overspeed and stall protection. I want a skilled pilot to sit down and feel almost no difference from directly controlling an aircraft save for not needing to touch the trim wheel.

Having "stick" set rate while ASAS is engaged would probably be the best solution. PID requires very little modification to track a reference that rotates at a constant rate. And this would work naturally with the fine adjustment mode that's already in the game. It'd let you make very small corrections or make serious adjustments to course, all with ASAS is engaged.

It all depends on where you are starting from. Do you know the basic mechanics? Forces, Newton's Laws? How do you feel about Trigonometry? Geometry? Linear Algebra? Any Calculus? There is nothing wrong with starting completely from scratch, but we need to know to make any recommendations.

L1 doesn't depend on which is which. L2 and L3 are swapped and their stability can change. L4 and L5 are likewise swapped, and their stability depends on the mass ratio. But otherwise, yeah, you basically have these 5 points defined for a pair of bodies, and it doesn't matter if they are similar in mass or not.

Yes. It's the L1 point.

For starters, you really feel the autopilot taking over. The overshot, the correction, all of the little adjustments it does. It's very different than letting go of controls on a trimmed aircraft. There is also how it responds to small adjustments. Say, I pull the stick very gently, then gently return it to neutral position. What will happen? The airplane will pitch up, climb a little and slow down as I pull the stick back. As I return it, it will dip, drop, and speed back up. When I let go of the controls, the air speed and altitude are essentially unchanged. It's like a damn cruise control. All because the trim remained constant until I let go of the controls, and by that point it picked up the same residual as before. In contrast, if I have the trim track the plane's attitude even when input is applied, and if I can make it work as described earlier, when you pull on the stick gently and then let go gently, the net result will be a slower flight. Finally, the dynamics are linked, as robot pointed out. Say I want to descend a bit. I pull back on the throttle, plane slows down just a touch, enough for reduction of lift to dip the plane down. It starts to descend, picks up the speed and finds new equilibrium in nose-down attitude; descending at a constant rate. Now, suppose I also decide to slow down a bit, so I pull back on the stick just a little. I have to keep pulling on the stick to fly slower as described above. But as I slow down, the amount of lift and drag also change. Now I need a different throttle setting to maintain descent. But the neutral position for throttle hasn't changed. Say I was flying slow already, so reduction in speed and corresponding increase in AoA forces me to increase throttle. As I slide throttle up, past neutral position, suddenly the reference changes and instead of nudging throttle up just a bit, the engine suddenly revs up like I'm trying to take off. That's not good. If you want a real world analogy that you might have actually come across without flying, have you ever driven a car with a crappy automatic transmission that switches with completely the wrong timing? It's kind of like that but with an airplane. It feels fake. It isn't any fun, and it can actually make landing more difficult than no assists. Precisely. Are there any other methods of looking after that? I don't have to predict necessary damping perfectly. If the plane ends up going a little faster or a little slower after the pilot lets go of controls, it's not the end of the world. Just so long as it settles down and can easily be adjusted with small amount of input.

Are you sure? What about the Roche Limit? I mean, I'm sure it works a little different when two bodies are almost equally massive, but it's hard to imagine the tidal effects not to be catastrophic.

Entirely possible. I never tried to estimate the degree of instability. All I know is that some sort of correction would be required. It might be a very small amount, making it entirely sustainable.

The way you fly an airplane is you adjust air speed with attitude corrections and you adjust rate of climb/descent with throttle. Yes, if you want an immediate response, it's the other way around, but for sustained flight, it's all about balance. And yes, the two are dynamically linked. I did actually take all of that into account. The entire model included the climb rate, bank angle, etc. And it derived the equilibrium conditions for the aforementioned controls. The problem was that this equilibrium was not dynamically stable even after coupling is looked after. I want the system to actively adjust while pilot is flying, but only to make sure that the response is fluid. If a player makes a correction, response should be as immediate as if the skilled pilot applied the same correction, re-adjusted trim, and relaxes on the stick. And the reason I can't simply have an auto-pilot is because the pilot should be able to apply greater input for a maneuver, and said maneuver should be executed as if no controller is in place. I want the plane to be easy to fly for a beginner and I want a skilled pilot to not feel any restriction with this system.