K^2

Here is a very useful graphic. Look at the total absorption spectrum. Everywhere water vapor can make a difference, it's already saturated. More or less water vapor in atmosphere makes no difference. Methane isn't on here, but here is a graph, a bit less precise, that puts it into picture. So methane doesn't make a difference either. CO2 is really the only worrisome one, and even it is saturated in places where it could do most damage. On the graph, you can see several small peaks near 10 microns. That's all that's going to contribute to global temperature increase as carbon dioxide concentrations increase. We also have some mechanisms to keep CO2 concentrations in check. Specifically, the biosphere. Biomass increases as the CO2 concentration does, and typically, amount of carbon in biomass is roughly equal to that in atmosphere. Since the rate at which carbon from atmosphere is fixed into the biomass is directly proportional to the biomass, and anthropogenic CO2 output is on the order of 10% of total, we have a good resource there still. Another thing to keep in mind, the reason C4 pathway has evolved and started displacing C3 pathway is CO2 deficiency. Most of the plants, including most agriculturally significant plants, are CO2 concentration limited. Increasing CO2 concentrations would result in increased yields in most food crops. Basically, the environment responds to our increased CO2 output with increase in food production and ability to absorb CO2. The total human output can roughly double without running any risk of a runaway effect, and while weather pattern changes are possible, things like world-wide hunger that alarmists like to scare everyone is are not in the cards. Just the opposite.

There is a very small range of altitudes over which it will help, and you'll be paying for it with increased mass and drag. There is simply no way to use this to make a launch cheaper.

No, that's not one of the advantages. 30km off the ground, optimal TWR is still about 2, and you are going nowhere but down with anything less than 1. Entirely workable. Except for the size of the "railgun". (You don't actually want a railgun, but rather a maglev linac. But that's semantics.) It's not quite as bad if you want to shoot cargo, but say you want to launch humans. That puts the cap at about 8G. So lets say 8km/s at 80m/s2. Acceleration will require 100s, which is survivable at 8G by trained crew, but in that time your ship will travel 400km. So you are going to need at least 400km of rail. This is a big deal even on the ground, but getting that to float in the upper atmosphere is just way too challenging. Also, if it gets even a little bent due to the winds, at 8km/s that can be catastrophic. Launch loop follows the similar idea, but it has some added advantages in terms of stability and wind-resistance.

I mistyped "drag" instead of "lift" where you highlighted, yes.

Anything based off Energia would be absolutely awesome. But I'd stay on the skeptic side until they actually build something. You really can't trust most of the claims coming from Russian aerospace these days.

There are some papers out there that describe null geodesics of the Alcubierre metric. (Clark et al., Muller et al.) These are very technical, but the conclusion is pretty straight forward. Standing on the bridge of a warp ship, you will only see a fraction of the universe. There is going to be a blind spot behind the ship from which the light cannot reach the bridge. However, you won't actually see a blind spot, because the portion of the universe you can see will be stretched to fill the 360 degree view. Similarly, if you turn on a lamp on the ship, there will be a dark spot ahead of the ship where the light from the lamp will not reach. So even if you shine light straight ahead, it won't come out from the warp bubble going straight ahead, but rather at an angle.

You seem to have a strange perception of what ATCs and pilots do that is incongruent with reality. Pilot's job is keeping a plane in the air. Their knowledge of avionics and aerodynamics is limited to what it do, not how it does it. They have mechanics and engineers to worry about the later. Same deal with ATCs. They can know a lot about regulations and equipment, but specifics of operation isn't part of it. My university has a good aeronautics program, teaching pilots, ATCs, and engineers. I've taken some classes from them back when I could do it for free as an undergrad. Trust me, a typical pilot and ATC know absolutely nothing about underlying tech.

It does. It's from the wrong era. It's not completely pointless even now, mind, but it should be balanced with things that actually explain what and why. I mean, take the same complex numbers as an example. Ok, we've seen plenty of examples of where they are used in this thread. But why? Why do they pop up all over the place when every measurable quantity is a real number? You learn the full answer is you study abstract algebra, typically around your 3rd or 4th year of undergraduate degree in pure mathematics. Field of complex numbers is an extension of the algebraic field over rational numbers. In simple terms, and dropping some nuances, complex numbers are important because some of them are roots of polynomials with real coefficients. Well, that's simple enough, polynomial f(x) = x² + 1 obviously has no real roots, but it has two complex roots, which is nice, but why should anyone care? Honestly, if it was just about the roots of polynomials, nobody would care. This is where group theory and analysis come in. In particular, Lie groups make a grand entrance. Long story short, because this would take up half a text book, any time you have infinitesimal transformations of any kind, the total transformation can be written as eix for some x. This is the reason why you see complex exponents show up in so many solutions of differential equations, and consequently in every branch of physics from mechanics to relativistic quantum field theory. Naturally, it's not necessary to learn all of the details of why it works this way, unless you are getting really deep into theory, but it helps when there is some natural progression to things. When you are presented with some examples of where things are used as you go along, and maybe learn some fundamentals of higher maths along with it, rather than just treat it as something too complex to grasp.

This isn't the whole answer, but it's a big part of it. These are binding energies of stable nuclei. Note that iron has the highest binding energy. That means to make iron into a heavier element you have to add energy. Up to iron, energy is released as elements fuse together. From this graph, He4, C12, O16, and Ne20 immediately stand out. You expect to see a lot of these four elements in a star, and you, in fact, do. The reasons why it works this way are a bit complicated. So first of all, neutrons and protons are fermions. That means that two cannot be in exactly the same state. They can, however, differ only by a spin. So at the lowest energy state, you can have two neutrons and two protons. That's He4. This group of four is so tightly bound because of that, that it behaves almost like a single particle. In fact, it has a name. Alpha particle. Well, if you consider heavier nuclei, the protons and neutrons in it still like to keep that tight packing, so they are often found in groups of four. Consequently, C12 nucleus can almost be pictured as three He4 nuclei bound together. There are a lot of experiments that confirm this. Ne20 is the next interesting case. Just like with electron shell, once you fill out the ground state, at a higher level you have two vacancies for particles with no angular momentum, and six for particles with orbital angular momentum. Levels are nowhere as neatly arranged as in the atomic orbitals, but up to this point you can use roughly the same rule of thumb. As the result, Ne20 has a full shell, giving it a total of 10 protons and 10 neutrons, and a rather high binding energy. After that more complicated effects take over, and the curve becomes fairly uniform as it peaks at Fe56 and then comes down. So why did I say that this isn't the whole story? Take a look at beryllium. You expected to see Be8, didn't you? Pants to that, says nuclear physics, laughs wildly in your face, and jumps out of the window. The fact is, a He4 is so stable that a Be8 almost instantly falls apart into a pair of these. Oddly enough, a stray neutron in Be9 prevents that decay, making it the only stable isotope of beryllium.

Because any monkey can plug numbers into equations. In fact, they have computer programs for that now. Any job that requires you to do just that pays about as well as working registers at McDonalds. Engineer's job isn't to compute some relevant quantity for a specific system. Like I said, there is computer software that will do it for you more often than not, and nobody is going to pay you good money just to type in numbers. An engineer's job is to find an arrangement of parts that gets the desired values within tolerances. That means solving optimization problems more often than not, and that requires understanding of differential equations and optimization methods. If you actually want to be good at it, the later requires you to understand mathematical analysis, which goes way, way beyond calculus. If you are getting a D- in high school algebra, cut your losses and consider a major in a soft science or liberal arts. You aren't going to be an engineer. And statistical mechanics, and electrodynamics, and electrical engineering, and normal modes in classical mechanics, and... Should I continue?

Relativity is relative, and that's useful to keep in mind. From perspective of people aboard the ship, the ship's mass never changes. (It's the universe around them that does weird things.) So you should immediately see why it won't work.

The only real mystery is why anyone still flies these deathtraps.

Lets take 1kg. Even with atmospheric effects, it takes less than 9.5km/s of delta-V to make LEO. That's roughly 45MJ of energy. What has 45MJ of energy? 1kg of gasoline. That's right. With perfect efficiency, you need 1:1 of fuel to payload to make LEO. If we convert this to electric energy, it's even cheaper. 45MJ is only 12.5kWh. I pay about 11 cents per kWh. So if I could launch cargo with 100% efficient magrail, I could do this for less than $1.40 per kg. Even at efficiency of a real magrail, I should be able to get it under $2/kg. That's about 10,000 cheaper than by rocket. And don't get me wrong, this is a lot of energy. It's just that we're dealing with lots and lots of energy on daily basis. That just isn't a problem. Efficiency is the problem. Rockets just aren't efficient. They aren't efficient in terms of energy use, or other resource use. The huge quantities of fuel we are forced to burn, while expensive to begin with, also force the use of huge fuel tanks and rocket engines, which are also absurdly expensive. There are, without a question, far, far more efficient ways to launch cargo. And like I said, we can drive the cost of actual launches to a percent of a percent of what we are spending now. It's just a matter of building required infrastructure which, at present, just isn't feasible, let alone commercially viable. No, it really wouldn't. Rotovator will have its place, but not on the Moon. Unlike Earth, the Moon does not have sufficient mag field to provide boosts to a rotovator. You'll have to run a reaction engine of some sort on the rotovator itself. Most likely an ion drive. Power might be solar, but propellant would have to come from the Moon and will make up a significant fraction of the cargo you lift on each turn. And if there was no competition, that would be fine. But on the Moon you can literally just build a magrail of sufficient length to launch things at orbital or escape velocity. No atmosphere. Lots of places with sufficiently level surface. Throw a nuclear power plant there, and you have the cheapest launches you can imagine. Cargo bound for Earth could be launched directly, requiring only minor corrections on the way. Anything heading for Lunar orbit would just need a burn to circularize, which can be done with conventional rockets without much fuss. On the Moon, there is no reason to use something else. Where rotovators might come really handy is lifting things off the surface on the moons and minor planets far from home. The awesome thing about rotovator is that you can pack it up and send it from planet to planet. This is something you cannot do with any other method discussed here.

Hm. He was the guy that Prometheus stole the fire from, wasn't he? I don't think it'd fit. If I recall correctly, he strove for perfection in his works. Not very Kerbal of him.

Then we couldn't go anywhere in reasonable time! Think about it, you got rid of the light speed limit. It'd take you a year to get to current light speed at acceleration of roughly 1G. So in 50 years, taking half of that to accelerate and half to slow back down, you'd only cover 250 light years. But with the speed of light limit, eventually, space contraction starts working in your favor, and in 50 years of ship time you can make a round trip to Andromeda. Yeah, millions of years would pass on Earth, but without the speed of light limit, it's not possible to make the trip at all.

If you are building a space elevator, you can make the crew cabin arbitrarily well protected from radiation. That's not one of the problems.

Food isn't so much for energy as it is for entropy. I mean, sure, if you are a predator, you need energy to chase your food, but if you didn't need food in the first place, there would be no need for chasing. The only way for life to persist, however, is by maintaining low entropy. Hence the self-replication, hence the need for food, and all the rest follows. Conservation of energy is one of these laws that's so fundamental, I'd be really paranoid about messing with it. The only way I can see it being violated without everything falling apart is if time is periodic. Then, instead of energy, you'd be dealing with quasienergy, which isn't strictly conserved. It'd be interesting to mess with some constants. Speed of light, plank's constant, etc. I'm sure there is a way to adjust these to get some interesting macroscopic effects without all of the nuclear physics and chemistry falling apart. It's just not something that you want to be able to get wrong. Oops, you've tweaked the strong interaction constant, and now neutrons are slightly lighter than protons. Everything just collapsed into neutron stars.

You are probably going to start seeing diminishing returns with higher order RK. This is a bit hand-wavey, but basically, the Nth order RK is going to be "seeing" a polynomial expansion of your potential. Unfortunately, expansion of 1/r around some r=R is given by a series (-1)nxn/Rn+1. This is geometric convergence, which isn't the worst thing in the world, but it still means you have to fight for each digit of precision. What's worse, when x/R is small, such as slow moving object far from source of the potential, the series converges quickly, and you can get away with low order RK anyways. When you start seeing RK giving poor results, it tells you x/R is large, and higher order RK method is going to give improvements that much slower. So going to higher order RK ends up giving you least improvement where you need it most. Variable time step is a good idea. It's going after that very x/R term. Since x is roughly proportional to time step and velocity, you can actually keep it constant and have the same quality of integration everywhere. Of course, as R gets smaller, velocity increases, so the time step would have to get very small close to sources. And you'll have to figure out how to keep track of different time steps for different objects in simulation. So it's still not trivial, but definitely something to try. I have been wondering whether it's possible to build a set of collocation points for a 1/r potential to integrate it exactly. I haven't seen anything like that in the literature, so I'm guessing that even if possible, it probably goes really bad when multiple sources are present. Still, I think I'll try it at some point to see how and when things go wrong.

Space elevator concept has a lot of technical problems. I'm not sure it will ever be practical in its standard telling. There are a lot of launch loop proponents on this forum. That would require some sort of a linac in its design. (Railgun is terribly impractical, there are much better linac types for the job.) Launch loop has an advantage of being almost reasonably sized, but still presents many challenges. It might be the most practical way to launch cargo and even crews into LEO at some point, but not any time soon. Various tether proposals are a great compromise between an elevator and a dynamic solution. Most of the current ideas are still a bit too grand to be feasible any time soon, but they are also much more scalable, so we might see something workable in the observable future.

I don't see why you need a toilet on a private jet, at least in U.S. There are places where it's harder to find a rest stop on a freeway than an airport. And if I own an airplane, there is no way in hell I'm letting someone else have the fun of flying it. Besides, something like Cirrus SF50 Vision is cheaper than Avanti, even a used one, will eat way less fuel, and would be easier and cheaper to store due to smaller size. Honestly, the only advantage Avanti has is the range. Almost 3x as much, but like I said, airports are like mushrooms after a summer's rain around here, and you'd want to stretch your legs and use the rest room about as often as you'd need to get more Jet A. If I had $1.5M to blow on an airplane right now, I'd get Vision or something similar. In the foreseeable future, however, I'd be lucky to scrape up enough for a 152. Or maybe an Icon, if I find good work closer to the ocean.

The point is that VLJs are in the right price and capability range to do precisely what you have talked about. Cater to the needs of the wealthy. A typical business jet is still designed to carry a group of people, or it ends up being too expensive. The neat thing about VLJs is that we couldn't even build these just a short time ago. Not with the sort of efficiency they have now. All thanks to miniaturization of turbofan engines. Similar thing can happen to a supersonic flight.

The fact that VLJ market is booming right now suggests that we might see supersonic and hypersonic private jets in the near future. I think some of the suborbital research could transfer to private flight. Whether we'll actually have private suborbital spaceplanes is another question. I'm guessing not without some really major breakthroughs in propulsion.

These come to us from Greek via a some other languages. In Greek, Earth is Γη (Gi), hence apogee means furthest point (along orbital path) from Earth. Similarly, Ήλιο (ÃÂlios) is the Sun. So we have aphelion to denote the part furthest from the Sun. Same deal with perigee and perihelion, but these denote the closest point. In principle, if you know the Greek name of the object, you should be able to construct the proper term for the apoapsis and periapsis of this particular body.

Yes, that's why I mentioned optimization problems. There are some cases when it's worth trying to work through polynomial forms analytically, but gravity isn't the case. You are better off treating it as finding a root of a general, non-linear system of equations. There are some solvers for that which you can try, or write your own. So long as you don't have anything too wild, Gauss-Newton algorithm should converge for a gravity problem. If you'll feel like going for NASA grade precision, give it a try. It's a challenge, but the sort that makes you feel good when you get it working. Whether you need it or not is a different question. If you want to be able to plot space ship trajectories or predict paths of comets, you do. You can test yourself by comparing your integration to data from JPL's Horizons. Pick a comet that passes close to a planet, and see if your computations agree with NASA's predictions. If you don't need that sort of precision, and you just need something believable, then explicit methods are fine, and yes, higher order methods will definitely work better. The only reason Verlet is so popular is that it does extremely well with harmonic potentials. So if you model collisions with Hook's law, you don't need anything fancier. Hence for most video game physics, Verlet integration is the only thing one ever needs to know.

I was hunting it in the morning as well, but it was a bit hazy in the eastern sky. I managed to get a solid fix on Spica, γ, and θ Vir. By eye, I could just barely make out γ with the edge of my vision. And I think I was able to just see 49 Vir through the telescope, but your picture clearly shows that if I could barely make out 49 Vir, I had no hopes of seeing ISON. Tonight looks like it will be even worse, but maybe I'll get lucky in the next few days. With a clear sky, I should have no trouble spotting it. By the way, what do you use for stacking?