K^2

My favorite example is the fact that MRI stands for Magnetic Resonance Imaging. While what it does is actually NMR Tomography. Nuclear Magnetic Resonance. They dropped the word "nuclear" from the name of the medical device, because it scares people. It has nothing to do with nuclear decay, nuclear energy, or ionizing radiation of any kind. But just having the word in there would be enough for people not to get MRI scans. So yeah, I'll say it again. We need better education.

No, they are not. Russian for black hole is "чõрýðѠôырð," which literally means "black hole". You might be thinking of some other language, but it's definitely not Russian.

Orbits don't work this way. Earth's orbit is stable. So a small deviation results in planet still returning to the point at which deviation occurred a year later.

Apparently, WinE is being developed for ARM Android. That might be an option for running KSP-TOT along with MCR on an Android device. It won't be fast, though.

Hm. It might not be so bad. I used to do a lot of code in Matlab, but switched over to Octave in the past few years. I can take a look at it. If it's just the GUI stuff, it might not be so hard to port. Edit: Nope, never mind. These .fig files would be a nightmare to try and port.

Historic reasons are strong here, but you also have to keep in mind that there are a lot of places where pi appears by itself, and where we'd have to start writing tau/2 instead, which is even more inconvenient than writing 2pi. The most trivial example is pi r², but it's all over the place.

You've obviously never watched Iron Sky. (It's on Netflix, by the way. I highly recommend.)

In simplest terms, for a 2-body system, Lagrange points are points where you can put a 3rd body so that it stays there. In more precise terms, Lagrange points are extrema of the effective gravitational potential of the two-body system. For example, if we consider the Earth-Sun system, there are five Lagrange points. The L1 is between Earth and Sun, L2 is always behind the Earth, L3 is always on the opposite side of the Sun from the Earth and L4 and L5 are leading and lagging, respectively, in Earth's orbit. Most of these points aren't stable, but they have stable orbits around them. (Halo orbits, Lissajous orbits, etc.) If you want a satellite that stays in the same position relative to both Earth and the Sun, these are the points you'd put your satellite. So L1 is useful for solar observatories, and L2 is good if you want a place where sunlight does not interfere with you watching the sky. Other three points aren't particularly useful, but they do tend to capture asteroids. Not so much in the Earth-Sun system, but very much so in Sun-Jupiter L4 and L5. That's where the Trojan asteroids are located.

Very important distinction, by the way. Though, it only becomes meaningful in context of General Relativity.

Whoever said that does not understand anything about celestial mechanics. With the exception of the few launches that result in debris or ships escaping Earth's gravity completely, all of the things either remain in Earth's orbit or decay back to Earth. That means that the total momentum of the Earth system is preserved, and Earth will continue on the same exact trajectory around the Sun, no matter how many satellites we launch.

Yeah. As I pointed out in another thread, you can install Octave on an Android phone. That software is more than capable of doing all the computations you need to do a Moon landing. P.S., it's free. So that should answer your other question. Of course, you'd still need someone with knowledge and experience to actually run the computations.

ZetaX is kind of right. Jumping at the last moment effectively doubles the braking distance, which has potential to cut forces by as much as a half. That means that it increases the impact speed from which you can walk away without injuries by about 40%. On the other hand, if we are talking about survival, you basically sacrifice your legs to the impact. There is no way to replicate the same thing with a jump. I mean, no matter how hard you jump, you won't be able to break your own legs. So contribution of the jump is absolutely minimal, and if we are talking about a lethal fall, jumping won't make enough of a difference.

Here is the check. If the bullet is traveling at half the speed of the train, something went wrong.

You should be checking your numbers to see if they make sense, though.

Special Relativity is a sub-field of General Relativity. So technically, saying that this is so according to GR isn't false.

No, because it doesn't help you any. Creating matter takes up energy, so you'll have the same net efficiency. Say, you have exactly 1kg * c² of energy. Your first option is to focus that energy into a beam of light. That will get you exactly 1kg * c of impulse. Your other option is to convert some part of it into matter, and use the rest to accelerate matter. Suppose, you created some quantity m of matter. That leaves you with (1kg - m) * c² of energy to accelerate it. The total energy of that matter, once you accelerate it, is going to be γmc², which still has to be equal to total energy you started with, 1kg * c². So γm = 1kg. On the other hand, the impulse you are going to get is γmc, and with γm = 1kg, that's the same 1kg * c of impulse that you'd get with light. So it really comes down to which one you can do more efficiently. Convert energy to light or convert it to matter and accelerate it. In practice, converting energy to matter tends to be inefficient, so you are better off with a photon drive. Now, if you happen to have that mass already sitting around, then you are cooking with gas.

The most plausible way time travel can work* is by requiring that the "time machine" exists from the time of destination to the time of origin. Think of it as more of a tunnel than a vehicle. (Primer actually did a pretty decent work of it.) So the fact that you cannot send a message to yourself now merely says that there is no time machine available to you that goes to this particular time. It doesn't mean that you won't have access to a time machine of some sort in the future. It might simply be one that doesn't carry you far enough back to deliver such a message. *The only well-tested theory that currently predicts time travel is General Relativity, and it has some requirements that make it tricky, but not impossible. It might never be feasible, but it sets the standard for the way time travel can work and the way any possible paradoxes are resolved.

This is basically how rocket stages work. And it runs into the same sort of problem. If each earlier stage has to be 20 times or even more larger than than the next one, you plausibly can only ever have a few stages. Eventually, you still run into the same problem as with a single stage. The faster you want your final speed to be, the exponentially larger the rocket and amount of fuel needed has to be. Staging simply lets you drop heavy engines you no longer need to carry a smaller rocket. And, of course, as you near the speed of light, speeds no longer add the same way they normally do, so you'll never get past speed of light. But even getting to any noticeable fraction of speed of light is practically impossible with chemical rockets, and insanely difficult even with nuclear propulsion.

There are many simple ways to get a turn without overshooting. Difficulties start when you want it to be optimal in some sense. For simple maneuvers, you can use PID, for example. That's what KSP uses for ASAS. It's not great for rotations, but you can figure out the right coefficients to make sure you never overshoot. If target is moving, you can also have PID work in a rotating frame where it's roughly stationary. It's far from perfect, but it's simple, and it's enough in a lot of applications.

I found that in most problems of this type, the optimization algorithm is iterative, and you can put a filter update and optimization iteration into the same loop. That way, you get continuous tracking without major overhead. So for the most basic example, write functional you want to optimize, get the latest position/velocity, run Kalman update, run a single step of Gauss-Newton on the input vector and functional to be optimized, rinse, repeat. (P.S. I've written something like this for Wires in GMod to fire tracking missiles at other players on the server, albeit, with a simpler filter and just a simple Newton algorithm step. Was fun.) But I have a feeling that all of this is a bit overwhelming for the OP. I'd recommend starting with something much simpler.

You use linacs to accelerate said hydrogen to get thrust, as people have already implied. Which does have potential to have best ISP, but you basically have to have matter/anti-matter reactor to get that. Otherwise, having some sort of reaction mass is going to make a huge difference in efficiency. Even interstellar hydrogen is better than nothing.

First of all, at 0.99999c, your proper velocity* is only 223.6c. So it would take you well over 400 years to cross 100kly. And you got your math backwards in map frame. At that speed, you'd traverse 99,999ly in 100,000 years. Finally, I think that's what SargeRho was talking about. He just didn't bother to verify any of the numbers. * Proper velocity is defined as distance of map time traveled per unit of proper time. In other words, how far you travel through the galaxy in a given amount of ship's time. This speed can exceed speed of light due to structure of Minkowski Space. Which is another reason to think about it in terms of proper velocity. It gives you a good idea of how much dilation the ship will experience, how long it takes to cross a certain distance, and how much energy and momentum the ship has. A ship traveling at 400c proper velocity will cross a certain distance in the same time as a ship traveling at 200c proper velocity, because both are basically going at nearly the speed of light, but the former will age half as much as the later. And that's useful information here.

Even in the States $30M USD aren't the same thing today as it was in 2008. In Russia, things are much worse. You can't just watch the way Ruble slips relative to Dollar. You have to take a look at the way prices and costs have been increasing across the board. The difference between buying power of $30M USD in Russia in 2008 and today is very significant. I'm also sure you realize that amount that the money is going to buy you depends very much on the channels it ends up taking. Just because somebody figured out how to have part of the $30M settle in their pockets to make a profit, doesn't mean that the launches weren't made at a loss. The loss would simply be taken out of budget somewhere else, turning the whole thing into a grand laundering operation. Similarly, of the $70M per seat today, I would expect a large fraction ending up in pockets of officials across the chain. Since this is a deal between governments, I wouldn't be surprised if larger fraction is lost in various kickbacks. So again, you really can't be making a comparison here.

In a perfect world, yes. In the real world, axis of rotation will probably tumble, and you'll end up with a different RCS orientation than you started out with, requiring a different amount of RCS thrust to stop moving. That's even if you started out with a nice symmetry in RCS port arrangement, which isn't a guarantee. Result is that it can take more or less time and fuel to stop rotation than it took to start it, depending on how things align. Rotation optimization problems in 3D are actually crazy difficult, because rotations are cyclic, do not commute, and axis of rotation rarely coincides with principal axes. Fortunately, an approximate solution is almost always good enough, and these are easy enough to crank out.

Have you taken Russian inflation into account, though? Back when the tourist was launched, $30M was a lot more than $70M today by a wide margin. There is no question that Russians could do this for less if there was competition, but this wasn't a good comparison.