K^2

That depends. You need local coordinate system to draw the ship's parts. Also to simulate the forces on all of the ship's parts. Clearly, a real ship can rotate. So the side/port vector will change with the ship's roll. If you want to simulate flight, you should keep track of it. And yes, errors will accumulate, but if you have stable flight, that will be consistent with typical effects of things like parasitic drag and other sources of torque on the craft. On the other hand, if your simulation doesn't care about the ship's roll, and you wish to simulate it as if the ship was maintaining constant attitude, your best bet is to simply choose a vector that's orthogonal to heading and the radial. In other words, just take ship's position vector in global coordinate system, which is along the radial, and cross it into ship's velocity vector, which I assume you treat as your forward vector. The resulting vector will be in the port direction. You just need to normalize it. The only potential problem is if ship's velocity becomes purely radial. You might want to check for that if you think it's ever a possibility.

I'm a little disappointed that this only works out due to silly US date format. I was going to wait for April 31st, but then I realized a flaw in that plan. I guess, I'll celebrate with some cheesecake. It's not a pie, but with above in mind, I find it appropriate.

Neither causes the other. As constants of motion, they are alternative representations of the same quantities. But energy and angular momentum are conserved quantities in a more general scope. So they are certainly related, and the later pair is more fundamental, but it's still not a cause and effect situation. Because gravity inside Earth starts to drop a few km in and goes to zero at the gravitational center of the Earth. The gravitational force bellow surface is roughly linear on the large scale, so if you were to dig out a tunnel, the falling mass would, indeed, follow an ellipse with center at the center of the Earth. But that's because we aren't talking about object orbiting a point mass anymore.

Or even just a pendulum with small oscillations. But yeah, it's 2D harmonic oscillator. It's separable in (x,y) coordinates and periods match on both axes. Any generic enough PDE solver should be able to. Just enter equations of motion for the differential equations to be solved.

You are mistaken. The gravity must scale as r instead of 1/r² to produce an ellipse centered at the body. 1/r produces completely different orbits, most of which are not closed.

They are. And Russia does not have the resources to retrofit them or get new modules they'd need in place for this. It's just loud words from politicians. Pay no attention to them. Russia might pull modules out of spite, but they'll end up being a dead weight.

A custom balanslcer is a very simple circuit to put together.

NASA has some . That should be enough even for some good 'chute data. There's also an option of dropping things off high altitude balloons. You can get one high enough up to simulate lower Martian atmosphere.

Hm. It does have sufficient payload capacity... It will be a tight squeeze, and there won't be much in terms of life support, but one complete U.S. Senate to low Earth orbit is entirely within reason even for Block I.

You might not get an actual boom, but you might, and there will definitely be heating, burning, and boiling electrolyte escaping the battery. Not a pleasant thing to be around.

Oh, Li-Po will just straight out explode with that sort of abuse. You can't even charge them as a parallel or a series circuit when they are in a battery pack. Each cell needs to have its own current regulator. There are types of rechargeables that can handle recharging from each other, though.

Flat spin is definitely a possibility. The only way to really deal with that is automatic cutoff and RCS response. If critical engine failure is detected automatically and opposing engine is cut off immediately, which is possible to do with a rocket engine, any remaining angular momentum can be absorbed by RCS even in total vacuum. Re-entry on failure danger is always there, regardless of engine configuration. There are a whole bunch of situations that can cause loss of propulsion during any stage of the ascent. And it is possible to design ascent profile to give a safe re-entry on failure. It would increase delta-V requirement, reducing payload, but if we are going to see regular commercial operation, which is the only scenario where Skylon-like craft make sense, we will need to see such measures taken. 2% fatal failure rate may be acceptable when you only expect a bit over a hundred launches in three decades, but if you plan to have hundreds of launches per year, it will be a PR nightmare. Total engine failures will happen to space-planes, and they will need to be constructed to handle such an emergency.

We aren't talking about Space Shuttle. It can't have balanced thrust by definition with tank attached, and without that tank, it can't use its main engines. It's a moot question. What we are talking about here is critical engine failure on something like Skylon. Something that's inherently balanced, still has TWR for vertical ascent, has aerodynamic capability for runway landing, and would become out of balance with an engine failure. And all you are going to do is the same thing you would on an airplane. Cut thrust, maintain airspeed, and continue flight until you can do an emergency landing. The fact that your engines are capable of 1+ TWR doesn't mean you have to use it.

I don't know about that... Loss of critical engine is a pretty typical scenario in multiengine aircraft, and aerodynamic forces are sufficient to maintain controlled flight. I don't see why this wouldn't apply to a hypothetical space plane with balanced thrust. Deorbiting burn would be a pain to perform with unbalanced engines, but there's no reason you wouldn't be able to perform an emergency landing if an engine failed during takeoff or reentry.

Just to clarify this a bit. Total mechanical energy of a satellite in a n elliptical orbit is -GMm/(2a), where G is gravitational constant, M and m are masses of the two relevant bodies, and a is the semi-major axis. (This assumes M >> m.) The potential energy of the satellite at some distance r from the center is -GMm/r. The difference between these two energies is kinetic energy of the craft, which is mv²/2. Solve that for v and you will have the speed of the craft. Getting orientation is equally straight forward, but you use conservation of angular momentum instead. The quantity vtr, where vt is the tangent velocity, is conserved. Furthermore, precisely at apsides v = vt. You can then get radial velocity from speed and tangential velocity using Pythagoras' theorem.

Open up any graduate textbook. Go to the index. Start reading until you find something catchy. Worked for Valve.

Sure. Pretty much anything that "consumes" energy does just that. There are limitations, but all of them are basically just the result of a requirement that total entropy increases, not just local entropy. For example, if you have a hot object and you want to make use of that heat energy, you have to make sure the heat flows from hot object to cold one.

Fine grain conserves entropy absolutely. Coarse can increase, but it's averaged out, so there aren't any random fluctuations there, either. And S(t = 0) can be anything without violating conservation laws, so long as dS/dt = 0. Same as it is with energy. Entropy doesn't really measure disorder. It is a measure of chaos, but in the Chaos Theory sort of sense. Picture a classical system in a particular state. I can encode coordinates and velocities of all particles as a single vector. So a state of the system at some time t is just a point. Now, I take a neighborhood around that point, and I watch how all of the states in the neighborhood evolve. The distribution of states at some t2 > t is a measure of entropy. Roughly speaking, the change in entropy corresponds to change in volume of that neighborhood. Of course, if we map all of the points one-to-one, volume is unchanged. (Liouville's Theorem.) On the other hand, if we take sort of a new bounding volume to see how much spread there has been, there can be a volume increase. This is fine grain vs coarse entropy. In mathematically precise statement, for fine grain, we only consider the exact mapping of initial to final states. For coarse entropy, we also consider an infinitesimal neighborhood of each state as part of the new volume. It's this averaging out in coarse entropy that prevents fluctuations from being a factor. Or, again, if you want to be mathematically precise, because we consider a neighborhood of each point, you cannot end up with coarse entropy being smaller than fine grain entropy. Which means that coarse entropy can increase, but it can never decrease. At best, random fluctuations can keep it from increasing.

Nope. Just not how entropy works. Even in Classical Mechanics things are way more complicated. When you add QM into the mix, it gets really tricky. It's a trivial theorem in Quantum Mechanics that entropy is conserved. (<S> = Tr(ln(ÃÂ)), d<S>/dt = [H,S] = 0.) So we're back to the distinction between fine grain entropy and coarse entropy. And coarse entropy doesn't allow for fluctuations like these.

No, because if your final altitude is low, you are wasting a ton of dV on that transfer to high altitude, which might actually be greater than savings on inclination change. For very small inclination changes it's often most efficient to do inclination change at your initial or final orbit (whichever is higher) and do a standard Hohmann in between. For very large inclination changes, it's best to go to the edge of SOI or Hill Sphere, do the inclination change there, and then return to your target altitude. For everything in between, there's the sweet spot somewhere above the higher of the two orbits and you need to do an honest bi-elliptic optimization. Also, the limits of how high is "very high" and how low is "very low" is entirely up to the parameters of initial and final orbits.

I'm pretty sure Rosco knows how to compute dV for inclination change at a given altitude. He seems to be interested in finding best altitude to do so. I can't help you much. Every time I need optimal bi-elliptic, I end up writing a script in Mathematica to compute dV given altitude of intermediate node, and then optimize that value numerically. Given the monstrosity that is the general form of that dV equation, I don't think there is an analytic solution. If you don't have access to Mathematica, this works equally well in Matlab or its free cousin Octave. I'm starting to think that we might just need to set up a community pool of various KSP-related Octave scripts.

It takes very little radiation for the right materials to glow in the dark. Watches that used phosphorus and radiation source to make marks permanently glow in the dark used to be commonplace back in the day. So it's entirely possible for whatever it is to be perfectly safe. Maybe if somebody had a full readout of these markings it'd be possible to say more.

Eve escape from 1 bar will still cost you over 4.5km/s in aerodynamic and gravity losses. That's more than twice what it would be from Kerbin's surface. This is due to combination of increased scale height and surface gravity. Of course, that's still a steal compared to 8km/s extra dV you need when lifting from sea level. Likewise, our own Venus is going to be enormously difficult to lift from, even if we can manage to build hardware that survives presence on the surface. If we are ever to have a sample return mission from Venus, an aerostat or blimp might be the best option of accomplishing this.

Adding a closed time-loop wouldn't offset global entropy. Just local. And as pointed out earlier in this thread, a refrigerator can already reverse change in local entropy. If time was cyclic globally, that would be a much more interesting scenario. I don't think it's possible to cause that, since that requires a topology change, and there is absolutely no evidence that topology of space-time can be modified. (E.g., General Relativity tells us how to manipulate existing wormholes, but nothing about creating a brand new one.) In either way, thermodynamics of a cyclic-time universe should be similar to that of a static universe.

Launch in KSP from sea level is over 4km/s, of which 2km/s are due to drag and gravity losses. Launching from high altitude in KSP is huge savings. Launching from an aerostat on Earth would save you at most 1-2km/s out of ~9km/s budget. It's not bad, if you can make the costs of this minimal, but this is nowhere near the margin you'd get in KSP, and I have a feeling that the operating costs won't actually be any lower.