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Against the parachute line, of course! She was attached to it (her foot got tangled up in it). That proved to be enough to cancel both her and George Clooney's radial velocity relative to the point to which that line was attached (and as the estimates above go, that's half a metric ton at at least 1m/s). And then, all of a sudden, it is "freely sliding against her foot". I mean, yeah, it's plausible. We could assume that at large forces the rope is tight and friction is sufficient to stop those two with a jerk (although this is the point where the 350 or so kg of George Clooney and his equipment should have just gotten ripped from her grip), but when there's only a smaller force left it starts to slip and all. All in all though, there's quite a bit of handwavium involved. Less handwavium than using a fire extinguisher to propel herself to the chinese station, but still quite a bit. Before anyone accuses me of trolling, yes, the concept is valid, but the long and almost static scene where she is holding on to Clooney and saying "don't let go" at the very least does mislead into thinking "ok, they've stopped, now just gently pull back, your foot is safely tangled up back there". And I don't remember seeing the parachute line slipping against her leg (like I said, I'd really want to study that scene carefully again).

PS Frankly though, in a rocket we're generally stuck with a fixed Delta-V budget and then all that could possibly matter is traveling at the highest possible speed when burning. Still trying to figure out a scenario, where we could need to optimize for anything else...

That's just not true. Energy is conserved in any inertial frame of reference, it's just a matter of deciding what energy is useful. When I got the result that suggested having as low exhaust velocity as possible, I compared the energy of the rocket minus the about-to-be-expelled propellant as the starting energy with the energy of the rocket after expelling the propellant after the burn. Now that indeed is a quantity that is dependent on the frame of reference. If we sum up all energies (i.e. also take into account the kinetic energy of expelled propellant), then it doesn't matter which frame of reference we choose, the increase in energy will always be dm*v^2/2 (where dm is the differential of mass expelled, v is the exhaust velocity). However, as we don't really care what happens to the propellant after we lose it, it makes little sense to take into account it's energy after the burn.

The weight of a marble? Really? Was that tether coated in Teflon and grease, that she struggled to hold that weight? I'd sooner go with the opinion, that the makers of the movie made an outstanding job of this problem of centrifugal force pulling the astronauts apart being as unconvincing as possible in that scene. I'd like to see that scene again, but I struggled to find it on youtube (bummer...), however in the theater not for a moment did I have the thought, that they were actually spinning around the station much.

Not quite. I minimized useful chemical energy for a given increase in orbital energy (though that probably leads to the same thing). And I clearly pointed out, that that would lead to an increase in propellant used. However, you ignored my last question. In your scenario you suggest to have exhaust velocity equal to orbital velocity. To get a result like that, what should one be seeking to optimize?

No need to go about time-dependent interactions. Let's just stick to infinitesimally short burns and differential equations :-) That's what I did right now and came to quite a surprising result. I tried to find the optimal exhaust velocity of the propellant in order to get the largest energy increase of the orbit (i.e. the increase of the kinetic energy of the vessel in the reference frame of the parent body) compared to the energy extracted from the propellant (for simplicity's sake I disregarded waste heat and such as we're only interested in the kinetic stuff anyway). It turns out, the smaller the exhaust velocity, the better (for a given amount of chemical energy used). And, of course, the larger the velocity of the rocket, the better too. Obviously, with smaller exhaust velocity you will need to expel a quadratically larger amount of propellant though. So this leads me to the question "what exactly are we trying to optimize here?". Chemical energy of propellant to energy increase of orbit? Delta-v budget to energy increase? Or something entirely different?

That's the problem though! The mechanical energy of the system is not conserved, regardless of coordinate system as chemical energy of the fuel is being converted into kinetic energy.

If we learn to manipulate stars, drawing energy from them as necessary, I'd give an higher upper limit around 1E40 years.

In terms of dV spent to increase/decrease the energy of your orbit by a certain amount - yes, it is most efficient to burn at high speeds. It's a reversible process.

K^2, there is something in your reasoning that just doesn't let me accept it. You are saying, that energy lost by propellant is necessarily transferred to the kinetic energy of the rocket? Imagine if we expel propellant at double velocity of the rocket relative to the parent body. The expelled propellant will have the same kinetic energy as before (it will just be travelling in the opposite direction), however the gain in the kinetic energy of the rocket will be considerably greater. Someone mentioned black holes on the first page, by the way. Is the Oberth effect still just as valid when general (and/or special) relativity kicks in?

Sure it does. But a matching matter-antimatter pair isn't exactly an "arbitrary object". Also, the observable universe does not seem to contain too much antimatter either.

There is no straightforward way to convert arbitrary objects into energy.

Oh, good one! Well, as long as the entropy of the universe has room to increase, everything's cool. This has been pictured in this awesome video:

Oh, that is awesome! As a kid I had an awesome sci-fi kind of book written by an author from Soviet Russia. Four youngsters were given an interesting device that allowed them to modify some laws of physics, such as reducing friction to near zero values, adjusting the speed of sound, turning time backwards and such. When someone flipped the switch to turn off energy conservation, a pebble was thrown at a mountain. By laws of conservation of momentum the mountain got upturned and started sliding off the island it was sitting on, whereas the pebble shot off into space at relativistic speeds.

I think, the current version doesn't have this anymore. The community has been so active, that testing is now a closed process - the efforts of a select few are already sufficient for the QA process. That said though, I haven't experienced crashes in a long while now (what am I doing wrong???!).

By the looks of it, some mods end up being picked up on by the devs and making their way into the stock version. I'm pretty sure, that deadly reentry will end up in the game sooner or later, but right now it is also available as a mod. I too prefer to play stock, though.

Well he didn't say that really. If for the same atmospheric pressure the function of an air-breathing engine is more or less the same, it's reasonable to assume, that the partial pressure of oxygen is also the same. Given, that the rest of the atmosphere is more or less inert and can be considered buffer gas (as is the case, say, on earth and perhaps, by extension, on Kerbin) a different concentration of oxygen will lead do a different behavior of the engine. So if the engine functions as normal, we should expect a similar oxygen concentration. Admittedly, that may not be too valid if, for instance, Laythe's is composed of heavier or lighter gases, thus having a different speed of sound which, undoubtedly, would be important for an air-breathing engine.

Emilynn and Hellou in Brotoro's Laythe missions are just too awesome not to have female Kerbals.

The simplest implication of that is that maneuver nodes should not allow to predict the point of entry into the sphere of influence. I.e., it's fine to calculate the closest approach to a celestial, but you should not get the information for the next conic. That would also mean, that maneuver nodes will be useless to plan gravity assists from planets until you actually science out their parameters.

Our moon heats up to 200c (and cools down to -170c) because it rotates so damn slow (thus being exposed to light and dark for extended times). And because there is no atmosphere to redistribute the heat evenly across the moon. However, the bulk of the sunlight actually goes towards heating the ground on earth as well. It is then convection, not radiation, that transfers the heat from the ground to the air above it. That is also a reason, why it is much colder in the mountains at high altitudes, that would not be the case had the sun heated the atmosphere directly. For the same reasons, if the air temperature is as warm as 4c on Laythe, it is reasonable to expect, that the top layers of its surface are also close to that value, no more, no less.