Z-Man

To clarify a potential misunderstanding (I read that wrong myself first): Of course a baseball passing by at .9999c will have a much bigger gravitational effect on you than one passing by at .99c. However, the effect is still tiny, and no matter how much energy you pump into the ball, the effect will be weaker than what you'd get if you convert the energy into mass and just place it next to you. The speeding ball has the severe disadvantage of only being close to you for a tiny fraction of a millisecond.

Let me rephrase my earlier statement. Standing still without using power or using arbitrarily low power is only possible if you allow direct or indirect interaction with the ground. The rock and dead man directly interact with it. The helicopter indirectly interacts with it because the air it pushes against is held up by the ground. A sci-fi hovering device using polarity reversed tractor beams to keep its distance can also use as little power as circumstances allow. The EMDrive claims to be no such device. It claims to work in a vacuum. So if it can produce 33 kN from 1 kW while hovering, it also needs to be able to produce that in any other reasonable situation. Easy small modification: It also needs to produce the same thrust while ascending with 10 cm/s. In which case, it will increase the potential energy of whatever it is pushing up by 3.3 kJ each second (use Heimdall's formulae, I'm personally using g = 10m/s2 for convenience), so output power would be 3.3 kW. More than the input power. The same argument can be made, using higher ascend speeds, for any direct reactionless power-to-thrust engines as long as they are more efficient than a photon drive. If the device is as efficient or less than a photon drive, the speed required to break energy conservation becomes c or larger, and the argument breaks down.

True. However, you get graphene from graphite by peeling off the layers, which breaks those weak bonds. If you stack them again with nothing in between, the bonds should be re-established. If you put "glue" in between, the story is different, of course, and what you get strongly depends on the glue.

And to pinpoint the specific mistake, a also enters with a plus sign into the deceleration phase. You have it with a minus. (If you want it with a minus, use your first equation, but with a v_0 equal to your max velocity.)

From the perspective of an observer gently floating down with 10 cm/s, 3.3 kW. And you're allowed to switch to that observer's view if the device is supposed to also produce the same thrust in a vacuum. You would not be allowed to if the device in question was, say, a solid floor. (The force to hold up 3.3 metric tons is 33kN, by the way.)

Stacked layers of graphene ARE graphite. I would not expect any extra advantages that may come from your sheet being more regular than natural graphite.

Well, at least that claim will be easily falsifiable. John FX: Difference being, the early combustion engines still worked without a shadow of a doubt. You put gasoline in and got a reliable and easily measurable amount of work out of them, far more work than could be explained by the fuel just flowing down (but also not so much that they'd violate known laws of thermodynamics).

No need to go over the mass of the bodies! You only need to know two laws. The first is that gravity acceleration goes down with the square of the distance: I : aG® = C / r2 With some constant C. The second law is that of the centripetal acceleration of circular motion: II : actp® = v2 / r From the surface gravity of Earth and equation I, you extract C: C = surface acceleration * (diameter/2)2 Then, for r = orbital radius R of the moon, you set aG and actp equal, because that is the state of equilibrium (faster or slower movement would yield an elliptic orbit, escape or crash) C / R2 = v2 / R => v = sqrt(C / R) And you'll probably find that it's hilariously fast.

The cannonball thing is the only thing with a remote chance of being practicable. Yes, the balls would be the propellant, but the key thing is that they would be recyclable; the other ship would catch them. Now you only need to find a way to launch them with 22km/s+. Easy! Compared to the other suggestions, I mean. Catching can happen at arbitrarily low relative velocities.

Ah, right. I misread what you wrote in your original post then when you said you set v0 to 0 specifically for vx. And didn't you also say TWR peaks at 3?

You built that in explicitly with the v0 parameter for vy. If you force that to zero, If you take that out (and I think you should, now that you brought attention to it) you only get finite thrust at the start. The same is true at the end: You can only get the behaviour out of the process that you explicitly allow for in the parametrization. But yeah, if you only optimize for total dv spent without TWR limitations, easing the throttle down at the end may be a good thing, Oberth and all. And even with TWR limitations, Kerbin has such an insane atmosphere thickness to radius ratio that just leaving the atmosphere gives you more than enough time to push to orbit efficiently even with lower thrust. Maybe h is not the best argument to parametrize after? Maybe the total energy per mass ( g h + (vx2 + vy2)/2 ) or some modification would be better? If the rocket is not increasing that one steadily, it's doing something wrong

That depends a lot at where you mark the end of the visible universe and which cosmological model you want to consider and how you want to make the mass appear. But the principle answer is easy: Figure out how the current density of the universe needs to be changed right now to completely stop the expansion. How much mass would you need to add to the visible universe to achieve that? That's your answer. The ballpark number to expect would be the total mass of the visible universe including dark matter and dark energy. Dark and regular matter apparently was dense enough to significantly slow down the expansion once, and you need to compensate for the extra dark energy that has appeared since them. So that would be about 1053 - 1056 kg. Err, and that mass has a Schwarzschild radius of 1010-1013 light years... where do you plan to put it? Of course, with that size, it no longer is an ordinary black hole, it interacts in interesting ways with the cosmological curvature and dark energy. The actual radius of the horizon would likely be much smaller. And that's the other way to get a bearing on your answer: The outer reaches of the visible universe appear to be moving away almost with the speed of light. What gravity force is required to reverse that? Right, an event horizon almost right behind them. So you can expect to need a mass big enough that it would usually generate a black hole with the radius of the visible universe. Well, if you magically let so much mass appear, you inevitably break the known laws of GR everywhere in the universe at least at one time. So you may as well do it in a way that everyone is "informed" of the new mass any time you like. Even in the "past".

Very nice. I see a small problem at the end of orbital insertion, though, probably not big enough to cause worry and easy enough to fix if it turns out to be relevant. Since you want vy = 0 at the end, you naturally have dh/dt = 0. If you have any x-acceleration at the end (and you should have), you have dvx/dt > 0 and in the parameter target function dvx/dh = dvx/dt / (dh/dt) Which would be infinite and the polynomial parametrization can't deliver that. The problem should manifest itself in the T(h) function: if the above is right, it should go to zero for h = hmax, which may not be terribly optimal. Easy solution: Add to the vy target function d * ((hmax-h)^(1/3) - hmax^(1/3)) d being a new parameter. I hope the exponent 1/3 is right, it should be what allows for a finite acceleration at the end.

Because they imagined a better life over there one way or another. Millions went because they were starving at home. You mean the modern Las Vegas we know now? Liberal gambling laws. That may apply to the moon, actually. No laws for now. You can do all the organized low gravity man on bear fighting you want!

That's not impossible in principle. However, the other ingredient you need to extract energy via a tether is an ionosphere that is stationary more relative to the magnetic field than to your craft. I don't know whether there is enough of an ionosphere where you want to place the probe, but if there is, it will also be moving along with Io.

You mean, in the general relativistic sense, like gravity does? That would be news to me. (And also way too weak to have any effect with that feeble input power.) Can you provide a source?Late edit: Something else is bothersome about that vacuum technobabble. They always cite the enormous energy density you get when you sum up all of the modes of the EM field up to the Planck Lenght when they argue how much untapped potential there is... Well, to a practical device, only a tiny fraction of that is accessible. How much? Well, give or take a factor of 1000 and some pis and twos we're going to drop right away, a microwave cavity has access to one mode of vacuum fluctuations, the one of the frequency it is excited with. Its energy is E = hbar * omega and that energy has to be though of as distributed over the whole cavity. If it were to flow freely, that energy stays in the cavity for the time 1/omega and is replaced with new energy to potentially exploit. So the total power usable is about P = hbar * omega2 And photons of that power deliver a force of F = P/c = hbar * omega2/c Plug in 1 GHz for omega and we get an estimate for the total thrust available: F = 3.5 * 10-25 N Ouch. That will not take anyone to Mars. Due to dimensional analysis coincidence, this is also the ballpark formula for the Casimir Force on the cavity from the outside, another possible logical entry point for determining the maximum thrust for a given geometry. A more thorough analysis will show you that you can improve the value by making the cavity flat in the direction you want the thrust in. Like what the Cannae drive is actually doing. Only it's not doing it enough, you'd need to shrink it down to the micrometer range. And you need to find a way to make the Casimir force only act on the backward side. A real one-way mirror would be neat. Hmm. Hang on a sec, I need to file a patent, think of a name and register a trademark. Then figure out whether it can work. Yes, definitely, that is the correct order.

Meanwhile, I have to give up looking for useful material on the Q-Thruster thing theoretical background. The picture Rakaydos posted earlier is all there is. It's from this paper: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf Needless to say, the picture is useless. None of the terms are properly explained. None of the individual bits are evident nonsense, but it's impossible to see how they should fit together. Link to the relevant talk on the Starship Congress 2013: Practically the same content. In both sources, they talk about a model of the vacuum developed by White that calculates stuff we already know about with great accuracy (that would be QED) and predicts that Q-Thrusters work (that wouldn't be QED). But that model is nowhere to be found in public view. I'd love to be proven wrong on that.

You are using advanced Fermi rounding here, rounding intermediate values to the nearest power of 1000. Text quotes in part from Wikipedia: That's a thrust to power ratio of 288 mN/kW. (Note the different units) That's 7 mN/kW at peak. A factor of 40 lower. That's 1.7 mN/kW. Even lower. The EMDrive like device tested at NASA really is quite similar to the original, the only difference is the added dielectric. And I agree with them that IF the device works, that's something that would help. So essentially, the NASA test says that at least 97.5% of the Chinese results are wrong. Chances are very high that the remaining 2.5% are also a fluke, despite all the effort put into the measurements.

That is as precise as one can get with words and the virtual particle picture.ZetaX: Sorry, I have to agree with Mazon Del that what you want is impossible. It would be impossible for any regular subject. You do not have enough time to read the original papers, but want the full math. That's a non-starter. In this special case, it's worse. The original material is severely lacking. The EM-Drive theory paper is known to be faulty for neglecting the force on the slanted walls. It uses pure electrodynamics, no quantum theory involved. There exist no paper on the Cannae-Drive AFAIK, all one can gather from their presentation video is that they did numerics. The recent NASA paper claims not to give any explanation in the abstact, but also mentions NUMERICS several times in the main body. You will not find a proper physicist capable of taking all that as input and producing an output that makes sense. That does not mean, of course, that any experimental evidence for these devices actually working should be outright ignored. Just taken with a good helping of salt until the kinks have been worked out and they have been independently verified (the Chinese don't count due to the hugely different value they measured). I do not mean to ridicule the researchers, only perhaps those who claim this is the final, irrefutable evidence of mainstream science being wrong and stuff. And yes, the original Q-Thruster as explained by Rakaydos is a totally different beast. I'll try to digest the material for that.

Our watermelons here are mostly spherical without being grown in zero gravity. The oblong ones you know must be a different kind, they would likely still be oblong when grown in space.

Splendid read. Also two links in (via Baez, also always worthwile), the full article (may no longer work by the time you click it): http://rghost.net/57230791 So yes, the information in Wikipedia is essentially correct. They tested the Cannae Drive, a dummy modified Cannae Drive without the slots, and a device very similar to the EMDrive (though never referenced as such), key difference being that this one also was half filled with a dielectricum. And test loads to verify they got no thrust/torque from cables and stuff. Power levels were 17 Watt, tops, a rare case of XKCD getting numbers wrong. That the dummy device produced the same results as the real device is not terribly surprising: The slots are way too small to have a significant effect on waves of that frequency. One more little observation: They do not say which way the thrust went when they mounted the devices the other way round. I'd assume it also changed direction, but I also would assume you put things into a vacuum chamber to test them in a vacuum, so there. And on the pictures, you see that the devices are almost touching the vacuum chamber walls. If it's not thermal effects from the air inside the chamber, definitely near field effects are next on the suspect list of perfectly normal explanations.

Umm, if you mean actual height of 72km, that is almost certainly too late to be optimal. By the time you reach that height, your apoapsis is already way too high for anything close to an optimal flight for a typical rocket. If you mean "until your apoapsis as displayed in the map screen is at 72000 m", yeah, that would not be the worst rule of thumb.

Well, to their credit, those particles do exist and their effects have been experimentally demonstrated... It's just 1. They are just a pretty picture of what the nontrivial vaccum of QED looks like; it is useful for some problems, but not all. 2. They pop into existence with zero combined momentum and to vanish again, they need zero combined momentum. You can't just let them show up, dump momentum into them, then bugger off. You either need to dump enough energy into them to turn them into real particles (nothing gained then) or they use their power of quantum precognition (complaining that this is not a thing? See point 1.) and not turn up in the first place or refuse to interact with your device. And none of the original explanations for the EMDrive and Cannae Drive even use virtual particles. They're purely classical (relativistic) electrodynamics. It's at this point massively unclear to me what kinds of devices were tested, though.

Watching. Get a kid. Mine woke me up for Curiosity

This one not a press release (The arsenic life one was). It's not even a scientific publication. It's a conference paper. Blowing it out of proportion is entirely the fault of the press and enthusiast community.