K^2

It's possible to come up with differential geometry for space-time where light bends away from the flat Earth, creating effect of the horizon. Essentially, it's a slightly more complicated version of Coriolis Effect.

Discworld doesn't really get into physics of it, beyond the very basics. Though, it does have some very neat ideas. What it comes down to is that if you wanted to come up with a world which is much like our own, and would be indistinguishable from just some basic observations, it's not that hard. But we have too much data. There are satellites, the GPS system, cosmology and all sorts of obsrervations of the space around us. The topography which includes curvature, the time zones, and just general topology of the world. And then there are experiments that look at Earht's gravity variations and measure the rotation due to inertial effects. Too many points of data. Now, it's entirely possible, and almost rivial, even, to construct a coordinate system which is entirely cyllindrical, in which Earth's surface is a disc. (Ok, technically, one point will be missing in the mapping. But you can't physically approach it.) Then you can construct differential geometry that allows for entire universe, with all of the bodies in heaven to move the way they do. And at the Earth's surface we'd be experiencing the gravity that we do. Problem is, this is just a coordinate transformation. It's taking the world as we typically think of it and casting it in a weird coordinate system. Physics allows for it. It's the same sort of deal as with making Earth the center of the universe. You'll end up with all sorts of weird laws for motions of things, but otherwise, it will be entirely sensible. And all it is is taking something that's very intuitive as a sphere, and making it into a very counterintuitive disk.

Totally. Absolutely ignorant. Serious grade nonsense. But yeah, things weren't really moving faster than light. Universe was expanding faster than light. (Still is? My cosmology is rusty.) The speed of light limit is a local one. So it's ok for two remote objects to recede from eachother at any speed, provided that the space-time in between is sufficiently warped, which was definitely the case. It's only when things are close together, so that space-time in between is sufficiently flat on that length scale, that things can't move faster than light relative to each other. It might sound like a pretty major loop-hole, and it is. It's exactly what warp drive is meant to exploit to allow FTL travel. Of course, warp drive is theoretical, while FTL expansion of the universe agrees with observation. As for light "not existing", it's not exactly right. All of the fundamental fields were in place from the start. It's just that in that original mix, distinguishing between different interactions was complicated. Electromagnetic interactions had to decouple from everything else before you could really talk about light as such. But because all of the fields were in place, speed of light was already a thing.

I would be willing to bet that the original primary host wasn't human, but some other predator. The secondary host could have been some related wild species as well. Evolving all of that behavior from scratch during the period of domestication would be unlikely, but if the adaptation was simply to switch hosts, it seems quite plausible.

I've pointed out problems with gas giant as a parent planet on the first page.

As usual, weather promises to be cloudy around here. Fortunately, I'm moving to a much sunnier place in a week. Unfortunately, it'll be too late for this particular comet.

Computing gravitational pull isn't the hard part. Caching it is overkill, and is likely only to make things more complex than they are, since you'll still need to compute corrections between the grid points. I'm guessing you've never studied the topic of integrating equations of motion. Simply computing forces isn't sufficient. Forces are going to change from one frame to another, and if you do updates as if they are just spikes of impulse at each point (Forward Euler), you'll end up with huge error accumulated. This is true even without involving gravity. For that reason, video games typically use Velocity Verlet. But for gravity, even that is absolutely terrible. The gravitational potential is 1/r, which means no power expansion is ever going to be exact. Worse yet, in n-body problem, the bodies are in motion. Which means that there is no coordinate system (Such as barycenter coordinates for 2-body problem) in which energy is conserved. So even if you could construct a proper conservative integration technique, it would be useless. What does that mean in terms of the game? That results of integration aren't going to converge. No matter how small time steps you take, over large enough time frame, the error will be too high. That wouldn't be too bad if you only had to do this once. I mean, it's a game, it doesn't have to have NASA-grade precision. But then any tiny changes in initial condition would result in different integration results. This could still be ok if no forces were ever applied to ships, but add any kind of force on the craft, and everything flies to hell. Did you notice that sometimes, when you have a very iffy intercept, the predicted trajectory starts to flicker between two states? Well, that's how absolutely everything in the game would be. Every single trajectory would jump all over the place, and maneuvers as simple as Mun intercept would be come almost impossible. It's possible to improve on that. You can use very complex implicit integration techniques, similar to these that NASA uses, to greatly improve precision. This is where CPU intensity comes in. These are very heavy computations. And they can still only tell you where a particular asteroid or a comet will pass within a huge margin of error. That's ok for real space flight, and for hard-core simulators, because you never expect to just do a burn at LEO, and do a perfect insertion into Moon's orbit. You'll have to do additional burns along the way, as you see that what you predicted in original computation isn't matching the real world. A long interplanetary mission would have many scheduled correction burns which would be adjusted as tracking data is updated. But this would fundamentally change KSP's gameplay. It would take mission planning from something that everyone can do, to something where you'd need a master's in celestial mechanics to understand. Making the game too complex for its own good both in terms of internal code and in terms of gameplay. There is a sort-of compromise that might be workable. Instead of true n-body problem, you can do a perturbed central potential problem. This would involve computing dynamics of the orbital elements that describe the conic section instead of dynamics of the actual craft. This would give you a lot of interesting features. For example, it'd be entirely possible to have Lissajousand Halo orbits around Lagrange points. It'd also allow for things like orbital precession due to the oblateness of the planets. A lot of interesting, fun things, which would still allow for fundamental gameplay to be pretty much the same. It is still way, way more complex computationally. And I'm not sure about stability near edges of Hill spheres. Could make for an interesting mod, however. I'll have to look into it.

Absolutely. If it wasn't plausible on Earth, it wouldn't be significantly more plausible somewhere else. What I'm getting at is the fact that, usually, evolution doesn't result in more complex life completely replacing simple life. If simple self-replicating RNA was a thing on Earth a few billion years ago, I'd expect some of it to still be around in that original form, or something closely resembling it. Not as a mechanism in a comparatively complex bacterium, but free-replicating in organic ooze. However, we don't see anything like that outside of the lab, despite suitable environments being available. Ocam's razor cuts both ways here. If life on Earth started from a bacterium, then we wouldn't expect to find a precursor. We would also expect absolutely all life to have a common origin. Abiotic origin would allow for multiple ancestors. Panspermia makes a lot of things a lot simpler. But this is just what makes me lean weakly towards panspermia. What I'd like to see is a lot more research done on Mars, since it's the only likely origin besides Earth. Even simply knowing more about its formation, and gauging whether it could have been habitable early enough to allow for life to start there, evolve into something complex enough to survive travel, and hitch a ride to Earth in time would be a great start. As you've pointed out, it'd need a considerable head start for necessary adaptations. Of course, jackpot would be finding actual life there, confirming common origin, and making sure that it's not a modern contamination. But that might be too much to hope for.

Ok, I think I have all of the formulae derived, but I can use some help checking the math. This probably mostly goes to Mazon Del, but if anyone else wants to take a crack at it, feel free. Just to briefly cover the basics, I start out with Hamiltonian formulation. For central potential: H0(qi, pi) = (1/2m) (pr² + pθ²/r²) - mμ/r. Given generating function S(qi,αi), such that pi = ∂S/∂qi, we solve Hamilton-Jacobi equation: H0(qi, ∂S/∂qi) + ∂S/∂t = 0. That gives us new coordinates, αi, βi = ∂S/∂αi which are constant in time. Solving for S(qi,αi), we find that α1 = mμ/(2a) = -E, α2² = μm² a(1 - e²) = L², β1 = T, and β2 = Æ. Here, T is time of periapsis passage. In other words, anomaly is zero when t = T. Similarly, Æis angle of the periapsis. So given these four parameters, we know the exact trajectory the satellite takes in central potential. Up to this point, I've compared to standard texts, and everything seems to match. So I don't need any verification on constants of motion. From here on, however, things get a bit more fuzzy. We wish to consider a perturbed potential H(qi, pi) = H0(qi, pi) + U(r, θ). As a consequence, we have following equations of motion for the constants. β'i = ∂U/∂αi α'i = - ∂U/∂βi I'm using the primed notation to denote derivatives with respect to time. Naturally, in a physics simulation, what I actually have available are forces, which are related to ∂U/∂r, and ∂U/∂θ. And I don't need to worry about alphas, because rate of change of energy and momentum can be trivially expressed in terms of state variables. What I need are the β'i terms. The following is known. r = a(1-e²)/(1 - e Cos(ν)) r = a(1+e²)/(1 + e Cos(ν)) θ = ν + ÆHere, ν is true anomaly, and that's the only term that depends on T. Specifically, it is a function of t - T. So ∂ν/∂T = - ∂θ/∂t = -θ'. After expanding U in terms of alphas, taking derivatives, and plugging everything back in, I got the following expressions. T' = β'1 = ∂U/∂α1 = r(∂U/∂r)/E Æ' = β'1 = ∂U/∂α1 = θ'( er Sin(θ)/(1 - e Cos(θ)) (∂U/∂r) - (∂U/∂θ) ) These are the values I need verified, to make sure I didn't mess something up. I'll also check this with a simulation. But since dependence of true anomaly on time is not exactly trivial, I'm going to have to work out a good way to do this. Edit: MAJOR derp. I took ∂U/∂T, which is ∂U/∂β1, instead of ∂U/∂α2. As a result the expression for Æ' is actually correct expression for -E'. And it is. If you work it out, that is exactly work done per unit time by external force on the orbiting body. So at least, that helps me verify some of the steps. Minor derp. Got signs wrong in the radius equation, so I ended up with true anomaly counted from apoapsis instead of periapsis. Fixed that now. So I still need to derive the correct equation for Æ', but T' should be right, and I'd still appreciate any checks on that.

It definitely lacks validation. But given that all of Terrestrial life has common origin, and we have fossils and modern analogs of pretty much everything down to the oldest bacteria, yet no trace of the much simpler precursor that could have spontaneously formed in the primordial ooze, I find an idea that Terrestrial life doesn't have its origin on Earth to be an appealing one. That said, it's no more than a hypothesis, and even if it's true, Mars is a much more likely suspect, simply due to proximity. So yes, I can definitely understand your complaint.

Yeah, they launch Dragon over the Atlantic, so that could be it. But how would contamination get onto Russian part of the station, where only Soyuzes and Progresses dock?

I was going to make an estimate on probability using statistical mechanics and the lightest species of picoplancton I could find. Google Calculator insists that it is zero. (Something on the order of exp(-10^10).) Definitely not air currents. I suppose, there could be some plancton floating frozen in LEO due to some asteroid impacts or whatnot, but I would look for man-caused contamination first.

Good idea. And we can have software checks to make sure that neither valve is open when it shouldn't be. If just one opens up briefly due to a random bit flip, it's not a total loss. As far as I know, vacuum-rated valves are more about the type of lubricant used, than the valve itself. So it should be reasonably priced. The sort of valves they use in projects where they need perfect vacuum, these are pricey. But we don't care if we end up "contaminating" the vacuum slightly. So long as lubricant lasts through the mission.

Actually, the net gravitational effect will be weaker at .9999c than at .99c. Has to do with factor of 2 for gravitational lensing vs classical photon trajectory. When they started it, they were flying blind. The critical element is Yang-Mills Theory, which wasn't developed until 1950s. If you start with U(1) symmetry and apply Yang-Mills, you can build a pretty good topological model of electromagnetism, which you can expand into a differential geometric interpretation. And KK model was eventually reconsiled with that. But yeah, it ends up not very practical anyways.

Not really. Gravity isn't just about mass. A fast-moving object has high energy, but it also has a very high pressure term in the stress-energy tensor. So the net effect is insignificant. A simple way to think of it is that if you have a very, very fast baseball fly past you, from perspective of the baseball it's you who is moving near speed of light. Would your trajectory be affected by a baseball if you're flying at near speed of light by it? No. It's just a baseball. So neither would a very fast baseball have any effect on you. Read this Both. If you just want to describe electromagnetic field, Maxwell's Equations are sufficient. Unlike Newtonian gravity equations, Maxwell's Equations are exact. However, if you want to describe interactions between electromagnetic field and matter, you might have to consider Quantum Electrodynamics. This is only relevant to very high energies on very short scale. Like collisions between nuclei. There, you need QED to describe electromagnetic interactions properly. When you dig deep enough in both, QED and General Relativity are built on the same principles. GR isn't quantized, but if you just look at the underlying field theory, they are the same. The difference is that GR deals with symmetries due to translation and rotation in space and time. As consequence, it can be interpreted as curvature of space-time. Electrodynamics has to do with different symmetries. So while they can be described as curving of some sort of space, it's not a very useful description.

Which were built by professionals and extensively tested. We can't afford construction, testing, and insurance costs this would require. We might be able to attach an electrospray thruster, but at this point, I don't see any reason for one. We don't need reaction control, since magneto-torque is quite sufficient. And from ISS orbit, decay time is sufficiently long. I'm still open to suggestions on a propulsion mission instead of the bio one. It just seems to me that the only options available are either already in common use (like the electrospray), are guaranteed not to work (gyros, etc.), or require a much larger satellite to test properly (like tether). This still, potentially, leaves options for something like a high ISP beer can ion drive. The ISP of electrospray is pretty low, and conventional ion drives tend to be heavy and bulky. There ought to be something in between, suitable for a cube sat.

Neutron stars collapse somewhere between 2 and 3 Solar masses. So that is the minimum mass for a black hole formed during a supernova. A black hole would be stable with a much lower mass, but yes, there is no mechanism known that would produce them. Some have suggested that black holes of all manner of sizes could have been produced during Big Bang, but we have no evidence of any sub-stellar black holes being around.

Short of software error, I do not see why it would open early. It is pretty likely to get stuck shut, bu that's not a big deal. As for software, there are more serious risks there, bugs that can result in total loss. Fortunately, software can be well tested on the ground. Plus, we might actually need to vent atmo in case of pressure buildup. So I am all in favor of a vent valve. So long as it is light and simple.

If the ground effect on EDF is anywhere near as significant as it is for heli, you wouldn't even need to worry about extra power. If you have enough thrust to hover and climb on 16 fans, you'll be able to have a soft landing on 8-12. I don't know about generators, but the battery backup is definitely an extra safety feature. Although, part of the reason this thing has batteries is to get that extra thrust for hover without having to include a large generator. So I'm not sure how safe that thing will be if the generator and/or batteries bite the dust. The thing doesn't look like it can glide very well, and forget about autorotation with EDFs.

Actually, you'd build the city on the interior of a paraboloid. Think of the shape the water surface makes in a spinning glass. The local gravity will vary depending on distance from the center of rotation, but it will always point directly towards the floor. If you build the whole thing large enough, Coriolis forces are going to be low, so you'll feel like you're walking around on a level surface, even though you are inside a giant paraboloid. You'd probably build habitats near the 1G area, and keep various life support equipment closer to the center.

Yes, most commercial autopilots will have altitude and heading holds, besides the air speed hold. Though, on some planes, it's literally just a wing leveler + "cruise control". In either case, the principle of operation is the same as that of cruise control. You just have a few extra degrees of freedom it operates on.

There is only so much we can bring either way. And at some point, there will bee too much oxygen in there anyways. Point is, water isn't the limiting factor. Alternatively, it might be a good idea to have something in there that converts plant matter back into CO2 and water. But we have to make sure that it doesn't mess with the rest of the experiment. Just one more reason we really need to have a biologist for this.

What are you guys talking about? We've had cruise control on cars for decades now. I mean, that is the appropriate comparison to a typical autopilot.

They do talk about it on their site. Not in too much detail, but the gist of it is that their VTOL system doesn't rely on power transmission or tilting via heavy shafts. Power is obvious, these being the EDFs. But I think their plan for tilting is to use thrust from the fans themselves to provide torque. I don't know if that's supposed to be achieved with thrust vectoring or differential thrust. Either way, it's a neat idea, which would reduce complexity, cost, and weight. But I have serious doubts about these guys being able to execute this. Especially with aft set of EDFs being in the exhaust stream of the fore EDFs. This can result in all sorts of oscillations if the EDF sets are free to swivel about the support. Again, their site claims that they have electronic/algorithmic solutions for this sort of stuff, but I'd have to see it to believe it. Ayup.

You can't protect it from hard radiation, but the levels are acceptable for the duration we are looking at. UV radiation can be adequately shielded from with a sheet of glass. I'm not sure we need this. Net water consumption will be limited by CO2 availability. (Roughly, 6 CO2 + 5 H2O -> C6H10O5 + 6 O2 for cellulose synthesis.) We can't possibly bring enough CO2 to exhaust all of the H2O present as moisture in the soil or whatever substrate we will end up using.