K^2

Promissing start. Looks like ISS will finally get its supplies.

No, you cannot do that. Without getting into details, it'd be a violation of conservation of momentum. You need an actual medium with an actual physical mass to scatter the light from. So are regular particles. That's not what makes virtual particles virtual.

Detonation, sure. And that and conflagration involves combustion, of course. But "explosion" is not really defined in physical chemistry as such. Even detonation does not have to be explosive. There are experimental solid boosters that work via detonation. That's why I asked to define "explosion". Depending on context, any violent disintegration seems to qualify.

Seems unfortunate to loose the cargo when a software contingency would likely have been sufficient to assure safe(ish) landing.

I have no idea if it'd actually be possible given all the hardware involved, but it would have enough dV to "turn around" and return to Earth within a few hours.

Here are a few more for aerodynamics. The drag is already on there, but I've edited some variables for the conformity and added a description. [TABLE=class: grid, width: 1500] [TR] [TD]Name[/TD] [TD]Equation[/TD] [TD]Where[/TD] [TD]Measured in:[/TD] [TD]Purpose[/TD] [/TR] [TR] [TD]Drag Equation (FD)[/TD] [TD=align: center][/TD] [TD] à= Mass density of the penetrated fluid v = Flow velocity relative to the object CD = Drag coefficient A = Cross-section area [/TD] [TD=align: center]Force[/TD] [TD=align: center]Drag generated by a body moving through fluid/air at sub-sonic or low supersonic speeds.[/TD] [/TR] [TR] [TD]Lift Equation (FL)[/TD] [TD=align: center][/TD] [TD] à= Mass density of the penetrated fluid v = Flow velocity relative to the object CL = Lift coefficient A = Planform area [/TD] [TD=align: center]Force[/TD] [TD=align: center]Lift generated by an airfoil, such as airplane's wing.[/TD] [/TR] [TR] [TD]Lift Coefficient (CL)[/TD] [TD=align: center][/TD] [TD] α = Angle of attack (in radians) [/TD] [TD=align: center]Dimensionless[/TD] [TD=align: center]Lift coefficient for a thin, symmetrical airfoil. Valid only for small angle of attack.[/TD] [/TR] [/Table] P.S. I would advise replacing "Measured in:" column with "Dimensions:" column. Units depend on your system, but a length in equation will always be a length, and so on. So that's a useful bit of information

Define "explode," then.

Yes, it's just one number. But it's a different number for every angle Φ. You just generate a list of Φ to plot results against, same as a bove. In Matlab, you can just do phi = 0:0.1:2*pi; Likewise, you can generate all thetas in one go as theta = 2*pi*rand(1000,1); That will give you 1,000 random initial orientations. So then your code for computing a list of classical correlations might look something like this: c = zeros(length(phi)); for j = 1:length(phi) y = sign(cos(theta .+ phi(j)) .+ pi); c(j) = mean(x .* y); end This assumes that x, theta, and phi are already computed, of course. The +pi bit is just there to account for the fact that two particles are exactly opposite in direction. Just a shortcut for the odds of it being same or opposite sign. You can do this in Matlab in one ligne. y = x.*(sign(rand(1,1000).-(cos(phi(i)/2)^2))); I'd bet your book describes an actual experiment done with optical excitations. They are relatively inexpensive to set up in a lab, but they have some limitations. Like, it's hard to do rotations by arbitrary angles. So instead, it likely uses a discrete set of angles, and "random axis" means one of the few very specific ones randomly selected. What I describe above is a more general case. It's possible to make this into an actual experiment, but it's a more complicated one to cary out. You have to get creative with NMR spectrometer to do measurements in arbitrary bases. But I've seen it done. Not sure if anyone has actually carried out this exact experiment, though. On the flip side, it's much more straight forward conceptually. So I'd start by simulating and understanding what's going on with this one. And then moving on to ones that are easier to set up in the lab, but harder to understand.

That's what they said about this Dragon flight when the last Progress failed to reach orbit. But yeah. Hopefully, we won't see two Progress failures in a row.

With the Progress, doesn't this make two in a row? That's a serious kick to the teeth right there. Fingered crossed for M-28M.

First of all, it's not about probabilities, but rather correlation. You need correlation as a function of the angle between the two bases. While both classical and quantum measurements predict the same probabilities, they predict totally different correlations between the two measurements. Because both measurements have zero mean and unit deviations, correlation is just Corr(X,Y) = E[XY] for two measurements X and Y. But more fundamentally, you do not seem to understand how the entanglement works. Lets start with a classical theory. Suppose that spin axis makes angle θ with your measurement axis. Classical measurement tells you that you will measure spin Sign(Cos(θ)). That still gives you 50/50 odds if you don't know θ, but if you do know θ, then it's a fixed quantity. Lets look at it backwards. Suppose you did make a measurement, and you did measure spin +1. What is θ? Well, you don't know, but you can say for sure that it's between -90° and 90°, because these are the only values of θ that give you positive Cos(θ). So now, lets say you have a duplicate of that spin with exactly opposite angle (θ+À). Naturally, if you measured +1 on the first, you'd measure -1 on this one. But suppose, you measured this one in a different basis, say, at some angle Φ to first measurement. What are the odds that you measure -1 now? Well, it depends on what θ was. But if Φ is small, almost any θ will give you -1, and if Φ is close to 180°, almost any θ will give you +1. And therein lies the correlation. So here is a rough outline of what your classical computation should be. 1) Generate a list or random angles θ. 2) Generate a list of Sign(Cos(θ)), call this list X. 3) Generate a list of Sign(Cos(θ + Φ)) for a bunch of values of Φ from 0° to 360°, call that Y. 4) Compute correlation as Sum(X(i)Y(i)) / N, where N is the number of Φ values you used. 5) Plot the correlation as a function of Φ. You should see something that's straight line rising from -1 to 1 from 0° to 180°, and then falls back again from 180° to 360°. Now, quantum measurements are much more complicated conceptually, but almost as easy to evaluate. I won't walk you through the entire logic, but just what's relevant to simulation. From perspective of the simulation, it doesn't really matter what the initial state was, other than that it was entangled. As soon as you measure first particle, entanglement tells us state of the other. So you can seed first measurement, X, with random values. You can use the same X as classical result, for example. The important bit is that you use that to compute measurements on Y. So, suppose you measured +1 on the first particle. Just like in the classical case, you know that second particle has -1 in the same basis. But what are your odds of measuring -1 in the basis rotated by Φ? Well, it's <-1|Exp(iSx Φ/2)|-1>² = Cos(Φ/2)². Likewise, probability of getting +1 is Sin(Φ/2)². Note that Cos(Φ/2)² + Sin(Φ/2)² = 1, because total probability needs to be 1. And so you have your rough algorithm. 1) Generate a random list of +1/-1 values X, or just use the X from classical case. 2) For each value X, generate corresponding Y by generating a random value r between 0 and 1, then have Y = X if r > Cos(Φ/2)² and have Y = -X otherwise. Note that you need to do this once for each Φ. 3) Compute correlation as above. 4) Plot correlation as function of Φ. This time, you should see something that looks like a Cos curve. @Steel, it's very easy to program entangled particles in Matlab if you know QM and a bit of linear algebra.

Lets start with a perfect circle. Distance around orbit is 2ÀR. Velocity is Sqrt(µ/R). (Where µ = GM is gravitational parameter.) So T = 2ÀR/Sqrt(µ/R). This simplifies to T = 2À * Sqrt(R³/µ). Now, the cool thing about Kepler's Laws is that they tell you that period depends on semi-major axis only. Not on eccentricity. So the general formula is identical T = 2À * Sqrt(a³/µ), regardless of whether it's a circular orbit or not. To work out semi-major axis from period, just solve that for a. Square both sides, find a³, and take the cube root of that.

Linear algebra and associated numerical methods is the most common place where you find it called that. Specifically, finding highest eigen value and associated vector can be done by taking the matrix to a high power. But any time you might be thinking of function as an operator, the name comes up. Oh, and yes, convergence is only fast for small eccentricities. I should have clarified that. That is the case for most objects in stable orbits, so in practice, you rarely need to worry about it. But if you happen to have a comet on near-escape trajectory, you might want into other methods. Newton's works, of course.

Power method is your best bet. M = E - e sin(E), we want to solve that using power method, so rearrange it to read E = M + e sin(E). Start with a guess. In this case, E0 = M is a good starting guess. So your first approximation is E1 = M + e sin(E0) = M + e sin(M). Now take that and plug it back in. E2 = M + e sin(E1). For anomalies, power method converges absurdly fast. Typically, 2-3 steps is all you need.

@Nuke: Block compression algorithms of the kind you are looking at are very inexpensive to decompress, which is why they are favored for graphics, but they are very expensive to compress properly. You either have to spend a lot of time computing correlations, or you end up with very poor quality. What you should be looking at is something like JPEG. It's also a block compression, but it's done in frequency domain, allowing you to reduce bit depth on high frequency data. Typical JPEG just uses standard discrete cosines transform, but there are fancier methods using wavelets. The transforms table can be pre-computed making it a very fast operation. The output also tends to be very easy to compress with Huffman as your second stage, which JPEG makes use of. Again, very fast operation if you pre-compute the trees. JPEG-like algorithm will give you better performance, better quality, and less data to transfer. The stages of JPEG compression are as follows. 1) Convert RGB to YCbCr. 2) Reduce the resolution of chroma components. (Typically, each 2x2 becomes a single chroma pixel.) 3) Perform DCT on each block. (Typically 8x8 blocks for each channel.) 4) Multiply each component by pre-determined factor, keeping only top few bits. Typically 8 bits for lowest frequencies, and dropping down to 3-4 for highest frequencies. 5) Perform Huffman compression on the stream to get final output. Steps 2, 4, and 5 are what gives you the actual compression, and each one's technically optional, but they really give you incredible results when combined. You can do 10x compression with little quality degradation.

There is an asymmetry, which requires misalignment. With perfectly aligned optics, the only breaks in symmetry are related to optical axis. E.g. lens flares. Image posted has broken symmetry which implies that either lenses aren't perfectly parallel to each other, or not perfectly parallel to the sensor. This is also very common for amateur astronomy telescopes. If mirrors/lenses aren't absolutely perfectly aligned, you'll have blue/red aberrations on stars/planets that are always angled the same way.

Yeah. Means lenses are just a tiniest bit out of alignment.

Well, sure, Orion's budget is overblown. That's WHY we have contracts for Boeing and SpaceX to build "cheap", reliable rides. And yeah, I'm sure given the budget and time, either one of these could have built a better capsule than Orion for less. But you still can't just take Dragon 2, give it a good boost, and wish it luck for a month-long BEO mission. It doesn't have life support for that sort of duration. It doesn't have room for such life support. Sure, that stuff can probably ride in an extended service module, and you can probably patch it into the main systems of the capsule. And you can probably have some sort of flexible hoses in the dragon capsules to collect human waste. You can add thicker walls for radiation protection. You can buff up the heat shield... Problem is, at that point, you're starting to approach costs of building a capsule that was meant to have all these things from the start, and nowhere near the safety of one. Each of these "upgrades" is additional points of failure. Systems that are either poorly hooked up or lacking redundancies because they are afterthoughts. This is a bad idea all around. Sending Dragon 2 to BEO would be like the sort of things Soviets did with Voskhod missions in the mid-60s. And then, they had a reason for it, at least. There is no good reason to try and make Dragon 2 do something it's not meant to do. It's a good, safe (presumably) orbital shuttle. That's what it should be used for. And Orion is a big money sink, but BEO missions is what it's meant for, and what it really can do quite successfully when it gets finished. There is no reason to interfere with that. Would it make more sense to wait a few years and then start a contract with a private company, like Space X, for a proper long-duration capsule? Maybe. There's no guarantee that a reputable company would take such a contract right now. Money for Dragon 2 flights won't dry out for a while. Money for Orion could be canceled at any moment. Few companies would take that risk. So it costs us more to do it this way, but it's getting done.

Apollo 17 was nearly two weeks long. Do you recall toilets on LM? Sacrifices, they have to be made. Things like extra radiation shielding, extended life support, and larger heat shield, on the other hand, are going to make a drastic difference in safety of the expedition.

A large airliner on final can also be as bad as 4.5:1. Of course, that's largely due to flaps and less-than-optimal angle of attack. But that's why it has engines to compensate. So the actual slope it follows is much gentler. And what the hell do you fly, Camacha, with a 35:1 glide? 10:1 is generally pretty good for something that isn't built to be a glider. A lot of general aviation and airliners (clean, cruise) fall near there. I can believe 15:1 for high-performance aircraft, but I've never seen anything close to 35:1 that isn't built to be a glider. In fact, just a few decades ago, that would have been considered a high quality sailplane. Of course, now with all the fancy materials, they're doing better than 70:1. You don't really have to land in one of these if you don't want to.

I can, indeed. Actually, General Relativity and Quantum Field Theory are rooted in the same principles, despite independent discovery. When you get right down to it, they are the same theory. The difference is in which gauge groups are used and whether quantization is athing. The barebones QCD, for example, has the U(1)xSU(2)xSU(3) gauge symmetries, while General Relativity arises from considering all possible translations and boosts/rotations in space-time as a symmetry. This is the Poincare Group. Quantization is where things get complicated. It's what makes Quantum Mechanics quantum, so it's a rather important feature. But trying to quantize a theory that includes gravity leads to all sorts of problems. While no fully generalized Quantum Gravity theory exists, there are a number of very good approximations. Mean Field Theory approach, for example, produces a theory that covers everything from particle physics to neutron stars. Unfortunately, it breaks down near Plank Scale, as does just about every theory we have, and so it does not work near event horizons of black holes. But that's basically the only thing we still cannot properly describe. Quantum Vacuum at the event horizon. In everything else, our limitations are purely computational. Modern theoretical astrophysics has a branch that's basically particle physics of neutron stars, and that simply wouldn't work if gravity and quantum physics were completely incompatible. The math just gets all sorts of hairy.

Streess-energy, actually. Light bends space-time just fine despite having no mass.

Nah. It surpassed that by miles near the end of 50s, when people realized that General Relativity and Quantum Field Theory are two sides of the same coin. And since both QFT and GR have been tested to more than 12 decimal places, there is not a single theory that can boast being even remotely as close to being certainty.

It's not like anyone famous ever got a Nobel Prize for discovering something like a photoelectric effect over a century ago, or anything. Yeah, I'm being facetious. But it's basically the same thing. The main difference is that electrons are thoroughly delocalized in graphene, so if you excite them with coherent light source, such as, say, a laser, you end up with the same coherence on the emitted electrons. And because electrons act as a wave here, you end up with a directed beam. Neat stuff, but it's honestly not rocket science. More like undergraduate level solid state physics in any decent university.

Yeah... Dragon isn't built for interplan. It might manage a Lunar mission, but you aren't going much further than that for just so many reasons.