Enthalpy

I've suggested bigger chips in direct contact to pass many links by capacitance. A 2000 ball Bga package measures about 45mm*45mm to transmit 1000 signals - fewer and smaller is possible. 1 cm2 chips offer then ~200µm*200µm per link; 20µm air gap make 18fF while each pad and preamplifier load with 200fF if a 10µm oxide or polymer layer is purposely produced, so the signal is huge. A nitride layer would protect the electrodes well. The boards are not aligned to <200µm: the chips have several electrodes per link, and the electronics chooses which ones are the best. This is done at boot time and maintained permanently; compensating mechanical movements is easy at many Gb/s. The misalignment and movements can exceed the size of a link. If the position of a link on the chips is adjusted to, for instance, 1/5 of the link's size, the receiver could have one electrode per link and the transmitter 5*5; I prefer to have 5 electrodes per link at the transmitter and the receiver, which suffices if they're elongated and crossed as on the sketch. Routing such modules would be difficult at the end of signal vessels; they fit better near the centers of two superimposed computing boards to connect them, or spread among the computing chips, or possibly as combined computing and connection chips. Marc Schaefer, aka Enthalpy

Computers represent numbers on a finite number of bits, for instance 32. When an integer result is outside the range of possible values, it gets truncated to the lower bits. In other words, the result is represented modulo 2^32. When subtracting a big number from a small one, the result modulo 2^32 is almost the "normal" result - it is just 2^32 bigger, hence the leading ones. This is the proper result to be expected, and most standards define it that way. The computer couldn't give a "better" result anyway. Interesting: the same range defined by 32 bits can represent a signed integer just as well. The most usual convention (called complement to 2... not used with float numbers!) is that a signed integer goes from -2^31 to +(2^31)-1 inclusive. Then, the same hardware does the +-*/ operations properly, without any modification, on unsigned and on signed integers. From your example, the leading ones tell that the difference is negative, just fine. The only difference is how the computer tells if the operation has gone past the range. Usually, it sets an "overflow" bit if the unsigned range is exceeded and a "carry" if the signed range is exceeded. A few compilers propose to check at every operation if the range was exceeded; some do it as a default, most don't. The C standard is to avoid checking, since this is faster on most machines, and aware programmers make use of this as a feature.

To pass links from a board to an other, I had also suggested capacitive transmission modules, here are sketches: A transmitting or a receiving module has only small silicon or SiGe signal chips, cheap and power-saving, that live longer than light emitters. Four chips per 16 links make shorter and easier tracks. Thin polymer or ceramic should protect the electrodes. At 0.5mm gap and 0.4mm offset, a 0/0.8V signal passes 1.2fC peak through 3fF roughly. The receiving pad's capacitance is 50fF and the transimpedance amplifier's 200fF, so 3nV/sqrt(Hz) and 10GHz bandwith make 75aC noise: not a limit to the throughput. 50+200fF at the transmission pad cost 0.8mW per monodirectional link at 20Gb/s. Marc Schaefer, aka Enthalpy

If many links must pass from a board to a parallel one, for instance if using the previously suggested vessels an crossboards, short optical links are an option. A pair of light emitting and receiving modules may look like this: For instance 6mm*5mm modules can have 36 balls to pass 16 monodirectional links each. 17 or 18 light emitters and receivers carry the links between the boards, with signal chips that chose the healthy opto chips and drive them or process the signals. Future big opto chips may integrate several emitters or receivers; presently, GaAs photodiodes can integrate a preamplifier. The module's fine printed circuit board can interconnect the signal and opto chips, or a big signal chip carries the opto chips. The opto chips have a wide divergence and angle of view. Lenses make the light parallel between the modules to tolerate misalignment, say 0.5mm; they can be molded after the opaque polymer. Soft lashes absorb stray light. Without lenses, much power would achieve a only a noisy signal. With lenses, one D=8µm Vcsel consumes 4mWe*3V half of the time, so 13 links per node draw 80mW per computing node at each jump. At 10Gb/s and 850nm, one third of the emitted 0.75mWo hit the 0.5A/W photodiode to produce 0/12fC per bit. A low-power bipolar transimpedance amplifier can have 2nV/sqrt(Hz) noise, the photodiode 2pF: over 5GHz, the noise is 0.3fC. 20Gb/s still offers some margin. Marc Schaefer, aka Enthalpy

Or live in France, where they call them Foucault currents because he was a Frenchman. English-speaking countries call them "eddy" for the same reason.

Earnshaw's Theorem is so misleading that it would be better to forget it altogether. Especially, it applies only without gravity - a situation uncommon where humans live. For instance, a square of pyrolytic graphite floats over a group of magnets and has a stable position, without any contact.

No suggestion for a power supply, but I suggest that you measure the efficiency by yourself, since 94% at 400kHz is, err, unexpected. Maybe under some conditions and at one operating point, which will not be yours - so design the cooling for bigger losses than 6%.

The calendars with 28/29/30/31 days must inherit from lunar calendars as well. Though, the lunar ones I've heard of add a special month some years in order to re-synchronize with the seasons. This means a maximum 14 days bias, a significant drawback. And since the Moon's period is no integer number of days, well, you guess.

Hi simina11, welcome here! Are any prentheses missing in P=RT/V-b ? Does TR/P =V apply here despite b?

Slightly bizarre idea... 67P/Churyumov–Gerasimenko looks like two bodies that assembled loosely. I suggest instead (not even a claim, rather an idea to chew on) that it can have been one sigle, more regular body that has lost more material at what looks now like a neck. This apple core model could for instance have occured as the object's axes had a different orientation. What is now the neck was then the equator and was more or less ecliptic. It received hence more sunheat and sublimated more quickly. After the object got its shape, it tumbled to rotate around the biggest moment of inertia, or flat if you prefer. That's the behaviour of all objects that aren't perfectly stiff; some dissipation process reorients the rotation axis, and maybe deformations of the snow or dust suffices. This could have happened over one orbit around the Sun, with the equator melting when near to the Sun and the axis tumbling when far, or over many orbits, the first ones melting the equator, and the most recent ones tumbling 67P but not having already made it more spherical. Enjoy!

Hi Jim! Your English works, no worry - and it isn't my mothertongue anyway, so I'm just happy that we share a language. 350 bar is a standard pressure, and you could store pure oxygen, provided you keep much of the CO2 and H2O in the cylinder during exhaust and suck little oxygen at each cycle, to limit the temperature. Similar things are done on torpedoes. Piston engines are not used at full-size rockets because: They're too heavy! For instance the RD-180' turbopump on Atlas has 100MW shaft power (135,000 horse power). It weighs under 1 ton and is as tall as a person. This boat http://en.wikipedia.org/wiki/CSCL_Globe has a 70MW piston engine, cute picture there http://gcaptain.com/worlds-largest-containership-also-sets-record-for-largest-engine-ever/ that's how turbines and pistons compare... Or just have a look at a compressed car engine: the turbocompressor has about the same power as the rest, yet is tiny. Turbines are simpler and more reliable than piston engines. That was the basic reason for airliners to switch to gas turbines. Existing piston engines are too small for a launcher, so reusing a design is no option. For a much smaller rocket, it's better to put pressure in the propellant tanks, or to use an electric motor plus batteries. Electric motors are much lighter than piston engines and batteries are lighter than a pressure tank for air or oxygen. Then, pumps for propellants also are of centrifugal type because of the mass, and an electric motor fits their rotation speed while a piston motor doesn't.

"Parallel layers" must be an over-simplification for graphite. Since all available graphite is far from the theoretical density (commonly -10% or -20%, where pyrolytic graphite is the least bad), the order must be very loose. That's something not observed with other materials; for instance metals have the same density to ~0.1% whether single-crystal or polycrystaline, and so does silicon even if amorphous, so even tiny crystal must hardly explain graphite's abnormal density; I suspect the stacking of 2D layers to be very bad.

Nature doesn't help much neither, because a year contains no integer number of days, so even a simple number of seconds in a day wouldn't fit the year simply. The Republican calendar also changed the number of days in a year, and because of that, it would have shifted horribly in less than a century.

The pitch (or reference for A) is arbitrary, as tell its fluctutions over time. As well, it tends to be 444HZ in the US versus 440Hz in Europe, so instruments difficult to tune (xylophone, clarinets) are pitched at 442Hz. Renaissance intruments were pitched as low as 415Hz (with bigger fluctuations than today) hence are hard to use today. That's a half tone lower. Tuneable instruments like stringed ones suffer a lot if asked to play at today's pitch. Some musicians are said to have an absolute sense of pitch, needing no reference to tune an instrument. One of my violin professors claimed he did, the other not. I'm not quite sure whether they could tune a broadband instrument like a Theremine, or only a string instrument (the sound gets more brilliant when the string tension lets the sound become faster in it than in air, and this happens just below the proper tune), or only their usual instrument (they show many resonances, rather sharp). ---------- The equal-tempered scale has nothing magic and is really arbitrary. By chance, twelve equal half-tones fitted approximately the scales used before in Europe, and they ease playing and tuning. But they do not sound well nor avoid unpleasant beats. Violonists need to learn to play according to the equal-tempered scale, and it's neither natural nor easy. Fifths and fourth fit well, but especially small seconds do not; 23/12 does not fit 6/5 from the natural scale, and sounds really badly on a violin. An other strong example is 11/10 and 12/11 that give 1.5 half-tone. You know, when hunting horns play so badly "out of tune", that's when they use the 11th harmonic. It's a perfectly natural frequency proportion and is used in Turkey for instance. But we're educated to find it "out of tune" because it's outside the equally-tempered scale. The 7th harmonic as well, say on a trumpet, sound "too low" for our habits despite being a natural tune. Traditional music from Greece, Romania, Hungary uses such intervals, as conventions differ.

Hi Habbababba, welcome here! I'm very pleased with your suggestion. Though, other people here may understand the topic better than I do. Trying to compare : BF3 boils at 173K while CF4 boils at 145K despite having more atoms. Whether carbon is easier to polarize than boron is unclear to me, but the four fluorines making the carbon inaccessible do favour the gas. This goes in the direction of BF3 interacting by sub-molecular permanent polarization. On the other hand, SF6 boils at 209K, but is bigger, so it gives no clear hint to any explanation. As an orientation for the BF3 molecules in a solid, and for a few molecules in a liquid, with each rim facing the centre of a neighbour molecule, you have the example of solid benzene http://en.wikipedia.org/wiki/Benzene(picture top right) though it doesn't have to result from a permanent polarization in benzene. ---------- I dislike some wording details in Wiki's article http://en.wikipedia.org/wiki/London_dispersion_force because in a stationary state, electrons don't move nor flee in a molecule: they're immobile, in the sense that the amplitude (not the phase) of their wave function is static. So it's not a matter of "instantaneous" position. The proper formulation is abstract, alas: one has to write one single wave function for the electrons that interact, as psi(r1, r2)*phase(t) for two electrons, and this psi - which is stationary - contains the electron interaction in that it differs from any psi(r1)*psi(r2). At any instant, you may find an electron anywhere according to psi(r1, r2). It's the probability or finding a second electron at one place that depends on where you have located a first electron.

Clearly a resonance. I noticed some in bathrooms I used. If a note is stronger but the neighbour half-tones (F + - 5.9%) are already less strong, then it's not a consequence of your perception. Typical selectivity of a room resonance. Bathrooms show it more easily when their walls are smooth, hard, parallel and uncovered. Other rooms use to have more complicated shapes and absorbing materials like fabrics. Also, big rooms have their resonances more closely spaced so we don't notice them so easily.

One other design using cross boards has vessels (as for blood) made of printed circuit that gather the signals from and scatters to the computing chips, which help the computing boards to carry the many signals to the cross boards. They add circuit area and volume, and can be dense while the bigger computing boards don't have to for their other goals; can be perpendicular to the computing boards and parallel to the cross boards, which may help pass the signals. As an example, the W=5mm h=2.4mm vessels can have 12 signal and 13 ground layers to carry >112 links each. 4 vessels then carry all links for 2*16 nodes to and from 127 other computing boards. Note that the cross boards have short notches here, leaving room to spread and carry the links, while the computing boards have deep notches that may almost swallow the cross boards. ---------- To let the links jump between the vessels and the cross boards, the facing packages can have photodiodes and Vcsel (vertically emitting laser diodes). Kind of eyelashes, at one or both sides, can dim parasitic light between the links and stay soft enough. One package can be 5mm*14mm to have nearly 70 contact balls and carry 28 signals, so 4 packages per example vessel suffice. This leaves 2.5mm2 to let each link jump. ---------- Alternately, capacitances can pass the links between the packages at the vessels and the cross boards. Just d=0.5mm facing an other at 0.5mm distance make 3.5fF for each link (and even less because ground tracks run at both packages between the electrodes of different links to reduce crosstalk): not much, but well enough for an integrated receiver at 20Gb/s situated <3mm away. I prefer the capacitive coupling over the optical one: It's more reliable; it's cheaper; It saves power. With light or capacitances, very little silicon is required to process the links, so a small dice in a bigger package that makes interconnections looks preferable. With light, the many emitters and receivers would be small, and to the sides of the processing silicon rather than on it; with capacitances, the package just provides additional electrodes, which a polymer or ceramic thin film can protect. ---------- If the emitter and receiver for capacitive coupling are close enough, their electrodes can be much smaller, so two bigger chips pass as many signals as the package contacts can, like >500. Then, the silicon chips (or GaN - something for signal processing) can carry the electrodes directly, for instance on their back side through vias if they're flip mounted, with a durable nitride protective layer. Alignment of the emitting and receiving packages stays easy if the chips have more electrodes than they pass links and map the best electrodes to each link. This is done at power up in a very quiet environment, or rather dynamically. The transmitting chip can have fine electrode subdivisions in the N-S direction and the receiving one in the E-W to limit complexity. The undriven electrode subdivisions can serve as ground to reduce crosstalk. The many-links packages don't fit the vessels so well, but can make massive connections between computing boards parallel to an other. Light beams could benefit too from plethoric receivers (and maybe emitters) chosen dynamically to carry many links, over a distance with some optics. Though, it gets reasonable only if the processing electronics is on the optical chip. Silicon Schottky maybe, or very dissimilar epitaxy. Examples of computers are to come. Marc Schaefer, aka Enthalpy

A nice place to put Ceres on an Earth orbit might be on the same orbit as our Moon, 60° before or after it. This makes a stable configuration, as is observed with planetoids on the same orbit as Jupiter (known as Trojans) or as Earth, and with moons on the same orbit as other moons around Jupiter and Saturn. That's one place where Nasa could put the asteroid they plan to bring back. Though, I don't know if it works with two moons of similar mass. Call it gravity gradient if you prefer so. Nearer to the Earth or the Sun, the attraction increases, while the centrifugal force at identical revolution period decreases, and this is expressed as a gradient, which is responsible for tides on Earth and is also commonly called tidal effect in space technology. This gradient affects the orbits: Sun's gradient affects our Moon and the satellites around the Earth, and Earth's gradient affect the satellites around the Moon. It's strong enough to be a technically important perturbation to geosynchronous satellites around the Earth, despite the Sun is so far away, and Earth's gradient is much worse for satellites around the Moon. I have no piece of software for that. The ones that make sensible predictions work only when all masses differ enough from an other so that the lighter one doesn't influence the heavier, or so little that the effect is added afterwards. Even then, software predicts the position of satellites only to a few months. The full "three bodies" or N-bodies problem, where masses can be similar, is not solved analytically (Poincaré told it couldn't), and for a century, it was believed that the solutions were unstable. Meanwhile, astronomers have observed planets around double stars where they weren't expected, both orbiting far from two close stars and orbiting near one star of a loose double system, so at least some solutions are stable at astronomical timescale. Software consistently lets one body escape from a three-body system despite we see planets, and for long, people considered this represented the true behaviour, but it seems now to be software imperfection like rounding errors or step size. The worry is: how to prove it?

Yes! But what I've read - and have no opinion about - is that orbits around our Moon drift over just a few decades to either crash on the Moon or leave its attraction, because the tides by the Earth and even the Sun are so strong. No worry with a spacecraft, more so with a Ceres or even a small asteroid.

I'm pretty sure your physics course will contain the necessary academic knowledge, well-ordered and explained to be learnt. Professors are there for that purpose. But what you could do by yourself, which is often too little taught because of a lack of money, and because it takes much time, is experiment. Do it at home on the topics that permit it. If you have time left during the course, ask to access the labs and tinker. Depending on what kind of physics, you can also study the documentation by providers of apparatus, materials... That's neglected by academic courses. When learning electronics, study the manufacturers' datasheets. If optics, the components descriptions at suppliers. And so on. Important to know what exists presently, what is feasible, and what the profession is interested in. There are also free journals for that. Try to grasp some scientific and technical culture outside the topics you study. You will always need mechanical drawing and manufacturing whatever your occupation, knowledge about materials of course, elementary chemistry obviously, as many effects as possible (piezoelectric, magnetostriction, acousto-optic... there are thousands) and so on and so forth. Not necessarily to model in details nor produce something by yourself, but know that this exists and has such capacity - culture, enough to think at it when needed and call the specialist. Make many friends. Learn foreign languages.

The asteroids are distributed along a few distances and inclinations in the belt, and this suggests that they result from few previous massive bodies. Jupiter destabilizes only some orbits in the belt, which it resonates with. These are the locations void of asteroids. The observation confirms this simple theory. http://en.wikipedia.org/wiki/Asteroid_belt Elsewhere, asteroids stay up to now. A heavier body would do it equally well; it's attracted more strongly by Jupiter and the sun, and is has more inertia, so its own mass has no effect - as long as it influences Jupiter little. What's possible is that Jupiter perturbs the formation of a planet by creating collisions in the material; until we observe enough planetary systems, this remains just weak models. The stability of an already formed planet is not in doubt.

With non-human technology, the Earth can get an other moon. I suppose a Ceres size wouldn't destabilize our Moon if the added orbit differs enough from Moon's one - both would be abnormally big as compared to Earth, which has already the biggest moon relative to the planet, if we don't count Pluto here. Our Moon wouldn't help much a capture, so the technology that brought Ceres to Earth would have to make the capture too. Reaching a low Earth orbit is about as costly as bringing Ceres near to Earth, so a high orbit is more economical - but with unknown technology this may not be a limit.

Sounds good - our Moon being near to the ecliptic plane. And this holds for the southern hemisphere if you formulate it "facing the nearest pole" instead of the North.

There are already minor planets between Mars and Jupiter so some orbits are stable. As long as these planets don't perturb Jupiter, they can be much heavier than Ceres and the orbit will be just as stable. Only a few distances to Sun are made unstable by Jupiter's influence. It's where no asteroid is present: at 2.50, 2.82, 2.96, 3.27AU from te Sun, where the period resonates with Jupiter's one. See http://en.wikipedia.org/wiki/Asteroid_belt That tells that a planet could last there. Whether it could form is an other story... My gut feeling is that we have only computer simulations up to now, which is an extremely weak evidence. The same simulations also claimed that no planet could stay around a double star, but meanwhile they are observed, so I'd say: wait until we know what exists or not at other planetary systems, and forget any prediction meanwhile. You know, past theories also claimed that giant planets are gaseous and far from the star, but meanwhile giant planets are known very close to their star, and some are rocky. It's just that a viable theory can't result from a single observation, and what we imagine to be necessity is merely a fit to the observation.

The biggest current airliners weigh not far from 570t and their tyres have far less contact area than the sketched feet, so the robot could stand on a landing track. A soft terrain would be more difficult. I suggest thick and highly damping shoesoles to reduce the shocks on the robot and on the ground. For balance, the robot could have very long feet, rest on their complete length but walk or jump on their tips, like kangaroos do. A tail could help. For the 24m tall robot of post #8, let's imagine it has a 2mm thick steel skin (ariliners would have aluminium or carbon instead, and you might rather consider a bulletproof fibre like aramide on a foam). 1500m2 skin then weigh 24t, with the skin stiffeners 50t, with some skeleton possibly 200...500t, so the crew could be bigger. 500t *4g on one 2m*2m foot press 0.5bar which is comfortable. A 5t*1.5g elephant presses 5bar on two D=0.3m feet and fits varied dry terrains. We have already built mobile machines much bigger and for bad terrain, cute examples: http://de.wikipedia.org/wiki/Datei:Bagger-garzweiler.jpg http://en.wikipedia.org/wiki/File:Garzweiler_Tagebau-1230.jpg(check the bulldozer for scale) http://en.wikipedia.org/wiki/Bucket-wheel_excavator http://de.wikipedia.org/wiki/Schaufelradbagger In short: I've nothing against your sketch in post #8.