K^2

I've covered LEDs. I don't consider it significant. Who cares if these only work during night? That's really when you need them most. For day time, one can use conventional paint. The total surface area that gets painted is very small, so it'd be an acceptable sacrifice. And I covered flat surfaces. Again, the system needs to only to conform to the following: 1) Have good traction, 2) Be cheaper in the long run than asphalt. I've shown that energy generated covers costs of the tiles, making them cheaper in the long run. Traction qualities are good. That's all you need from the road. Everything else is secondary concerns. If we were discussing asphalt right now, you'd have a much longer list of problems with it. Like, it melts in the sun. It gets totally destroyed by winter weather. It gets rolled into waves by vehicles. All in all, it can go from seemingly undamaged to absolutely undrivable, potentially leading to major accidents, in a matter of days. Compared to that, all of your complaints about solar roadways are irrelevant.

Read this for all of the equations and the way they connect. Real world drag is a bit more complicated, but KSP uses a fair estimate.

Check out GoDores' link. Rotax are a very well known name in the Ultralight community. These are fairly reliable, fairly inexpensive engines. They don't give you all that much power to work with, but if you are going to build your own plane, you'll want it to be an ultralight for both the cost and legal reasons. And Rotax has engines plenty powerful for that. They aren't exactly cheap, but neither are motorcycle engines. And make sure you know what you are doing. If you are good with tools, you can just get some plans for building an ultralight. They usually involve a Rotax engine. If you want to design your own from scratch, learn the theory first. The good news is that with an ultralight, it's more likely to not fly at all than fly dangerously, but there are still a few things you should learn about flight stability to minimize the later possibility. Oh, and check with your local laws. In United States, you just want to make sure that you fit the Ultralight category, and then follow the basic rules. No flying over cities, no flying at night, etc. And if you are within 30nm of class B airport, they require Mode C transponder, so you'll probably want to stay clear of these.

A sports motorcycle engine is powerful enough for a small plane, for sure. I mean, hell, a Cessna 152 only has something like 110HP in it, and my Ninja 250 has 35HP, and it's a very small bike. That's already enough power to fly an ultralight. An engine from a modern 600cc bike is enough to push a 152. And there are even larger bikes, with engines big enough to get a 172 off the ground. So in principle, you can easily take a motorcycle engine and fly with it. The main problem, however, is that vehicle engines aren't designed to operate at full power, or anywhere near it, for very long. Sport motorcycle engine will probably be better than a car engine in that regard, but you still aren't going to be able to fly on one for long without running into problems. An airplane is going to run at 70%-80% power most of the time, 100% during takeoff and climb, and only go bellow these settings for landing. A typical motorcycle engine will call it quits pretty soon under these conditions.

I didn't have a coin nearby. I flipped a key. It's flat, and spins around the long axis just the same. It came up "tails". By the way, what we're looking at here is the binomial distribution. While the expected average number of "heads" is n/2, the standard distribution is sqrt(n/4), which is quite significant. At the moment, the split is 15:25, which is 40 coin flips. So the expected split is 20:20 with variance of ±3.1. The actual split is less than two standard distributions off, which is a likely enough outcome.

No, actually, as usual, he has absolutely no clue what he's talking about. Friction coefficient of the glass to rubber is as good as that of concrete, and you can get the rest with modifying the surface. The road is only responsible for these last few parts of the millimeter. The rest is handled by the tire. Ever wondered why it has treads, and why it's illegal to drive on a bald tire? Anybody with the most basic understanding of physics knows that glass is a good driving surface. And glass isn't hard? Compared to what? Granite? Unfortunately, we don't build roads out of that, either. These panels need to last 2 decades at the most, because that's the life time of the solar cell, and glass is sufficiently hard for that. You know what isn't? Asphalt. The only reason we use asphalt in so many places is because it is cheap. Other materials have better longevity (no potholes every spring) and better traction. If thunderf00t ever got off his fat ass and traveled through some southern states, he'd notice that they rarely use asphalt there. Because it frigin' melts. What do they use? Concrete panels. They are larger than solar road panels, but they still use panel design, essentially, and they don't have any problems with it. In fact, roads last for many years without needs for significant repair. It's more expensive, but it works. So the glass tiles are going to provide a surface with sufficient traction and durability. So on the most important feature, strike one. They are perfectly functional. Of course, we get back to the costs. As I've said, the only reason we use asphalt is because it has decent properties, not good, but passable, and it is very cheap. So, thunderf00t looks at the cost of the glass panels, and screams that it's too expensive. Of course, if he'd bother to look at the price of a solar panel with the same surface area, he'd realize that it's much more expensive. So by his logic, obviously, nobody would ever consider installing a solar panel because of its costs, right? But in the real world, we like to look at what we are actually getting out of the solar panel. And even in United States, a solar panel pays for itself over its life time almost double. A solar panel with a tempered glass pane will also pay for itself even at current prices of electricity, and these are sure to increase. So strike two. Even though these things are very expensive in the short run, the electricity they provide over life time costs more. And you get a road you don't have to repair every year as a bonus. Moving on. The last part of it all that I consider important. Distribution network. Every morning when thunderf00t wakes up, goes to the bathroom, and flips the light switch, the light bulbs instantly explode, because he forgot that he has a 30kV line leading directly to his home. What? He doesn't? But how does he get the power, which can only be efficiently distributed using high voltage lines? Oh. He gets it from a transformer nearby, which gets its power from a sub-station which has already reduced the voltage? So moving power over shorter distances at lower voltage is ok? So all we really need to do is have the solar roadways plug into an AC converter every few hundred yards, and then collect power from larger and larger area to be directed to sub-stations? Huh. In fact, this can probably be done using the same infrastructure that already exists to light a lot of the roads. And that would be strike three. Power distribution isn't a problem at all. It might be in some areas. But the nice thing about the project is that we don't have to try and cover all of the US at once. We can start with medium sized cities in the South, where they already know the value of building roads to last, where they have more sunny days, and where there is sufficient number of roadways with power distribution in place already. There, it's simply going to make economic sense to build with these tiles instead of concrete tiles next time the road does happen to need repair. And these are the only things that matters. The rest are just gimmicks. Though, thunderf00t clearly doesn't realize how little power LEDs would need to provide some functionality at night or during the rain to make roads so much easier to navigate. But I don't even care about that. Or about the whole "recycled materials" crap. I don't care how they sell this idea. I'm not even sure this particular product is ever going to make it. But the idea of using solar panels to pave roads is absolutely solid. It makes both environmental and economical sense, and we are going to have that sooner or later.

I've discounted Pu-238 because of it's relatively long half-life and low mass defect. Nothing in 10-20y range is anywhere near as nice. But considering the reductions in necessary shielding, the fact that you'd need about 20g of fuel instead of something like 1g is not a big deal. So yeah, you are right. One could do this safely with Pu-238. And it'd actually only cost about $1M per phone, which is better than I expected.

Cell phone batteries these days are about 2.5Ah at 3.7V. That's about 35kJ. And a charge lasts about a day at moderate use. That's under 65MJ over 5 years. Most people change their phones at least that often. That's less than a microgram of mass defect energy. You can get that from a few milligrams of nuclear fuel. If you are stuck with efficiency of an RTG, that's still under a gram of fuel all in all. So yes, the answer is that you positively can build a phone that you will never need to recharge within its intended 5 year life span. And now for practical considerations. The nuclear fuel would have to be extremely unstable. The half-life would have to be on the order of a decade. That means, no naturally occurring isotope will do. This would have to be something you intentionally breed in a reactor. Expensive as hell and not even remotely environmentally friendly. Next, we go to power output. RTGs are not efficient, and you are not building a more efficient reactor on that scale. You'd be lucky to get 5% out of it, which means the reactor will be dumping almost 10W of heat constantly. You know how hot your phone gets after a long conversation? Picture that all the time. And now, the elephant in the room. Radiation. Most of the energy released by such a device is going to be in form of ionizing radiation. Unshielded, this power output would result in you taking a lethal dose in under a minute. Naturally, the very idea of making RTG is in absorbing radiation, but there are no materials that will absorb it efficiently enough on the scale of a cell phone. There is simply no way. Enough radiation will escape to make it a serious health hazard. At best, this thing might be safe enough for a quick phone call, and I wouldn't even bet on that. Maybe, there is sense of keeping something like this in a led-lined safe for emergencies, but I could think of a number of much safer and cheaper ways of getting power for one phone call.

Not instantly. And it has a very broad range of mixtures at which it is flammable. So if you have a leak, there is going to be enough in the immediate surroundings to catch fire. And if the leak happened while vehicle is parked in the garage, you're almost guaranteed an explosion.

But you can't "press them together". You have to change topology of the sheet to do that. Which you cannot do if you cannot unweave the fibers that make up the sheet, and weave them back together differently. Similarly, we have no way of changing topology of our space-time. It's entirely possible that primordial wormholes exist, and can be manipulated to create such "shortcuts", but you can't create a new one. There is no mechanism predicted or observed that alters topology.

We have. I believe, it was last year when they moved it up from suspected to be observed to confirmed. And it has nothing to do with gravity. It's responsible for some bosons in electroweak having mass, and contributes a bit to the mass of some other particles. But most of the mass is dynamically generated, anyways.

It's extremely straight forward. Gravity is a gauge force of the local Poincare symmetries. (Yang-Mills theory. Note: Wikipedia incorrectly states that it's an SU(N) theory. Yang-Mills is valid for any Lie group, including Poincare. Just in case you'll want to look this up.) The conserved charge of Poincare group is the stress-energy tensor, and it is also the charge to which the gravitational field couples. In other words, things that are source of gravity are also the things that are attracted by gravity. That answers part of your question. The other part is why these things have mass. Well, that's also pretty straight forward. The stress-energy tensor is a frame-invariant quantity, which, when projected onto a particular frame of reference, gives you the four-momentum density. (pμ = Tμνuν) In other words, once you pick a particular frame of reference, the gravitational field generated by an object corresponds to its energy and momentum. The Lorentz-invariant magnitude of the four-momentum vector is the rest mass. (pμpμ = m²) So it's not so much that mass causes gravity, as that anything that generates or is affected by gravity will also have mass. (That mass could be zero. E.g. photons.) Inertia is just as trivial. For free-propagating matter (as opposed to virtual or confined particles) the four-momentum and the proper velocity vectors have the same direction. That's a consequence of field equations for matter. And since proper velocity always has magnitude c, this means that any acceleration requires a change of momentum. Rate of change of momentum is what we call a force. So force is needed to alter trajectory, and that's inertia. I don't know how much it's going to help you in building a ship, but that's exactly how these things work.

You're not listening. They wouldn't even know that rocket is there. Equipment isn't designed to register launches of anything that small. If it was, the IR satellites would raise an alarm over a fireworks display, and the orbital tracking would be constantly reporting threats from meteorites on collision course. They simply aren't looking for anything that small.

That's not even a little true. People who don't study the subject seem to greatly underestimate how much we really know about it. We know how it works. We've basically known since Einstein wrote his paper on General Relativity. But there were a lot of open questions on whether it really works this way, why the curvature, and why it seems so different from other forces. We have answers to these questions now. In fact, we've had these for over half a century as well. We now have a unified model that covers all of the natural forces, and we know the conditions on generating said forces. But even all of that information is tangent to the main point. Had we discovered that Einstein's equations were wrong, we'd need to learn more about gravity. But they are not. And General Relativity already gives us way more information about the nature of gravity that we've known about electromagnetism by the time radio was invented. All the people had to go on were Maxwell's Equations, without having any idea why they work. And that's all you need to figure out how to generate electromagnetic waves, manipulate the charges, and build at least rudimentary versions of any electronic device we have today. If we ever learn to manipulate gravity the way we manipulate electric fields, it will not come from any new understanding of gravity itself. Just like our ability to replace radio lamps with silicon, and build computers that don't have to be a size of the large city did not come from any changes in our understanding of electrodynamics. We know how to generate gravity. We know how to manipulate it and make it do just about anything we want. What we don't know how to do is make the source smaller than a planet. But we have some ideas, and we are making great progress. Nothing to say that we won't run into impossible problems along the way, but we are definitely moving along right now.

A rocket with 1kg payload is not even going to make a blip on any early warning system. You're more likely to get in trouble with your local aviation authority than any government. In a long run, if these things do become affordable enough for some shady people to start making them, yeah, I'm sure they'll get more sensitive equipment and require formal approval for launch. But since that's not going to happen without some major revolution in propulsion technology, it's an academic point. So you just went from a ~9km/s requirement down to ~8km/s. That's not something an upper stage can manage. You still need most of your rocket, as well as one hell of a balloon.

Yeah, like I said, something a bit heavier than Uranus should be able to do the job with minimal damage. The larger you go, the "softer" you can make tidal forces. A rogue star could eject a planet with barely any tidal disturbance. If you look at the derivation of Roche Limit, you'll see where the tidal force equations come from. They are pretty straight forward, but might be a bit harder to visualize. For actual ejection, you can consider the motion relative to the center of mass. In that case, Earth and Rogue planet end up following hyperbolic trajectories around the center of mass, and you can use all of the math for such trajectories to make necessary computations. Just don't forget to shift things back to the frame of reference where Earth was initially motionless. For an estimate, you can neglect Sun's gravity here. You are just looking for Earth gaining 12km/s relative to its original state.

Rakaydos, you can't be thinking of gravity as curvature in the manifold, and then think about how gravity propagates through said curvature. Does that make sense? Wormhole, by the fact of its very existence, is going to affect gravity around it. And various massive objects near the wormhole are going to affect the wormhole, certainly. But you can't just say that if a wormhole links two points in 3-space, then massive objects on one side are going to attract objects on the other. Just doesn't work this way on this level. More importantly, even if there is indirect interaction, from our point of view, it will simply look like extra mass of the black hole at the center of the galaxy. It won't appear like an extra pull throughout the galaxy, which is what we're observing. Also, even if we prove that some of the supermassive black holes are actually wormholes, there is no guarantee that they link to anywhere in our space. Of course, if they are not traversable, and barring FTL travel, that is a moot point. There are statements that can be proven to be impossible to prove or disprove. That should pretty much put the rest of that silly discussion to rest.

If Sun was orbiting a point mass, dropping straight down cuts semi-major axis in half, so you'd be looking at (1/2)*(1/2)^(3/2) = (1/4)/sqrt(2) of the period. In practice, as you move towards the center, effective mass will decrease, so it will take a bit longer. So yeah, 1/4 is probably close to truth. No. The other side would also have an event horizon. It might be a wormhole, but nobody said that it's traversable. You can't pass through this wormhole without an FTL drive. Anything that goes in, from either side, would just get trapped in the middle. You don't need exotic matter to make a wormhole. You need exotic matter to make a traversable wormhole. See above. Again, you've misunderstood something. Actually, quite a few things. There is no "core". There is a singularity. It can contain a huge amount of mass, but calling it matter is a bit silly. There is no distinction between matter and energy at that point. And wormholes will also have one of these. Except that matter of "center" is a bit blurry here.

Particle formalism is a mathematical trick. Particle's indeterminate momentum/position is a consequence of said formalism. And the reason we rely on particle formalism is that we are dealing with an object we cannot directly experience, and that is very different from anything we can. So either of these works, depending on which aspect of it you focus on.

Correct. Proton does not use cryo-fuels, so there is no ice formation. Falcon 9 does. Cryogenic oxidizer, LOX, to be specific. Hypergolic fuels are self-igniting. It has nothing to do with them being cryogenic or not. As for gas used to maintain tank pressure, it can be LN2 generated, but there are a number of other alternatives. There are many gas generators that are non-cryogenic as well.

No. Earth-like world would have to approach too close to Earth. Tidal forces (or direct impact) would make it impossible to survive. Unfortunately, you do need a gas giant. Earth's orbital velocity is approximately 30km/s. To escape, you need to boost it to 42km/s. So you need to pick up 12km/s from a fly-by of the rogue planet. In principle, with point masses, you could get a boost to an arbitrary speed. The rogue just has to move fast enough. But you want the planet intact, and that limits the closest approach distance. The absolute minimum is Roche limit for a liquid body. For rogue of Earth's mass, that puts you at about 8,000km. The rogue would take up a quarter of the sky at the closest approach if it came that close. But that limit is just enough to prevent Earth from falling apart. You'd still loose a lot of atmosphere, and you are almost guaranteed all sorts of tectonic problems. Fortunately, tidal forces drop really fast with distance. At 20,000km, you'd experience less than 1/15th of Earth's gravity in the pull, and that shouldn't cause any catastrophic problems. Doing some orbital mechanics magics, we get maximum boost at that approach to be just 6.3km/s. Which will still knock Earth's aphelion well past the orbit of Mars, but it's not enough to cause a complete escape. As the size of the rogue increases, so will we have to increase the closest approach distance. With that in mind, the minimum mass required to completely eject Earth from Sun's orbit is about 18 Earths. That's a little larger than Uranus. And so, you certainly need a gas giant. As for how long the Earth inhabitants would have, it depends on the exact trajectory. But it's going to be matter of weeks before dramatic changes are felt, and matter of months before everything is frozen solid. Not much time at all. And that's assuming that the planet isn't launched on trajectory that takes it near Sol before carrying out of the system. It could be a fiery doom for all living, rather than a cold one.

That's actually a very good question. Just because something is receding from you faster than light, doesn't mean you can't catch up to it by moving at sub-light speeds. Because, assuming uniform rate of expansion, as you make your way towards the remote object, it would appear to slow down. You might just be able to catch up with some such objects. It's all going to depend on rate of acceleration of the expansion. And I honestly don't know if there is a way to go past visible universe or not without means of FTL travel. If I can find a reasonable approximation of the Universe's metric, I might be able to do some computations to find out, but I wouldn't know where to start without it. I can ask around.

Correction, from perspective of the ship, time flows normally. The reason the ship's computer would have trouble responding is because due to space contraction, the distance between origin and destination is effectively zero. Of course, that gives you the same result. Voyage time is effectively zero. But getting up to light speed in finite speed also requires infinite acceleration. So any interstellar mission is going to be acceleration-limited, even if you somehow found a way to provide all of the required energy.

You do get both contributions, though. And this doesn't just work this way for black holes. You have the same effect on satellites in Earth's orbit, and it has to be taken into account by GPS satellites, or any other means of precise radio tracking/positioning. Person standing on the surface is affected the most by gravitational time dilation, but only very little by Earth's relatively slow rotation. An astronaut on the ISS is affected by gravity almost as much, but also by high orbital velocity, so his clock runs slower than that of any person on Earth. On the other hand, a GPS satellite is on high enough orbit that its clock runs faster than that on the GPS receiver on Earth, because gravitational time dilation is much weaker up there, and it's not moving fast enough to compensate. The altitude at which time flows at the same rate for a person on Earth as it does for a satellite is about 3,000km.