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Tsiolkovsky equation was stated with specific impulse. And "specific" means per unit mass to everyone but the U.S. engineers. Tsiolkovsky woudl not use exhaust velocity, because there is no exact value for that. You can say that there is an effective mean exhaust velocity, and that it is equal to specific impulse, but you still have to define specific impulse first. So there is no reason to talk about exhaust velocity. Specific impulse is an unambiguous value, and that's what Tsiolkovsky would have used.

Physicist, checking in. No, Alcubierre Drive, by itself, does not allow for time travel. An arbitrary FTL drive is, indeed, a time machine, but there are restrictions on Alcubierre Drive specifically that prevent you from using it as such in flat space-time. One can come up with a suitable curved space-time which will have closed time-like curves which can be navigated under Alcubierre Drive. It is not certain if such curvature exists naturally, however. Creating something like that artificially is not something we can do with physics as we know it. On the other hand, principles that go into creating a warp bubble in the first place might be usable to construct a time machine completely independently. That, however, is not actually a problem with any of the physics we know.

There is some bad science behind Quantum Thrusters that resulted in them appearing to be over-unity efficient. From perspective of field theory, a good Quantum Thruster is just a very efficient photon drive. In other words, you need roughly 300kW of power per 1N of thrust. Which might actually turn out to be the best photon drive we can build, but without a matter-antimatter reactor, it's not sufficiently efficient to be of any use. If your power source is nuclear, your best bet is ion drives. You'll get better maximum dV for amount of fuel/propellant you bring.

It was most certainly not in original Tsiolkovsky Rocket Equation, because he was a Russian, and would have used Metric system. In which Specific Impulse is measured in impulse per mass, which is N*s/kg = m/s. These are units of exhaust velocity, and is, in fact, equal to the mean exhaust velocity. Americans have defined it as lb*s/lb, using pounds for both force and mass, as American engineers often do, which gave them impulse in seconds and the factor of g in the equation. The equation with g in it is a product of American space program.

Moon's orbit is pretty elliptic, by the way. It can take more than 5 days from a high point. But it's still in the ballpark of the figure Brotoro specified and it's computed exactly as he stated.

It's not just a change of charge. Any conserved quantities not carried by photon have to be exact opposite. Strangeness, baryon number, etc. There is also a time reversal, but that's a slightly confusing topic. There is a lot of mirror image quality to it. "Same, but opposite," if that makes any sense. Most importantly, if the universe was built up entirely out of anti-matter, it'd work exactly the same way. Which is which is entirely arbitrary. But yeah, in terms of gravitational interaction, matter and anti-matter are supposed to be identical. Again, we don't have actual experiments confirming this yet, but it's one of these things that really ought to work that way, and there are many indirect indications that it does.

There is no gravitational constant in these equations. There is Earth's gravity, but that's only there if you are using silly units.

There isn't a lot of electric field in most of the space, because matter is neutral on average. So it's not the question of how much it'd be affected. A charge particle on earth is affected by the same electric field in the same way as it is in space. But while gravitational fields far out in space can be significant, electric fields usually aren't.

You can count the average on just the time the machine is running. The idle time can (and, in fact, should) be used to check the neutral position.

Gravity has the same range as electromagnetic interaction. The difference is about the charge associated with the force. The relevant charge for gravity is the stress-energy tensor. So absolutely everything has gravitational charge. Electromagnetic forces are subject to electric charge, and there are plenty of electrically neutral particles. Photon being one of them. And in fact, it's true, that photon only carries gravitational charge. So gravity is the only force that will influence photon's propagation. Photon itself, however, it the gauge boson of electromagnetic force, so it will still interact with electrically charged particles. On average, matter is neutral in all but gravitational charge. That's the main reason you see gravity having such a long reach.

Same thing that would happen if you drop in ordinary matter.

That's actually entirely expected of your setup. It's pretty typical of the way most people swing on the swing set. And again, the critical test is that of average displacement. Your setup does not pass that test.

And the standard deviation is 4.24 on the left and 5.45 on the right. Both of which are greater than your difference. As a matter of fact, if I take each of these pairs, subtract left - right, and take standard deviation of that, which is statistically more meaningful, since amplitude is going to change through the experiment, I get standard deviation of 8.08. That's twice the average of this difference. This is what I basically expect from random chance. If you think this is a real, systematic difference, and if this statistics persists, you'd need to repeat this whole experiment about 40 more times. If this is a real effect, that will bring the error down, putting your result outside of 3 sigmas. But it's looking random so far, and I'm pretty sure the source of randomness are oscillations of the base and not any sort of bias.

The cause of nausea is Coriolis Effect. If you move your head in a spinning habitat, it results in forces on fluids in your inner ear, which end up sensing a different direction for "gravity" then what you perceive from your eyes and your feet*. From perspective of your brain, it is the same problem as caused by too much alcohol, for example, when inner ear also sends wrong information, and is interpreted as poisoning. Hence the nausea to try and get rid of whatever it is that got you poisoned. * There are 3 senses that help you determine orientation in space, not just two. Pressure on the soles of your feet is just as important as sight and inner ear. Usually, if just one of the three is off, but the other two agree, the two senses in agreement can override the one that isn't. Placing your feet firmly on the ground can often help get rid of the nausea induced by problems with inner ear.

It's not about ft/s vs m/s. It's about whether you use Newtons or pounds for thrust and weight.

1 hour and 45 minutes, approximately. The exact value can depend on the orbit a little. For a spherical planet, the equation is T = 2À Sqrt(r³/(GM)), where r is distance from planet's center, M is planet's mass, and G is gravitational constant. Real planets aren't perfect spheres, however, so there will be some corrections. I've taken r to be Mars' mean radius + 100km. But that's sort of an average. Can be a few minutes more or less for a particular orbit.

Small rockets are much harder to do efficiently than large ones, unfortunately. That's why you don't see a lot of dedicated cubesat launchers. They are usually taken "along for a ride" with heavier cargo. In terms of what they really use for real rockets, they are essentially the same equations, but the methods for solving them are more complicated. A general book on diff equations probably won't be much help on numerical methods, but there are books on numerical methods for solving differential equations. There is good info on Wikipedia, too. If you look up Runge-Kutta Methods, you'll find some good info to get you started. The other big difference is drag model. I'm pretty sure your rocket will stay strictly sub-sonic. Once you get into transonic regions, drag model changes a lot. Working out exactly how your rocket is going to behave as it goes from Mach .9 to Mach 1.1 is going to be very difficult. But that can be a fairly quick section, especially if you throttle up to punch through transonic faster. But then the supersonic flight will have a different drag coefficient, and as you start getting into hypersonic, things start to change again. This is something that a lot of numerical work would get into. The good news is that if your rocket is perfectly cylindrical, especially if your upper stages have no exposed fins, you can build a fairly simple numerical solver that will give you very good results. But you do need to understand a lot of hydrodynamics to write the code for it. There might be some libraries or even complete programs for it out there, though. And, of course, you'll need more realistic fuel flow solution. In that sample code, I've assumed constant fuel flow for constant thrust and constant ISP. That's not going to be the case for a real rocket. Be it solid fuel, hybrid, or liquid rocket, you will have variations in fuel flow throughout ascent. So you'll have a separate differential equation for mass of the rocket, which you'll be solving together with equations of motion as a system. It's not that much more difficult, but one is the first order and the other is second order, and it's something you need to understand how to deal with. If you understand completely how Runge-Kutta methods work, though, and how to apply them to higher order equations, you'll be able to figure it out, even if you end up using a more complex method as a basis.

In your case, centrifugal potential is no different from gravitational potential. It's really that simple. Another way to think of it, imagine a centrifuge that's already spinning. It starts out completely empty, vacuum, and you start filling it with liquid until it's almost completely full. Yes, the centrifugal force is going to pull the liquid to the sides, but at the center, you still just have vacuum.

Things like capilary pressure and osmotic pressure can sometimes work as negative pressure. But none of these things are going to affect boiling point as if pressure is negative. In fact, I'm pretty confident nothing will.

Looks like it. And while implicit Euler is an improvement, there are better, simpler methods. Even though it's not designed to deal with drag, Verlet should work extremely well here. Here is the basic code using Velocity Verlet as the integration method. rocket.m To run it in octave, just find create a file with this code somewhere, say, "C:\code\rocket.m". Start up octave, navigate to this directory using command "cd c:\code" and then just run "rocket". (Extension isn't needed. It will look for a .m file.) It's pretty basic, but you can probably figure out how to modify it to fit your parameters.

No, you cannot. For the same reason that gravity pulling down on gas particles never creates negative pressure in space. Vacuum is the most you can do.

I'd sign it too. In fact, I'd be entirely happy to do all the work of setting it up, if admins are too bussy.

Doozler has the right take on it. This is a much simpler problem if your variables are number of engines and the amount of fuel. And this isn't really an optimization problem. It's a simple algebraic equation.

Well, gravitons are tricky to talk about. There is not really a perfectly self-consistent description of them. But we can talk about photons. We've said that light can't get out, but black holes can have an electric charge. And then they do produce an electric field. If you've heard of gravitons, you probably know that photons carry electric field. So the million dollar question is, if photons can't get out of the black hole, how come it can still have an electric field. And the reason comes from differences between virtual particles and real particles. The word "real" is just used to distinguish them from virtual particles. Kind of like "real numbers". It doesn't make the other ones fake, or anything. The other term for them is "mass shell particles," but that requires understanding of what a mass shell is. In simplest terms, it means they have a relationship between their mass and momentum. They have a number of properties, but most importantly, they propagate through space the way you expect a particle to propagate. They move in direction of their momentum, and if they have mass, the velocity relates to the momentum. If they don't have mass, like the photons, then they propagate at the speed of light, but still in direction pointed to by their momentum. Another important bit is that they follow normal Relativity rules. All real particles travel along time-like trajectories. If no forces other than gravity act on them, they move along space-time's geodesics, which are the closest thing to a "straight line" in curved space-time. Inside the black hole, all time-like trajectories lead into the center of the black hole. That's why nothing can escape. In order to go from a time-like trajectory to a space-like trajectory, one must travel faster than light, and real particles simply cannot do that. Virtual particles play by different rules. For a virtual particle, relationship between the way it propagates and its momentum is nowhere near as rigid. It can carry momentum pointing one way to a target located in completely opposite direction. It does not, necessarily, have a well-defined mass. Though, it can still be massless. Most importantly, it can follow time-like paths. There are other limitations, however. They can only be force-carriers. They cannot simply fly off into the distance. They have to go from source of the force they carry to their target. They can take really odd paths getting there, but they can't go anywhere else. And they do have limited range. For massless gauge bosons, such as photons, the range limitation gives you inverse square law. For the massive ones, like the Z and W bosons of weak interaction, the range is far, far shorter. Which is part of why weak interactions are, well, weak. Because virtual particles can take detours, they aren't bound to time-like geodesics like the real particles are. And they can find their way out of the black hole. But as noted before, the only thing they can carry is the interaction force between the black hole and whatever happens to fly by. Since they can't interact with anything along their path, they do not violate cosmic sensor. So this is why electric field can escape the black hole, while light does not, despite both being carried by photons. Gravity is going to work in a similar way. Black hole does induce gravitational field in its vicinity, but no gravitational waves can escape it any more than light can. Any self-consistent description of gravitons as a particle would have to have a similar distinction between real gravitons and virtual gravitons to account for this. One last note. If you are wondering if this is all related to Hawking Radiation, yes, it is. Both are effects from Quantum Mechanics based around the fact that particles don't have to stick strictly to time-like trajectories. But Hawking Radiation does have quite a few other things going on.

Air-augmented rockets and SABRE are the two practical ways to use the general concept. But as you can see, both have to get rather creative to get around the problems Ralathon talks about.