K^2

Titan! There are several places in Solar System where life may exist. But if there is some life, say, on Mars, it could have gotten there from Earth. Or vice versa. We already know that organic materials can be lifted off the planet and end up on another planet, and we know that there are bacteria that can survive such a trip. So it'd be a hell of a discovery, but not necessarily a discovery of alien life. But Titan... If there is life there, of which there is some indication, it would be very different from life on Earth, making common origin with Earth's life extremely unlikely. If there is life on Titan, we go from one planet on which life evolved to two planets on which life evolved in a Solar system. We go from one point of data, which is useless, and tells us nothing about life in the rest of the universe, to two points of data, from which we can make an estimate for probability of life elsewhere. And if there is, indeed, life on Titan, it would mean that the galaxy is absolutely teeming with life. So yes, if there is one place in this Solar System that I would want to see a probe returned from it would be from Titan's soil.

But the other half are. Why don't you put some effort into it yourself? The other half aren't "google-able" because they are wrong questions. If you learned a little bit about how things work rather than try and memorize trivia, you'd understand why. And if you don't try to understand how these things work, just knowing these things isn't going to be of any use.

Right. Except that 2s is extremely low for specific impulse of an SRB. I'd re-check the thrust. Also, you wrote 0.150T the first time, and 0.150kT the second. If it's kT, that's 1,000 times more thrust, giving you 1,000 times higher specific impulse. But that's too high. Could this be something like 150kN by any chance? Or .150MN? That would give you 200s specific impulse.

NAR regulations recommend 1,000 feet clearance for any F motor launches. 400 feet for the C motors. So yes, if there is limited open space, definitely go smaller. Though, even with a pair of C motors your rocket might cover more ground if it goes off course and knock someone's window out. So be careful, and do the tests as far away from everything as possible to make sure your rocket flies true. For launch system, take a look at commercial systems. They aren't expensive, if you want to just buy one, or if you are required or just want to build your own, they might give you some good ideas. All of them effectively consist of a metal rod that can be angled for plane launches, a metal plate at the bottom of the rod to act as the firewall, and a tripod holding all of this fixed on the ground. For the electronic launch of multiple motors, what I found to work best is using commercial igniters wired in parallel and taking the wire to the car battery. Unlike the cheap AA battery launchers, the moment you touch wires to the car battery, the igniters will go off, so there is no guessing on when the rocket will take off, and you get as close to simultaneous ignition as possible. That said, even with simultaneous ignition I've had trouble keeping a multi-motor rocket on a straight path. If you want something reliable, it's really best to have one motor per stage.

You got total impulse in pound-seconds and then divided it by tons? "Well, there's your problem." If you insist doing this in imperial units, and assuming that these really are American Tons (though, metric and English ton are pretty close), then this is the correct way of walking through it. The total impulse is, indeed, 15,000 lb-s. You can divide this by weight of fuel in pounds to get ISP in the same convention that KSP uses. (It's also a standard one for Rocket Engineers in U.S.) So we have 15,000 lb-s / 7,500lb = 2s. This is a very low specific impulse, but that's what it works out to if this is, indeed, 300lb of thrust rocket. But lets pretend that this is correct. Specific impulse in units of seconds can be used with either units, but for sake of consistency, lets carry on with Imperial. delta-V = 2s * 32.2ft/s² * ln(4T/0.25T) = 178.6 ft/s. So where did these 32.2ft/s² come from? That's acceleration due to gravity on Earth and shows up because of relationship between pounds of weight and pounds of thrust. Equivalently, if you were to use this formula in metric system, you'd multiply by 9.8m/s², and in either case it has to do with your ISP being in seconds. Now, you seem to be using values for Advanced SRB mod. I'm not familiar with it, but I'm guessing the thrust is higher, with specific impulse closer to 200s. You should check these numbers. Thrust in KSP is usually given in kN. Also, the tons are metric tons, and each one is 1,000 kg instead of 2,000lb.

All rocket motors are a little different, but Estes G40 have about 1km/s of delta-V in them. You can probably expect something similar out of other G motors. Of course, that's without any payload whatsoever. Reasonably, you could expect about 400m/s out of your rocket. Again, most of that will be eaten up by drag, so in reality the rocket will never get even close to Mach 1, but it should still be enough to get a couple of kilometers of altitude out of it, at least. So yeah, a G motor should do it. It just needs a rocket with a nice, aerodynamic body and good stability. Keep in mind that as you scale up the motor, you need to scale up everything else. The amount of clear space for launch, distance between you and the rocket when you launch it, and so on.

In United States, there are no formal laws to prevent you from launching a rocket into space from your back yard. You'll probably run into all sorts of regulations if you try to make money off of it, but so longs as its a purely "amateur"* project, it falls under umbrella of amateur rocketry laws which are quite flexible. You would need a high power license which is not that difficult to obtain, and if you are launching anything serious, you should inform FAA so that they can issue a NOTAM to prevent a plane from flying into it. But all of this is fairly straight forward. It's not something you have to be a mega-corp to set up and file. Compared to the challenge of actually building a rocket that can reach space, let alone establish orbit, getting permissions for one is easy. That said, first "amateur"* rocket only reached space in something like 2010, and nobody came even close to establishing orbit yet. * "Amateur" in this context simply means non-commercial. People involved in all of the projects with any success have been anything but.

Most C engines are gun powder-based. Estes motors in the A-E range certainly are. To break 1.5km even in ballistic regime you'd need over 170m/s of delta-V, and at that point drag is going to be significant. These kinds of motors will only give you about 30s of ISP, so it'd be nearly impossible to break 1.5km. If you are really planning to go that high, you need to go with composite motors. These can have ISP well in excess of 200s. With one of these you can have effective delta-V nearing speed of sound, and that's going to be enough to give you 2-3km of altitude if drag isn't too heigh and you get your rocket to fly straight. The composites typically start roughly with the F class. These do cost 2-3 times more than regular motors, and they do require special igniters and launch system, but on the plus side, they aren't considered high power rockets, so you do not need special kind of licensing. All of the standard precautions apply. This is something to work up to gradually, and maybe I'd start with the D and E rockets, maybe even something with an E booster and C primary stage to see how far you can get that. But if you are going fore altitude, composites are your goal.

You are mixing units. That's not a good way to do things, and I'm pretty sure there is an error in your computations because of it. (But because you don't label all of your numbers, I'm not entirely sure. What's '3.75' in "ISP = 15000 / 3.75 = 4000"?) It's possible to do all of this in imperial units, but you will pick up a factor of 32ft/s² in there due to difference between pounds of force and pounds of mass. At any rate, it is way easier to convert everything to metric. There is also a difference of convention in ISP. It may be defined as impulse per weight or impulse per mass. You will then get ISP in units of seconds or m/s respectively. Your computations are set up to look as if you have specific impulse of 4,000s, which is way too much. Even NERVA only has about 800s, and to get 4,000s you need an ion drive. SRB would have something closer to 250s. And if you define ISP as impulse per weight, then the correct formula for delta-V is ISP*g*ln(m1/m0). The factor of g, which is Earth's gravity by convention, ensures that your delta-V comes out in m/s. Units are important. Always check them.

You have to make turns cost something. Like a very small amount of fuel, in this case, or gong for a complete solution with RCS fuel consumed and also optimzied for. That's the only way I know.

Wow. I know that almost every announcement about Uranus leads to some giggles, but this is just too much.

Well, there are real reasons why CO2 can have significant impact despite the fact that absorption is already saturated at these wavelengths and that it's a minor fraction of total absorption when compared to how much water vapor contributes. Basically, altitude at which IR equilibrium is achieved is more sensitive to CO2 levels than H2O levels. The problem is that we still don't know at what point that actually becomes a problem, because modeling this stuff is insanely difficult, and experimenting with it directly is not practically possible.

It's almost certainly Verlet. That's practically a standard in gaming industry. Mostly because Verlet is conservative (at least on average) under harmonic potential, meaning you don't run into problems with collisions.

Not to mention H2O being a much stronger greenhouse gas than CO2 and present in much higher concentrations in upper atmosphere. But yeah, yeah, I know about non-overlapping spectra.

Keep in mind that the error isn't necessarily on your end. KSP might be sloppy about integrating the forces. A naive Euler integration of drag while rocket is accelerating would result in underestimating drag, and that might be responsible for KSP rocket going a few km higher.

I think these two require clarification. We don't have evidence of climate changing this rapidly in the past, but the further back we go, the harder it is to detect rapid changes. Its very difficult to say just how rapid some of the past climate shifts have been. And some of them have been rapid enough to cause serious ecological problems. It's possible that these are also related to some mass emissions, like volcanic eruptions, meteorite strikes, etc. But we just don't know. There are some problems with data as well. There is major bias in where we have been taking measurements and what we are comparing them to. As for CO2 being the greenhouse gas, the main problem is with what we mean by the greenhouse gases. The greenhouse model of environment heating is simply wrong. An actual glass greenhouse placed in vacuum would have the same equilibrium temperature as a bare rock. The reason greenhouses work down here is because they are placed in an environment. The way the atmosphere heats up the planet is way more complicated and has to do with convective cycles and radiation equilibria at different altitudes. The atmosphere, in this case, works as a heat pump, not a greenhouse. If the atmosphere was perfectly stable, with no convective flows, CO2 in upper atmosphere would actually result in cooling, due to reduction in IR albedo. Despite that, many estimates on impact of CO2 are done based on the faulty greenhouse model. In fact, I have not seen a good workup on how CO2 actually affects global temperatures that takes weather into account. I wonder if that might be because "everyone knows that CO2 is a greenhouse gas." Nothing about climate is that clear cut. We need to be talking about it. We need to be doing more research. Convincing people that we have reached consensus is actually extremely counterproductive.

There is no consensus on anthropogenic climate change. There isn't even a consensus on which way the climate is changing. Basically, the fact that it's changing is pretty much the only thing everyone in the scientific community agrees with. But since it has always been changing, and none of the models in place are sufficiently good to even agree with the pre-industrial record, claiming that we know how humans are affecting it all is just silly. Now, I agree that it's better to be safe than sorry, and we know of ways in which we can reduce our impact on the environment, even if we don't completely understand what that impact is. And it's a good idea to try and scale back on emissions, try to stop deforestation, and so on. This is true regardless of whether these things impact global climate in a significant way. But it bugs me when people try and claim that we understand anything about how we impact global climate, that it's certainly for the worse, and that this is something that everyone in the field has agreed upon. This just isn't so. We don't know what we are dealing with, and there is no consensus. There is no need to misinform the public further to try and convince them to do the "right thing". Being responsible to local environment shouldn't be something you have to scare people into using a made up global crisis.

Oh? Such as?

Have you checked your solution against the analytic solutions for the simplified case? In other words, with simple exponentially dropping atmosphere, do you get optimal ascent at terminal velocity for most of the trip?

Much too small to detect? If your teacher actually said precisely that, I suggest you mention to him that police radar measures Doppler shift on a moving vehicle to determine its speed. Keeping in mind that police radars have been around since the 50's and they measure the shift caused by difference in velocity due to a few miles per hour. Ditto weather radar, which uses the same technology to detect movements of water droplets in the atmosphere. It's a small effect, but if it's what you are actually looking to measure, small differences between two frequencies can be measured extremely precisely due to effect known as beat in acoustics. The reflected signal and source signal are mixed, and the mixed signal is picked up by the receiver tuned to pick up much lower frequencies. Measuring the actual frequency that is picked up lets you determine the velocity of the moving object.

The effect is there and it's measurable, but in terms of sending/receiving radio transmissions it is not really significant at the speeds of typical spacecraft. Channel selection is going to be something like 1/100. So you'd have to travel about 1% of the speed of light to make a difference. This might be closer to 1/1000 in the microwave ranges, but it's still much, much faster than any spacecraft ever launched.

It's a matter of the rate at which the radiation is released. Yes, there is probably enough nuclear fuel in a large RTG to give everyone on the planet a lethal dose, but if you split the fuel up into small enough chunk, the rate at which the radiation is released by each one is going to be so slow that it's going to take longer than human life span to do so. Because Plutonium-239 has fairly long half-life, in tens of thousands of years, to give off dangerous levels of radiation it needs to be reasonably concentrated. That means if you spread the RTG fuel over a large chunk of Florida's coast, it's not going to be a total disaster. Situation with nuclear meltdowns is actually very different and produces short-lived isotopes that are the real danger, and there isn't enough fuel in RTG to result in a meltdown. But more generally, dispersal isn't going to be even that bad. The rocket will become a chemical fireball in the worst case scenario. That's probably enough to melt some of the fuel, but not to evaporate it. Most of the fuel will end up landing in a very small area. Some of it might turn into a molten spray and cover a slightly larger area. This can still be bad if this lands in populated area, but rocket landing in populated area isn't much better. Given typical trajectories, this will most likely result in some radiation of either area around the launch pad or over the ocean, but nothing too serious, so long as majority of the fuel is promptly recovered. All in all, it is a hazard, but not as bad as it might sound. It's comparable to all of the standard hazards of lighting a controlled explosion under a giant tank of (frequently toxic) fuels.

Bah, they really ought to have been more careful with names. Typically, the name "Classical Mechanics," is reserved for a much heavier course. I was about to write a couple of paragraphs warning people that Classical Mechanics is far more advanced than anything in KSP, but this course actually seems like it's designed to be an introductory one.

No. It's not true. The boiling point lowers. Boiling point is the temperature at which the vapor pressure is greater than ambient. Vaporization happens at any temperature. Water at room temperature evaporates. It just does so more slowly. And as it evaporates, it cools down. Unless humidity in the room is 100%, water left on its own will be at lower temperature than the air in the room. You are correct in predicting that water will cool to the freezing point. But it will not stop evaporating then, either. It will continue to evaporate even when frozen. So the correct sequence of events for a blob of water that got accidentally released into the vacuum of space is that it will first begin to violently boil, breaking down into many tiny droplets. These droplets will cool to freezing point and freeze. The result will not be quite like snow, because freezing will be very fast. It will be more of a frozen mist. That frozen mist will then, over time, evaporate completely.

Kind of depends on what you mean by a "neutral" observer. Basically, any observer's perspective is just as valid as any others. So there is no preferred observer, and therefore, there isn't anybody who's any more "neutral" than anyone else in any sense of the word that I'm familiar with. There is a somewhat special class of observer frames known as inertial frames. If you want to think of these as more "neutral," that's fine. But so long as you keep acceleration in mind, perspective of an accelerated observer is also entirely valid. But other than that, yes. Time dilation and space contraction are going to compensate for any disagreement between different observers. Unfortunately, it's not a terribly useful way to think about it if you want to actually predict what will happen. But if you just need a peace of mind, that works.