# Tullius

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1. ## Math for calculating orbital rendezvous manovers

Exactly that, if you have two sides, resp. the ratio of their lengths, you can get the angle with arctan, in the same way as you can get the ratio of these sides by taking tan of the angle. arctan is the inverse function of tan, i.e. arctan = tan^-1. What does inverse function mean? If I have a function f mapping x to y, then f^-1 maps y to x (provided that no more than one x is mapped to y). What does this mean for tan? tan maps angles in (-pi/2,pi/2) resp. (-90°,90°) (depending on your notation of angles) to values in the real numbers, and arctan maps real numbers to angles in (-pi/2,pi/2) resp. (-90°,90°). For example tan(pi/4) = tan(45°) = 1, and arctan(1) = pi/4 = 45°. Or take a look at this graph tan maps values on the horizontal axis (usually called the x-axis) to values on the vertical axis (usually called the y-axis), arctan does the inverse: it maps values on the vertical axis to values on the horizontal axis.
2. ## NASA SLS and Orion

It would mean starting from zero, or accepting Falcon Heavy and New Glenn as alternatives. And while the former isn't really interesting for the senate to fund, since they would see the results even later, the latter two are less capable rockets than SLS, which, while one would quickly see some results, would have difficulties even putting a space station module into lunar orbit. And if you start anew with private contractors, every development works needs to be paid for 2 or 3 times, since you want competition. Also, either NASA lets 2 or 3 companies build the rocket entirely on their own, which would mean that NASA has little influence on the design and you have to find as many companies willing to do it, or NASA does the development itself, but buys different parts from different companies, which would reduce the efficiency gains. In short, cancelling SLS now would not just mean a huge blow to NASA's manned space exploration, but also leave NASA with something that might not necessarily be better. It might be necessary to redesign some parts of SLS, like maybe find a private contractor to develop new, cheaper engines to be build in NASA's facilities, but just cancelling SLS and putting the whole work in the hands of private companies won't necessarily improve anything. On the other hand, if NASA finds out in 3-5 years that SLS is indeed a dead end, there is a good chance that SpaceX and Blue Origin might have developed by that point an acceptable replacement, which NASA could buy directly without any of the lengthy procurement procedures, since there are only 1 or 2 viable possibilities.
3. ## Math for calculating orbital rendezvous manovers

sin and tan are the trigonometric functions sine and cosine (https://en.wikipedia.org/wiki/Trigonometric_functions). arctan is the inverse function of tan (https://en.wikipedia.org/wiki/Inverse_trigonometric_functions).
4. ## Blue Origin Thread (merged)

I think that SpaceX just wants for the time being save money on the development of a specialised 2nd stage for Falcon Heavy. The Falcon 9 2nd stage is good enough for the first flights of Falcon Heavy and provides it with a meaningful payload capacity, even if it means that recovering the core stage will cost a lot more fuel and thereby cost a lot in terms of payload fraction. And lets not forget that SpaceX wants to recover 2nd stages, so they are planning for quite some development in terms of Falcon 2nd stages, unlike the first stages, where most of the development already seems to have happened. After all, Falcon wouldn't be the first rocket that got a new second stage at some stage in its life cycle.
5. ## zipline tower escape system

I think the "if something where to happen during ingress" is relating much less to problems that astronauts might have to get into the capsule, but to a mishap with the rocket happening during that procedure, which would force the astronauts (who cannot yet use the LES, since they are not yet secured in their seats with the hatch closed) and the support crew to get away from the rocket as fast as possible, i.e. to use the zipline. This is relevant, because in case of the Shuttle, the external tank would already be fully fueled before the astronauts and their support crew would access the tower. And it is quite likely that it will be the same for SLS. In short, the zipline is the rescue plan for those people that will access the tower with a fully fueled rocket sitting next to them on the pad.
6. ## Machine learning

The AI doesn't grasp anything, it just notices that certain combinations of actions lead to certain scores. If you look at the console output in the stream, you see after each try the line "fitness: ...", which is the score the AI received in the previous try (the higher, the better). And at the moment the highest achieved score is 6,9... I am still unsure what the "adj fit" in the table means; maybe it is something like the average score achieved, and thereby showing the progress. But I am really not sure; I just see it being higher, if I check back after a few hours. So the AI might notice that certain directions of thrust lead to good scores, but it won't notice the behaviour of the Pe independently of the rest. But most of its tries ending up in quick turns might suggest that it noticed that thrusting horizontally leads to good scores, since it increases the periapsis. And "will take some time", it something like the motto of neural networks. It took AlphaGo a couple of months to increase from barely the level of good European Go player to beating one of the best human players. And that despite running on a supercomputer. In the experiment above, we are not even at 6000 tries. But in the end, we all needed quite a few tries before achieving our first orbit in KSP. And we knew what an orbit is, and maybe also read up on how to achieve orbit in KSP. And now imagine someone, who starts literally from 0, knowing absolutely nothing about the task ahead.
7. ## Machine learning

The score that the AI gets as a result after each try is also based on periapsis and apoapsis height. Or put differently, the scoring system knows what an orbit is and gives the AI a score based on how good its achieved "orbit" was. But sure, the scoring is much more difficult in the case of KSP than those of Go or Super Mario. For Go, it could be binary (win = good, loss = bad), or for Super Mario, one would probably base the score on the distance travelled before it died (since after all, winning means travelling the whole distance of a level. Or, to compare again with Super Mario, while the AI doesn't know that, if it falls into the holes in the ground, it will die, it will notice after a couple of attempts that jumping over them allows it to travel much further than falling into them. And since travelling further is good, it will start jumping over the holes.
8. ## Machine learning

The whole idea is that the AI starts from nothing, and doesn't even know what it is doing. It can play around with certain commands, gets a few bits of information (such as the navball, the altitude, etc.), but it doesn't know what those commands and pieces mean or what is an orbit or gravity turn, as it should learn that all by itself. The only way the AI gets information about how well it is doing is after each attempt, when it gets a score. So the AI starts with a completely random behaviour and gets a feedback in the form of a score. If the score is good, it will be more likely to attempt something similar in the future, if the score is bad, it will be less likely. For KSP, this is not the best idea, since there are well established concepts of going to orbit, but it is a school project about applying neural nets to playing KSP. So it is no problem, if it is completely pointless. There have been others before that let a similar AI (based on neural nets) learn how to play Super Mario, or Google that developed AlphaGo to beat even the best human Go players. Those two examples need a bit more "creativity" by the AIs, since there are no well-established solutions for their respective problems, unlike KSP, where people have already written kOS scripts to fly rockets to orbit. And, besides the above, why should the AI fly east? You can achieve orbit in any direction, it is just a bit easier, if you go east. But the AI probably doesn't know that yet, and depending on the scoring, it might never learn it (if it is just about getting into orbit).
9. ## Book over Space propulsion system

Noticing that you are from Switzerland, I just checked on the website of the library of the ETH Zürich. While it is on loan from the ETH (and the EPFL), it is still available from one university in the NEBIS (https://www.nebis.ch/en/frontpage/). So if you are at a swiss university with access to the NEBIS catalogue, you might request it from there.
10. ## zipline tower escape system

Maybe some overpressure valve locking up or a fuel leak. But I think it is probably more about having an escape plan "just in case", than any specific danger. After all, needing 2 minutes to get away from the rocket is better than 10 or more minutes (just think of the distance they have to cover from the top of the tower until they are safe).
11. ## zipline tower escape system

No, 15 kg. It is a bit difficult to find informations, but Germany's similar ATF Dingo protected its crew, when it drove over an anti-tank mine with 6 kg of explosives. The explosion created a crater with a diameter of 2 metres and hurled the Dingo 2 metres sideways, but only 2 crew members got lightly injured.
12. ## Navier-Stokes Solution Effects

First, I am a mathematician that looked up on wikipedia what Navier-Stokes and the question are about and not a physicist, but I think that is not a bad thing for answering the above question. The Navier-Stokes equation, like the heat equation or most differential equations, can be solved numerically, i.e. approximately, and that to a rather high precision (given sufficiently large computing power). And that is also the most we can ask for, as explicit solutions generally can only be found for special cases. So everything is good and your question is pointless? Well, it is not so easy. If you want to approximate a solution numerically, it needs to exist and be sufficiently nice. And usually it is also very nice to have a unique solution. This is were the mathematics come into play. For the heat equation, under minimal restrictions on your domain (the shape of your object) and the initial values (the initial distribution of the heat in your object), you can mathematically prove the existence and uniqueness of a bounded solution (boundedness is good, since it prevents the temperature from rising to infinity). So while mathematics is in general incapable of providing us with an explicit solution, it ensures us that the equation actually makes sense for physics and more importantly that our numerical approach to find a solution is sane (approximating a solution, which does not exist or is not unique, doesn't make sense). For Navier-Stokes, we don't know under which conditions a solution exists: So trying to find an approximate solution might, under some circumstances, make no sense, since there is no exact solution to approximate. And to make matters worse, we don't know when this happens. So everything you do with Navier-Stokes on the beaviour of fluids is based on the wild guess that, in the case you are looking at, a sufficiently nice solution exists. Since the Navier-Stokes approach seems to work nicely in practice, people have come up with the hypothesis that there exist minimal assumptions for the existence of a sufficiently nice solution. If you prove that hypothesis, you would earn yourself a nice prize (the problem is one of the Millenium Problems) and would make the physicists and engineers happy, because you just told them that the approach they were taking all these years in approximating the behaviour fluids actually makes sense.
13. ## NASA's Mars Plan

Sure, it is ridiculously expensive, but if you bring everything to Mars with you, you know the stuff that brings you back. If you for example rely on ISRU for the fuel for the trip home, you have to be pretty damn sure that it works, while bringing the fuel involves much less risks. It is a station in lunar orbit and thereby can be used as a simulation for the transfer. We neither put humans into space outside of LEO for extended periods of time, nor have we tested any of the technology for the transfer flight. Lunar orbit allows for a return within a few days if something happens, while a problem half way to Mars can't be resolved by returning earlier. That is why NASA is taking this baby steps. They are slowly developing as much technology for a flight to Mars as their budget permits. But if no administration in 2030s decides to push for Mars at all costs, all would have been for nothing. But if an administration decides to do it, they already have some of the technology. On the other hand, were do you get a launch for 10 million dollars? Even SpaceX charges 60 million dollars for Falcon 9, maybe 20-30 million dollars if they get reusability working as they like. And that is without the cost of payload, which usually costs more than the rocket itself, especially if it needs to be newly developed for Mars. As are most technologies NASA plans to use. The only problem is that they were never used for that purpose and in that configuration. So you need extensive testing of all relevant components before you send a crew to Mars with no easy abort plan. Also Mars Direct involves a Saturn V sized rocket. And what is SLS? A Saturn V sized rocket.
14. ## Blue Origin Thread (merged)

They were a Lunar XPrize team until a few days ago, when they finally gave up, since they would only be able to launch their mission in 2018, and the deadline for the XPrize is end of 2017. Source: http://www.spiegel.de/wissenschaft/weltall/mond-mission-part-time-scientists-gewinnen-vodafone-als-partner-a-1139371.html (in German)
15. ## Blue Origin Thread (merged)

You also have that risk, if the ship is standing still. And New Glenn might be able to cope better with it, since it will be programmed that the landing spot will be constantly updated during flight, unlike Falcon 9, where the landing spot is probably somewhat hardcoded before liftoff.
16. ## Blue Origin Thread (merged)

Ok, didn't thought that they might indeed want to land on a moving ship. Increases the difficulty, since that gives no predefined landing spot.
17. ## Blue Origin Thread (merged)

I guess the barge won't move during the landing attempt. In the case of SpaceX, the barges can't move themselves (except for keeping themselves exactly at the landing spot), which means that they need tugs to get the platform out into the ocean and back into the harbor. Blue Origin uses instead a ship, which allows them to not need tugs, making the whole procedure simpler (and also they probably need a bigger landing platform for New Glenn than Falcon 9, which would mean bigger tugs). The only disadvantage is that a ship is probably more expensive, if you risk punching holes into it...
18. ## What is an orbit? How do we know? What the heck?

https://en.wikipedia.org/wiki/Hill_sphere i.e. Hill spheres are a thing in real life. It is an approximation of the distance at which a moon or satellite may be in orbit around another body (the moon needs to lie inside the body's Hill sphere). In practice, the limit at which a body may be in stable orbit is only about a third to a half of the radius of the Hill sphere.
19. ## Blue Origin Thread (merged)

The heaviest commsats already weigh more than 5 tonnes and are mostly limited in terms of weight by their launch vehicles. And considering Blue Origin probably wants a bit of extra margin for the first flight, using New Glenn for a commsat launch isn't the worst idea (especially, since Echostar probably gets a nice price for a launch on top of an untested rocket).
20. ## Blue Origin Thread (merged)

Why? Those additionnal flights were made possible by of the reduction in the Russian crews (from 3 to 2), due to budget cuts. So instead of flying some Soyuz missions with only 2 crew members, NASA purchased the third seat. Also both Dragon 2 and CST-100 are intended to do their first manned flight in May, resp. August 2018. CST-100s first flight to ISS is even only scheduled for December 2018. In short, the flights that NASA booked now will occur before Dragon and CST-100 can fly according to a regular schedule to ISS. And the option of the 2019 flights is if the schedules at SpaceX or Boeing will slip. Considering that by this 4 out of 6 permanent crew members will either be US or from US partners, there is maybe more available for SpaceX and Boeing than replacing 2 out of 4 Soyuz flights done every year.
21. ## Blue Origin Thread (merged)

Don't fall for the tricks of SpaceX's PR department: They want to be seen as the rock stars, while in fact there are lot of companies out there doing this kind of stuff. The only difference is that SpaceX has the funding, and for the funding they need the PR stunts. SpaceX won't enter lunar orbit, as did Apollo 8 or Orion will. But still, it will a PR blow for NASA. But also remember that SpaceX needs NASA, due to the billions of dollars NASA already pumped and still will pump into SpaceX. Without NASA, Musk would still play with toy rockets instead of real rockets. With that background, it is also no wonder that, according to Scott Manley, SpaceX is offering NASA the two seats on this lunar flight, forcing the two billionaires to a later flight, if NASA is willing to pay. This clearly shows who has the most money, and that is not the two billionaires. NASA won't drop SpaceX, even if it would mean that it would lose a "competitor", since that would mean that they lose their chance of a pure American access to the ISS and, let's not forget, SpaceX is responsible for 5000 jobs in the space industry, so the Senate wouldn't tolerate such a behavior from NASA. So NASA might decide to not fund ITS, in order to keep SpaceX away from the big milestones, but they won't drop the support for SpaceX's LEO operations. So don't wonder, if, during the coverage of that Moon mission, SpaceX is constantly thanking NASA for their support, even if NASAs biggest contribution would be the communication links.
22. ## Blue Origin Thread (merged)

Even if they would get the price down to shuttle levels for a number of launches equal to the one of the shuttle, they will never get the number of missions. Okay, NASA may send one probe (due to the payload capacity of SLS, of the billion dollar class) per year for the next 30 years with SLS, do a dozen missions to the Moon and 2-3 missions to Mars, before the Senate decides that they should shut down the program, since they achieved all goals (cf. Apollo). But that is still at most some 75 missions (and that is still a very generous amount), i.e. half of the shuttles launches. But you also need to put it into perspective: the shuttle needed much more flights to achieve its goals: 22 Spacelab missions, 10 to Mir, 5 for Hubble, 37 to ISS, and numerous other science missions or satellite transports. Every goal that the shuttle achieved or tried to achieve relied on numerous launches, as otherwise they wouldn't be worthwile. Would it be a problem, if one Mars mission costs as much as the entire American contribution of ISS (37 shuttle missions, all of the American modules etc.), i.e. some 100 billion dollars?
23. ## Lunar rescue plan?

The descent stage was pretty much dry after landing, i.e. the extra boost would have been mostly irrelevant. Also, as was the case with the extended nozzle on Apollo 15, there was quite some risk that the nozzle would be damaged on landing, making it impossible to use the engine again.
24. ## Blue Origin Thread (merged)

Sure, they might miss the schedule (or even it is quite likely that they will miss it), but it is theoretically possible. Depends on how it is done. If the Senate decides to cancel SLS in favour of private projects, then there is nothing preventing them from doing it. And relating this to the current administration is a bit difficult, since nobody really knows how their intentions are: Sure they want to save money, but at the same time they seem to have some interest in a manned Moon mission (even if it is just for the pictures on TV), since they are investigating for a manned EM-1. For the second part: NASA is free to create the requirements they want, i.e. to adapt them to ITS. Sure, they shouldn't make it too obvious, but finding some scientists saying that, if they want to go to Mars, they should "either go big or go home", should not be that hard. Also, there is nothing preventing them from buying part of an ITS mission to Mars, i.e. only pay for 2-3 of 6 seats. For example, in case of Red Dragon, NASA essentially gifted SpaceX the necessary capacity of the Deep Space Network (in return, NASA gets scientific and technical results of the mission). But in the end, I don't think that it would be really cheaper for NASA to fund commercial missions than doing it by themselfs: The commercial resupply missions will cost NASA a few billion dollars, and the commercial crew program already granted Boeing nearly 5 billion dollars and SpaceX over 3 billion dollars even before the first flight. Comparing those values to those of SLS program which will have cost some 40-50 billion dollars by the time of the prospected EM-2 mission, it is actually not that expensive, considering the relative size of the project. Do you really think that companies like SpaceX would be able to develop ITS for NASA at less than 10 times the cost of the Commercial Crew program? And grant to a company like Blue Origin the same support for the competition? So I think that the Senate, if they want to do the sensible thing (which is not guaranteed), will stick to SLS, if they want the US to do more in space than ISS and probes.
25. ## Blue Origin Thread (merged)

Why shouldn't SpaceX be able to pull this stunt off? By mid 2018, they have a good chance that they have a flight-proven rocket (Falcon Heavy) and capsule (Dragon). Sure, they won't have flown a BEO mission, but that should only be a minor hindrance. However, one must understand about this is that it isn't redoing Apollo 8 (like SLS+Orion on EM-2), but rather the Soviet Zond missions and their unmanned lunar flybys (hopefully with a better success rate than 1 in 5). And like the Zonds with their modified Soyuz capsules on Proton rockets, Dragons lunar flyby will be a dead end in terms of space craft development, since it is the maximum the given hardware is able to do. Sure, they have a good chance of beating NASA in putting humans into lunar space, but NASA will do it with hardware that after further development can support Moon landings. However, one should not underestimate the public opinion and the opinion of the Trump administration: If a private company can do it, why spend such a ridiculous amount of money on NASAs manned lunar (and beyond) program? But if SLS is cancelled and they still want missions outside of LEO, they have to fund a private company. In short, SpaceX will get its ITS program funded by NASA, just like they got funded their Dragon and Falcon program (2.6 billion dollars + technical assistance for Dragon to ISS!). I don't know, if Musk is speculating on this happening, but it would sure as hell solve his problem of funding ITS. This might also be the reason, why NASA is in some sense pushed to do EM-1 manned: They can show that they are just as good as SpaceX and they have the more capable hardware.